diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..931fc08
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,2 @@
+.idea
+venv/Lib
\ No newline at end of file
diff --git a/.vscode/settings.json b/.vscode/settings.json
new file mode 100644
index 0000000..7ad48a8
--- /dev/null
+++ b/.vscode/settings.json
@@ -0,0 +1,3 @@
+{
+	"python.pythonPath": "C:\\Users\\appa_\\AppData\\Local\\Programs\\Python\\Python38-32\\python.exe"
+}
\ No newline at end of file
diff --git a/DWDM .ipynb b/DWDM .ipynb
deleted file mode 100644
index 1b5209d..0000000
--- a/DWDM .ipynb	
+++ /dev/null
@@ -1,472 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 62,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# create database in the paper\n",
-    "\n",
-    "database=dict()\n",
-    "# database['sid']=[10,20,30,40]\n",
-    "# database['sequence']=[['a','abc','ac','d'],['ad','c','bc','ae'],['ad','bc','df'],['a','abc','d']]\n",
-    "# database['timestamp']=[[0,1,2,3],[1,2,3,4],[1,3,5],[2,3,4]]\n",
-    "\n",
-    "database['10']=[['a',0],['abc',1],['ac',2],['d',3]]\n",
-    "database['20']=[['ad',1],['c',2],['bc',3],['ae',4]]\n",
-    "database['30']=[['ad',1],['bc',3],['df',5]]\n",
-    "database['40']=[['a',2],['abc',3],['d',4]]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n",
-      "Input :\n",
-      "\n",
-      "1 2 269 4701 \n",
-      "\n",
-      "\n",
-      "\n",
-      "Time stamp\n",
-      "\n",
-      "[59.71594491384269, 620.9418924377105, 632.5470757282807, 766.0051342063122, 806.0901917840641, 962.0169388900936]\n",
-      "\n",
-      "\n",
-      "Sequence\n",
-      "\n",
-      "['9033', '184577138778', '128517057890', '404969087443', '07651739', '36279693']\n",
-      "dict_keys(['0', '1', '2', '4', '5', '6', '7', '8', '9'])\n"
-     ]
-    }
-   ],
-   "source": [
-    "# snippet to generate the dataset and pre process it \n",
-    "\n",
-    "\n",
-    "# create database\n",
-    "\n",
-    "# database = dict()\n",
-    "# database['sid']=[10,20,30,40]\n",
-    "# database['sequence']=[['a','abc','ac','d'],['ad','c','bc','ae'],['ad','bc','df'],['a','abc','d']]\n",
-    "# database['timestamp']=[[0,1,2,3],[1,2,3,4],[1,3,5],[2,3,4]]\n",
-    "#\n",
-    "# database['10'] = [['a', 0], ['abc', 1], ['ac', 2], ['d', 3]]\n",
-    "# database['20'] = [['ad', 1], ['c', 2], ['bc', 3], ['ae', 4]]\n",
-    "# database['30'] = [['ad', 1], ['bc', 3], ['df', 5]]\n",
-    "# database['cd40'] = [['a', 2], ['abc', 3], ['d', 4]]\n",
-    "#\n",
-    "# # print database\n",
-    "#\n",
-    "# for i in database.keys():\n",
-    "# \tprint(i, end=' ')\n",
-    "# \tfor j in database[i]:\n",
-    "# \t\tprint(j[0], end=' ')\n",
-    "# \tfor j in database[i]:\n",
-    "# \t\tprint(j[1], end=' ')\n",
-    "# \tprint()\n",
-    "\n",
-    "import random\n",
-    "\n",
-    "# lower = 111; upper = 999\n",
-    "# random_float = random.uniform(lower, upper)\n",
-    "# print(random_float)\n",
-    "def Randlist(start, end, num):\n",
-    "\tres = []\n",
-    "\n",
-    "\tfor j in range(num):\n",
-    "\t\tval=(random.uniform(start, end))\n",
-    "\t#\tval=int(val)\n",
-    "\t\tres.append(val)\n",
-    "\n",
-    "\tres.sort()\n",
-    "\treturn res\n",
-    "\n",
-    "\n",
-    "text_file= open(\"sample.data\",\"r\")\n",
-    "lines= text_file.readlines()\n",
-    "# line1= lines[0]\n",
-    "undelted_lines= lines\n",
-    "print(\"\\nInput :\\n\")\n",
-    "print(lines[3])\n",
-    "x = dict()\n",
-    "for i in range(len(lines)):\n",
-    "\tline1 = list(lines[i].split(\" \"))\n",
-    "\t# print(line1)\n",
-    "\tline1.pop()\n",
-    "\tlength = int(line1[0])\n",
-    "\t# print(length)\n",
-    "\tline1.pop(0)\n",
-    "\t# x= dict()\n",
-    "\t# print(line1)\n",
-    "\tlst = []\n",
-    "\n",
-    "\tfor j in range(length):\n",
-    "\t\tsizeoflistoftime= int(line1[0])\n",
-    "\t\t# print(sizeoflistoftime)\n",
-    "\t\tline1.pop(0)\n",
-    "\t\t# print(line1)\n",
-    "\n",
-    "#         listoftime=Randlist(0,1000,sizeoflistoftime)\n",
-    "\t\tlistoftime=Randlist(0,1000,1)\n",
-    "\t\tfor k in range(sizeoflistoftime):\n",
-    "\t\t\tline1.pop(0)\n",
-    "\t\t# print(listoftime)\n",
-    "\n",
-    "\t\tlst.append(listoftime[0])\n",
-    "\t# print(\"The list is :\")\n",
-    "\t# print(lst)\n",
-    "\tlst.sort()\n",
-    "\tx[i]=lst[:]\n",
-    "\n",
-    "\n",
-    "# print(x)\n",
-    "\n",
-    "# print(undelted_lines)\n",
-    "x2= dict()\n",
-    "\n",
-    "# item_alpha=dict()\n",
-    "# alphabet='a'\n",
-    "\n",
-    "for i in range(len(undelted_lines)):\n",
-    "\tline1 = list(undelted_lines[i].split(\" \"))\n",
-    "\t# print(line1)\n",
-    "\tline1.pop()\n",
-    "\tlength = int(line1[0])\n",
-    "\t# print(length)\n",
-    "\tline1.pop(0)\n",
-    "\t# print(line1)\n",
-    "\tlistoftime=[]\n",
-    "\tfor j in range(length):\n",
-    "\t\tsizeoflistoftime= int(line1[0])\n",
-    "\t\t# print(sizeoflistoftime)\n",
-    "\t\tline1.pop(0)\n",
-    "\t\t# print(line1)\n",
-    "\t\ttemp=\"\"\n",
-    "\t\t# listoftime=Randlist(0,1000,sizeoflistoftime)\n",
-    "\t\tfor k in range(sizeoflistoftime):\n",
-    "            \n",
-    "# \t\t\tif line1[0] in item_alpha.keys():\n",
-    "# \t\t\t\tpass\n",
-    "# \t\t\telse :\n",
-    "# \t\t\t\titem_alpha[line1[0]]=alphabet\n",
-    "# \t\t\t\talphabet=chr(ord(alphabet)+1)\n",
-    "\t\t\ttemp=temp+line1[0].zfill(4)\n",
-    "\t\t\tline1.pop(0)\n",
-    "\n",
-    "\n",
-    "\t\tlistoftime.append(temp)\n",
-    "\t# print(listoftime)\n",
-    "\tx2[i]=listoftime\n",
-    "\n",
-    "print(\"\\n\\nTime stamp\\n\")\n",
-    "print(x[2])\n",
-    "print(\"\\n\\nSequence\\n\")\n",
-    "print(x2[2])\n",
-    "\n",
-    "database=dict()\n",
-    "for i in x.keys():\n",
-    "    if len(x[i])>1:\n",
-    "        database[str(i)]=[]\n",
-    "        for j in range(len(x[i])):\n",
-    "            database[str(i)].append([x2[i][j],x[i][j]])\n",
-    "        \n",
-    "print(database.keys())"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0 2479 21545477 0440227660369838 6639792690549748 1247 1992 2535 509577449337 234347377188851892419486 15.469584262986613 75.6177321104664 155.78500287678798 173.64829834524076 455.4399385621556 500.484809781422 523.9953960957207 570.1059519605159 861.7382510468273 \n",
-      "1 076515427203 585473098827 5993 0991495663767993 060617988964 060610912787 40235242 245163928259 07033355589271699239 118.51177604665509 182.28992773802665 367.3632842084625 376.08000570181997 395.58320704113424 886.6666090937258 938.9197731893184 959.6817148375404 990.8099147450886 \n",
-      "2 9033 184577138778 128517057890 404969087443 07651739 36279693 59.71594491384269 620.9418924377105 632.5470757282807 766.0051342063122 806.0901917840641 962.0169388900936 \n",
-      "4 62737655 2654 478.2847102154313 911.4960984422834 \n",
-      "5 0149 35339471 5758 1491 5024 3812 155.00180545961194 163.6677920404198 617.7771644906031 633.6137864801188 676.8115396080481 942.4122063655578 \n",
-      "6 340447646487 521076377771 140555019708 357238757705 270941675713 0886287069187963857191259795 07236970 06255975 12.886202605772446 50.0837043321627 166.00945124360146 189.51248295548862 439.7787871131751 883.2450985837778 903.5302630767404 981.1772022893753 \n",
-      "7 7851 2053 58268595 1734 46.275544054731995 62.43536446145293 118.93634783391649 946.6968439733122 \n",
-      "8 72137771 5510 46529373 9928 67717774 31138769 45.93273726408731 95.04437502921293 161.27419795678634 365.551422010759 526.229583208764 854.5005573980293 \n",
-      "9 07656075 5735 3541 2715 2104 74.89404059066985 201.93216407003922 299.8990747881353 678.3754420434778 933.8630489489843 \n",
-      "[['2479', 15.469584262986613], ['21545477', 75.6177321104664], ['0440227660369838', 155.78500287678798], ['6639792690549748', 173.64829834524076], ['1247', 455.4399385621556], ['1992', 500.484809781422], ['2535', 523.9953960957207], ['509577449337', 570.1059519605159], ['234347377188851892419486', 861.7382510468273]]\n"
-     ]
-    }
-   ],
-   "source": [
-    "# print database\n",
-    "\n",
-    "for i in database.keys():\n",
-    "    print(i,end=' ')\n",
-    "    for j in database[i]:\n",
-    "        print(j[0],end=' ')\n",
-    "    for j in database[i]:\n",
-    "        print(j[1],end=' ')\n",
-    "    print()\n",
-    "print(database['0'])"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function to return time-intervals\n",
-    "def time_interval_itemsets(i,j):\n",
-    "    \n",
-    "    time_i=i[1]\n",
-    "    time_j=j[1]\n",
-    "    \n",
-    "    return(abs(time_i-time_j))\n",
-    "    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# itemset pair generation\n",
-    "def itemset_pair_generator(seq):\n",
-    "    \n",
-    "    itemset_pairs=[]\n",
-    "    n=len(seq)\n",
-    "    for i in range(n):\n",
-    "        for j in range(i+1,n):\n",
-    "            itemset_pairs.append([seq[i],seq[j]])\n",
-    "    \n",
-    "    return(itemset_pairs)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function to generate the time intervals for a sequence\n",
-    "def time_interval_sequence(itemset_pairs):\n",
-    "    \n",
-    "    itemset_pairs_time=[]\n",
-    "    for i in itemset_pairs:\n",
-    "        time_interval=time_interval_itemsets(i[0],i[1])\n",
-    "        itemset_pairs_time.append(i+[time_interval])\n",
-    "        \n",
-    "    return(itemset_pairs_time)\n",
-    "        \n",
-    "    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function to obtain the strength of a pair of itemsets\n",
-    "def strength_pair(itemset_pairs_time):\n",
-    "    \n",
-    "    itemset_pairs_time_strength=[]\n",
-    "    for i in itemset_pairs_time:\n",
-    "        \n",
-    "        itemset1=i[0][0]\n",
-    "        itemset2=i[1][0]\n",
-    "#         strength= len(itemset1)*len(itemset2)\n",
-    "        strength= len(itemset1)*len(itemset2)/16    # because each item has 4 characters\n",
-    "        itemset_pairs_time_strength.append(i+[strength])\n",
-    "    \n",
-    "    return itemset_pairs_time_strength\n",
-    "        \n",
-    "    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "metadata": {
-    "scrolled": true
-   },
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "# def main(): main function\n",
-    "    \n",
-    "for i in database.keys():\n",
-    "    itemset_pairs=itemset_pair_generator(database[i])\n",
-    "    itemset_pairs_time=time_interval_sequence(itemset_pairs)\n",
-    "    itemset_pairs_time_strength=strength_pair(itemset_pairs_time)\n",
-    "    TiW=TiW_sequence(itemset_pairs_time_strength)\n",
-    "    database[i].append(TiW)\n",
-    "\n",
-    "print()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 133,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "TypeError",
-     "evalue": "'float' object is not subscriptable",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
-      "\u001b[1;32m<ipython-input-133-497f86f28a8a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mitemset_pairs\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mitemset_pair_generator\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdatabase\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'2'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mitemset_pairs_time\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtime_interval_sequence\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mitemset_pairs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mitemset_pairs_time_strength\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mstrength_pair\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mitemset_pairs_time\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mTiW\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mTiW_sequence\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mitemset_pairs_time_strength\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# print(itemset_pairs)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
-      "\u001b[1;32m<ipython-input-67-18415b8a5708>\u001b[0m in \u001b[0;36mtime_interval_sequence\u001b[1;34m(itemset_pairs)\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[0mitemset_pairs_time\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m     \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mitemset_pairs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m         \u001b[0mtime_interval\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtime_interval_itemsets\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      7\u001b[0m         \u001b[0mitemset_pairs_time\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m+\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mtime_interval\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
-      "\u001b[1;32m<ipython-input-65-7d2c21c5a21f>\u001b[0m in \u001b[0;36mtime_interval_itemsets\u001b[1;34m(i, j)\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[0mtime_i\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m     \u001b[0mtime_j\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mj\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m     \u001b[1;32mreturn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtime_i\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mtime_j\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
-      "\u001b[1;31mTypeError\u001b[0m: 'float' object is not subscriptable"
-     ]
-    }
-   ],
-   "source": [
-    "# testing functions\n",
-    "\n",
-    "itemset_pairs=itemset_pair_generator(database['2'])\n",
-    "itemset_pairs_time=time_interval_sequence(itemset_pairs)\n",
-    "itemset_pairs_time_strength=strength_pair(itemset_pairs_time)\n",
-    "TiW=TiW_sequence(itemset_pairs_time_strength)\n",
-    "# print(itemset_pairs)\n",
-    "print(TiW)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function to calculate the weighting function of the time interval\n",
-    "def weighting_function(time_interval):\n",
-    "    \n",
-    "    delta=0.9\n",
-    "    u=1\n",
-    "    w_TI=delta**(time_interval/u)\n",
-    "    \n",
-    "    return(w_TI)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function to calculate the time interval weight of the sequence\n",
-    "def TiW_sequence(itemset_pairs_time_strength):\n",
-    "    \n",
-    "    total_strength=0\n",
-    "    weighted_strength=0\n",
-    "    for i in itemset_pairs_time_strength:\n",
-    "        \n",
-    "        w_TI=weighting_function(i[2])\n",
-    "        weighted_strength+=w_TI*i[3]\n",
-    "        total_strength+=i[3]\n",
-    "        \n",
-    "    TiW=weighted_strength/total_strength\n",
-    "    \n",
-    "    return(TiW)\n",
-    "    \n",
-    "    \n",
-    "        "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# function to check if a given sequence is a super sequence of the other \n",
-    "# checks if seq1 is a super sequence of seq2\n",
-    "def is_super_seq(seq1,seq2):\n",
-    "    i= 0\n",
-    "    j= 0\n",
-    "    \n",
-    "    while i<len(seq1) and j<len(seq2):\n",
-    "        \n",
-    "        if seq2[j][0] in seq1[i][0]:\n",
-    "            i+=1\n",
-    "            j+=1\n",
-    "        else:\n",
-    "            i+=1\n",
-    "    if j==len(seq2):\n",
-    "        return 1\n",
-    "    \n",
-    "    else:\n",
-    "        return 0\n",
-    "    "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "SyntaxError",
-     "evalue": "invalid syntax (<ipython-input-11-7b9adc04a8d9>, line 2)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[1;36m  File \u001b[1;32m\"<ipython-input-11-7b9adc04a8d9>\"\u001b[1;36m, line \u001b[1;32m2\u001b[0m\n\u001b[1;33m    def TiW_support()\u001b[0m\n\u001b[1;37m                     ^\u001b[0m\n\u001b[1;31mSyntaxError\u001b[0m\u001b[1;31m:\u001b[0m invalid syntax\n"
-     ]
-    }
-   ],
-   "source": [
-    "# testing function\n",
-    "# def TiW_support()\n",
-    "\n",
-    "count=0\n",
-    "for i in database.keys():\n",
-    "    seq1=database[i]\n",
-    "    seq2=[['ad'],['bc'],[]]\n",
-    "    count+=is_super_seq(seq1,seq2)\n",
-    "    \n",
-    "print(count/len(database.keys()))"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.7.0"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/DWDM.ipynb b/DWDM.ipynb
new file mode 100644
index 0000000..4f2ce99
--- /dev/null
+++ b/DWDM.ipynb
@@ -0,0 +1,702 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# create database in the paper\n",
+    "\n",
+    "database=dict()\n",
+    "# database['sid']=[10,20,30,40]\n",
+    "# database['sequence']=[['a','abc','ac','d'],['ad','c','bc','ae'],['ad','bc','df'],['a','abc','d']]\n",
+    "# database['timestamp']=[[0,1,2,3],[1,2,3,4],[1,3,5],[2,3,4]]\n",
+    "\n",
+    "database['10']=[['a',0],['abc',1],['ac',2],['d',3]]\n",
+    "database['20']=[['ad',1],['c',2],['bc',3],['ae',4]]\n",
+    "database['30']=[['ad',1],['bc',3],['df',5]]\n",
+    "database['40']=[['a',2],['abc',3],['d',4]]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": "\nInput :\n\n1 2 269 4701 \n\n\n\nTime stamp\n\n[94.36192205809746, 117.6714270956375, 483.9212648643609, 533.4169600885405, 558.400191175879, 753.794192889342]\n\n\nSequence\n\n['9033', '184577138778', '128517057890', '404969087443', '07651739', '36279693']\ndict_keys(['0', '1', '2', '4', '5', '6', '7', '8', '9', '10', '11', '12', '13', '14', '15', '16', '17', '18', '19', '20', '21', '22', '23', '24', '25', '26', '27', '28', '29', '30', '31', '32', '33', '34', '35', '36', '37', '38', '39', '40', '41', '42', '43', '44', '45', '46', '47', '48', '49', '50', '51', '52', '53', '54', '55', '56', '57', '58', '59', '60', '61', '62', '63', '64', '65', '66', '67', '68', '69', '70', '71', '72', '73', '74', '75', '76', '77', '78', '79', '80', '81', '82', '83', '84', '85', '86', '87', '88', '89', '90', '91', '92', '93', '94', '95', '96'])\n"
+    }
+   ],
+   "source": [
+    "# snippet to generate the dataset and pre process it \n",
+    "\n",
+    "\n",
+    "# create database\n",
+    "\n",
+    "# database = dict()\n",
+    "# database['sid']=[10,20,30,40]\n",
+    "# database['sequence']=[['a','abc','ac','d'],['ad','c','bc','ae'],['ad','bc','df'],['a','abc','d']]\n",
+    "# database['timestamp']=[[0,1,2,3],[1,2,3,4],[1,3,5],[2,3,4]]\n",
+    "#\n",
+    "# database['10'] = [['a', 0], ['abc', 1], ['ac', 2], ['d', 3]]\n",
+    "# database['20'] = [['ad', 1], ['c', 2], ['bc', 3], ['ae', 4]]\n",
+    "# database['30'] = [['ad', 1], ['bc', 3], ['df', 5]]\n",
+    "# database['cd40'] = [['a', 2], ['abc', 3], ['d', 4]]\n",
+    "#\n",
+    "# # print database\n",
+    "#\n",
+    "# for i in database.keys():\n",
+    "# \tprint(i, end=' ')\n",
+    "# \tfor j in database[i]:\n",
+    "# \t\tprint(j[0], end=' ')\n",
+    "# \tfor j in database[i]:\n",
+    "# \t\tprint(j[1], end=' ')\n",
+    "# \tprint()\n",
+    "\n",
+    "import random\n",
+    "\n",
+    "# lower = 111; upper = 999\n",
+    "# random_float = random.uniform(lower, upper)\n",
+    "# print(random_float)\n",
+    "def Randlist(start, end, num):\n",
+    "\tres = []\n",
+    "\n",
+    "\tfor j in range(num):\n",
+    "\t\tval=(random.uniform(start, end))\n",
+    "\t\tres.append(val)\n",
+    "\n",
+    "\tres.sort()\n",
+    "\treturn res\n",
+    "\n",
+    "text_file= open(\"Datasets/hundred.data\",\"r\")\n",
+    "lines= text_file.readlines()\n",
+    "# line1= lines[0]\n",
+    "undelted_lines= lines\n",
+    "print(\"\\nInput :\\n\")\n",
+    "print(lines[3])\n",
+    "x = dict()\n",
+    "for i in range(len(lines)):\n",
+    "\tline1 = list(lines[i].split(\" \"))\n",
+    "\tline1.pop()\n",
+    "\tlength = int(line1[0])\n",
+    "\tline1.pop(0)\n",
+    "\tlst = []\n",
+    "\n",
+    "\tfor j in range(length):\n",
+    "\t\tsizeoflistoftime= int(line1[0])\n",
+    "\t\tline1.pop(0)\n",
+    "\t\t\n",
+    "\t\tlistoftime=Randlist(0,1000,1)\n",
+    "\t\tfor k in range(sizeoflistoftime):\n",
+    "\t\t\tline1.pop(0)\n",
+    "\n",
+    "\t\tlst.append(listoftime[0])\n",
+    "\n",
+    "\tlst.sort()\n",
+    "\tx[i]=lst[:]\n",
+    "\n",
+    "x2= dict()\n",
+    "\n",
+    "for i in range(len(undelted_lines)):\n",
+    "\tline1 = list(undelted_lines[i].split(\" \"))\n",
+    "\tline1.pop()\n",
+    "\tlength = int(line1[0])\n",
+    "\tline1.pop(0)\n",
+    "\tlistoftime=[]\n",
+    "\tfor j in range(length):\n",
+    "\t\tsizeoflistoftime= int(line1[0])\n",
+    "\t\tline1.pop(0)\n",
+    "\t\ttemp=\"\"\n",
+    "\t\tfor k in range(sizeoflistoftime):            \n",
+    "# \t\t\tif line1[0] in item_alpha.keys():\n",
+    "# \t\t\t\tpass\n",
+    "# \t\t\telse :\n",
+    "# \t\t\t\titem_alpha[line1[0]]=alphabet\n",
+    "# \t\t\t\talphabet=chr(ord(alphabet)+1)\n",
+    "\t\t\ttemp=temp+line1[0].zfill(4)\n",
+    "\t\t\tline1.pop(0)\n",
+    "\n",
+    "\n",
+    "\t\tlistoftime.append(temp)\n",
+    "\t# print(listoftime)\n",
+    "\tx2[i]=listoftime\n",
+    "\n",
+    "print(\"\\n\\nTime stamp\\n\")\n",
+    "print(x[2])\n",
+    "print(\"\\n\\nSequence\\n\")\n",
+    "print(x2[2])\n",
+    "\n",
+    "database=dict()\n",
+    "for i in x.keys():\n",
+    "    if len(x[i])>1:\n",
+    "        database[str(i)]=[]\n",
+    "        for j in range(len(x[i])):\n",
+    "            database[str(i)].append([x2[i][j],x[i][j]])\n",
+    "        \n",
+    "print(database.keys())"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": "13', 154.27655069174318], ['3467', 158.9257075404158], ['6711', 258.5839633664695], ['15376643', 349.9020060487912], ['36299542', 403.7490447523271], ['6734', 405.66497458324227], ['21327396', 463.3482589936657], ['450855739488', 587.1213698437947], ['32467317', 775.4021670101178], ['37117635', 795.14558603152], ['4876', 833.2869468601693], ['38129296', 913.3353094793592]], '39': [['58356804', 188.27380850072072], ['56508723', 302.1287657305607], ['7080', 633.7902879764717], ['42468760', 643.4097362726027], ['03411805', 672.1271354781092], ['0827330049767473', 818.0452330831725], ['37714432', 831.110610419531], ['046724856353', 834.42492743159], ['10674047', 849.6727335377893], ['40565461', 990.3977108681311]], '40': [['31349119', 31.891536885160555], ['453352615619', 206.4333385525311], ['019829886879', 273.24855796464976], ['555963567534', 292.466259135657], ['357780329614', 322.3866106773929], ['16697090', 396.47430754030876], ['4001', 418.21163709351225], ['60847220', 575.1458587569429], ['76989662', 847.4267906438008], ['0229', 989.5529959164126]], '41': [['2963', 9.938559824748449], ['10653331489782858618', 111.72063917573006], ['0467130422725479', 137.13236763425041], ['0127516253087572', 174.55237624248198], ['3093328436277406', 222.9531422879554], ['04142065666869149300', 519.2819270917215], ['01380735334541974594', 662.6933284278309], ['2117408556796508', 839.4971814646399], ['0045119926549845', 909.3389776013278], ['18162393297779388080', 932.9211845998783]], '42': [['69629448', 206.115753383877], ['3726', 344.1096518966943], ['80969556', 362.43871421531117], ['1981', 751.2064952586994], ['39275321', 765.5183922091334], ['170424243461', 786.9233038857373], ['339835596241', 818.0596345990922]], '43': [['7705', 5.112878872794435], ['0744', 115.20021520184376], ['0070', 745.5231095366524], ['0075', 767.306933560284], ['97059978', 777.5133141336988], ['5270', 927.7454089920074]], '44': [['349135726810', 251.9629461903137], ['184445709402', 284.5222166540201], ['13395096', 531.2555180651001], ['1801', 814.7692951882668], ['1397', 919.9352615300394]], '45': [['649571018273', 32.846846506356606], ['62288341', 229.56345855337767], ['250529983212544961317455', 232.65501266160317], ['1312335140987101', 260.0854951280024], ['379049227375', 305.0794628732997], ['4213465451106771', 461.35958994243134], ['13342031237572277622770889059463', 483.8412398042794], ['5893609286728837', 528.775219365263], ['0681153720823491', 597.9816938142112], ['01630414218233909229', 833.6946585001294], ['01380272309332794372745585789062', 843.0030875242021], ['01170293178158938274', 857.1439144595893], ['1563560568797958', 945.9041984753479]], '46': [['12791792346739869728', 69.29864671049025], ['0684139715914953', 123.62596863398811], ['754878238375', 141.57738395724462], ['1917500461198436', 192.6712982396933], ['1831281738515928', 416.39734347783076], ['094613382774438656059764', 554.1062339730942], ['226461507671', 583.8836925149257], ['6918779692889591', 712.2429155098306], ['0057134544976725', 779.1919822466396], ['1079149121176804', 791.3155251556219], ['030328806228802681818672', 793.3454075589895], ['1005221154997353', 915.245199800749]], '47': [['67587101', 117.52892686249106], ['25122998', 161.80187771535614], ['1880288032797930', 163.55620314765218], ['35763661', 337.6346858030572], ['333866148905', 488.8327332048564], ['18442155', 499.15353466323177], ['82748783', 913.9624488768184]], '48': [['667492879623', 160.78250527263015], ['67617192', 483.42664653393973], ['3315432891939627', 580.401055553396], ['002723953204453468407926', 887.7959010249571], ['6220', 990.3799426494983], ['68049066', 995.2100966713873]], '49': [['9527', 105.68995942341563], ['74407845', 217.2144786705953], ['4908', 439.048388612723], ['19987269', 460.8543269118131], ['1816', 819.5210045617931], ['60928169', 977.8581064927039], ['4477', 980.26230323188], ['6749', 992.3586747265521]], '50': [['197924216315759475989913', 20.78245865270789], ['021202940845312239347031', 72.04733899726168], ['0155127620664737487150249461', 390.51836373438556], ['096649617528', 542.9464707326183], ['07452164328236685862', 598.0401053475784], ['30223298334159386045', 600.411037197927], ['02711813322638264929', 699.2649340220119], ['132720524168692481969532', 842.5421316699495], ['0116296157876640', 848.4795453762812], ['02650687572971898488', 996.0424996665888]], '51': [['02078595', 45.95057027494609], ['243193559567', 111.12242792867588], ['06066960', 155.5912511229598], ['02658447', 566.2097164962298], ['13042424', 614.0219123133794], ['3613', 907.9811842287994], ['8279', 920.4060663293956]], '52': [['60119364', 72.35871732323784], ['313491199548', 125.88438695518467], ['133752719752', 178.09643056872738], ['17679695', 190.1530518020985], ['4901', 199.32362851797237], ['49058982', 203.9281542822501], ['64997175', 249.68363817918726], ['3577', 274.2667425712446], ['4001', 314.681750379715], ['1301149129033441', 434.01442350804996], ['6919', 488.9891798575584], ['32817220', 675.1031831510519], ['6042', 699.8976770895116], ['44199662', 786.3789961852075], ['0070', 816.6125390667845], ['9054', 879.2621154350802]], '53': [['0874', 136.5956382689757], ['9934', 221.4958266092998], ['3984', 473.44254438910593], ['8285', 664.8506429848121], ['1877', 679.1075960159874], ['5471', 991.0187978560127]], '54': [['1362', 11.574497119254957], ['8404', 783.8251579269103]], '55': [['13452766769686179511', 21.711744951067978], ['29674734582661476195', 30.948238169248743], ['054210111859306631344773624186059119', 53.70012542212077], ['29804463688671369000', 126.41619543232207], ['1150531167438788', 128.79633778318887], ['08722181453362257510', 198.55137485482211], ['03652071328935773708542266547771', 472.1548016117789], ['0002186740019889', 479.2842039034747], ['18283899610668187123', 492.8341030790384], ['593573929153', 578.2312908925072], ['003412944469537867187220', 938.2889881552971]], '56': [['7203', 59.87863771279467], ['3461', 68.25901906780429], ['013944239448', 76.03929278196675], ['170937267653', 391.3237985609999], ['02294181', 451.80049640515386], ['245136655321', 488.9703472593147], ['242453098825', 565.7510810880843], ['3355', 803.0662501636166], ['0790', 864.3174629325239], ['7827', 886.7661932029193], ['6241', 922.3384075088536]], '57': [['06193592420267827986', 72.4613511255896], ['0430114617986111667471839517', 102.83196991906185], ['03041880425282798732', 140.41948191889475], ['2370604291709431', 235.58942267195638], ['63766771827482899043', 294.03695385057705], ['33383835643767957396', 386.82667379482007], ['160946696775', 453.77630006487726], ['0044171424106629756083518440', 518.0453351898624], ['1018109217311991466451716474', 577.5551136764409], ['01881504180619547192890298529916', 640.1707845216023], ['0183021005480738123435514149592483939954', 700.0027506099406], ['20732658522657247443', 808.8698527323486], ['228552496953', 951.3179235539548]], '58': [['0606276654417145', 76.59640135280755], ['1638318836064024462665319668', 234.301117593141], ['33114296537371707823', 490.5723685753209], ['12747098768380719836', 677.6025755623244], ['09507146742077219613', 737.6265936923943], ['19181930368038894751592868997002', 743.3552913533987], ['33344876536654797379', 752.7388871192923]], '59': [['5511', 250.11753496918055], ['1023', 795.9324708990302], ['8534', 846.7686969468075], ['3342', 858.8452455219424]], '60': [['61786961', 35.74795056027469], ['65168685', 341.1458474103766], ['68837406', 421.25591792501274], ['02695350', 431.32902461483593], ['5088', 496.4053482159134], ['186822545825', 536.6767570479535], ['066216307379', 626.3855204959164], ['63539593', 870.4282645780028], ['03978944', 903.9159070320768], ['6742', 977.67527374885]], '61': [['30184900', 27.182448752340214], ['0198207229887721', 86.5848466911131], ['18019195', 451.82063521789684], ['28157774801590449229', 592.4478132749338], ['06451920437248765562787687649338', 594.7642637151835], ['114623615437', 666.5749216057379], ['295630394469', 889.3232128057799], ['166958937316', 900.5630392092905]], '62': [['3212', 30.26192952177076], ['5317', 213.71908023947285], ['06459338', 274.7978115357467], ['8498', 356.55988244663837], ['30393278', 368.304710832807], ['129045785783', 389.94372640268415], ['068147346626', 486.8751375287661], ['3066', 494.6815298409287], ['01630476', 534.3351418891517], ['4463', 637.9199397477986], ['027218282890', 767.3698163347739], ['072753438982', 769.9908189912718], ['6045', 880.9110420191997]], '63': [['8384', 97.33295299534694], ['00617285', 194.24061771376867], ['2797', 364.1097542193107], ['9950', 462.5007310052821], ['8181', 727.3431563105771], ['1187', 964.7181296611686]], '64': [['2077213236676365', 67.18098713559573], ['0173336434914688', 173.33935362339693], ['11861453327071898911', 325.29509171959046], ['759782619954', 465.58799327757896], ['19705098', 471.2378433831732], ['0651174358866261', 660.4230245725424], 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625.8254649422387], ['7406', 763.2104708285594], ['9739', 769.9872638054451]], '77': [['7891', 107.73759392423898], ['1993', 132.29100184530685], ['212540665907', 219.498106316543], ['2031', 249.0867940208613], ['05381860450645799084', 466.7998770648875], ['126920583878', 641.9781467333137], ['17657598', 643.7068004931997], ['509467417524', 696.6394437020014], ['130032576011', 996.8440272968406]], '78': [['2991', 445.0946022569641], ['3122572971927448', 480.20468067689484], ['0440', 721.6377108059024], ['7389', 767.4753575324343], ['1759', 772.4973204666078], ['7583', 776.5542274955017], ['7661', 833.5859725461248], ['5477', 853.4818380581183], ['8540', 902.9056548582962], ['1825', 904.4220021420261]], '79': [['22178518', 39.41564491513538], ['027014906207', 80.46184860929961], ['205145256045', 253.45775947570826], ['70127211', 254.1613100029778], ['1006293847776784', 275.5799763541951], ['468891189627', 293.32441185281476], ['34575724', 343.4789805336828], ['08850968761283739250', 375.46545883813553], ['369737077580764677039219', 570.969288008921], ['0510', 661.360578065307], ['057711261725', 929.4792714635033], ['012116347511', 992.295464590148]], '80': [['17982182508589649841', 107.51843469049771], ['475155639739', 205.8606841273446], ['18663889522258177894', 290.97794830837944], ['1772257369437966', 318.88993042592284]], '81': [['04922921', 12.093493428638524], ['1536', 22.68852979689906], ['05389943', 428.3323697452349], ['510062256763', 468.6712002442455], ['3304', 708.4862978559], ['25809623', 837.7753514003657], ['26603405503469808148', 899.9103829114454], ['239628806161', 934.8466668015723], ['56617301', 985.1258777668636]], '82': [['3335562372277708', 147.6132144957244], ['41469124', 340.2848947037881], ['24517832', 474.5357095364696], ['3606408545659073', 618.7825301285728], ['064625055449', 776.0245585899607], ['2991327962259373', 826.9777739509994]], '83': [['3873495683798486', 63.25270959993357], ['1185501353115568', 379.93473160884037], 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['220034074202547756319852', 41.098546265466055], ['537558509761', 68.14407360003838], ['04405005564158116036', 79.41743823759428], ['24856353651279539748', 213.14659210802768], ['046019724429472873428669', 234.65363764897575], ['06461247230184898722', 250.3469199489683], ['25355850', 286.2044136142091], ['22362686509577448003', 416.35620268947537], ['369485188729', 630.864664484655], ['0237403763057832', 631.7223558465106]], '86': [['02677858', 60.93469723570877], ['8696', 111.525802920189], ['23393039395669217109', 239.67022420914853], ['68229840', 287.2285806416846], ['30043022328870508678', 378.52348452542896], ['5375585062119761', 435.9502422168884], ['3812', 574.1792643120222], ['9177', 794.9526239222142], ['4068411247937736', 825.8637892242293], ['682278557953', 864.3418919713445], ['18793335345079269195', 866.3586516659792], ['47288669', 948.95187986621], ['223636395380', 956.1154118065775], ['0139338944235050', 974.0910753205592]], '87': [['2155', 42.70078979114322], ['1779', 202.28830981575396], ['15421829', 215.274069757865], ['9372', 293.8763619578799], ['3927', 689.459422780048], ['31133403', 767.8720480808801], ['4809', 797.5355256528755], ['5779', 841.8586890719962], ['3421', 924.157584674172], ['6706', 947.2752961421467]], '88': [['06459338', 75.7249990411093], ['11464366', 195.80091071475547], ['65447392', 199.61289078728873], ['454997999841', 303.44001453985226], ['257352615619', 348.7319924504476], ['21756665', 428.0349783126991], ['0265', 611.8557175969662], ['33094169', 789.9210123084217], ['0476', 840.606035595798], ['57286225', 983.3675305940094]], '89': [['56497765', 70.02314834183609], ['23243928', 322.67964171128716], ['10159769', 826.1100273754423]], '90': [['081034668035', 34.568093650580664], ['062526765354712477689641', 119.17478333755038], ['013552129780', 281.15727488859545], ['393563428649', 358.5117217021342], ['17105050580793849966', 400.8660154228332], ['127417246272', 468.5728090032415], ['156345205959', 549.9804374323262], ['82109916', 585.9232781561078], ['0468', 724.7379852231876], ['286949717641', 781.032620156692]], '91': [['162257796270', 139.72115157194887], ['082743944693578083728595', 150.98170977146052], ['3449487670317179', 249.45814180151282], ['074610851469741088279532', 360.2771639711252], ['21555252654968799082', 449.5344001085978], ['086621554863', 626.7473737751747], ['0448302736529527', 746.0987417063544], ['18912201443379959921', 761.9382235493706], ['13622052371859468058', 793.251468931084], ['164322504920', 923.9095234202465]], '92': [['049219563257406054029060', 67.7994592288147], ['429460328185', 90.55765751497368], ['170348437012', 175.18763008761638], ['3046', 428.7194463384355], ['109223414652569387969799', 438.08473858321696], ['04058595', 473.51280565074336], ['547166739722', 530.2186612291414], ['1092173180519979', 740.0830438664235], ['19222237348357899925', 922.2988459676473]], '93': [['0397495650416677', 210.60233663708271], ['118522495568847586859185', 243.80679255901427], ['0612114520529757', 298.3544299484802], ['52888696', 340.00769710005886], ['11305680727592889775', 344.5407067459302], ['18688289', 561.9817882407824], ['256447026531', 603.8225621374676], ['16301983247531344594', 680.2034886045628], ['02651022421950509593', 792.6206994593924]], '94': [['7832', 622.8370409781619], ['1184', 821.5779830804609], ['3068', 968.1440749824385]], '95': [['04405650', 147.4755859004794], ['424653118760', 153.03308665973304], ['0341525268799082', 178.02336564992638], ['01612155', 666.2003772051797], ['3718', 677.743075095474], ['1452213741604976', 723.0312018880057], ['7167', 761.2168937013374], ['4047', 787.405427943779], ['8515', 791.0075447002556], ['188757588816', 896.5581858637164], ['49638884', 975.5581402269908]], '96': [['327833386685', 72.1058734085045], ['201735724013', 123.45348780300758], ['6491', 163.97022996205024], ['21645096', 330.06913347704693], ['2004327895329590', 471.78707404040375], ['02992804', 560.538275496416], ['7992873998869915', 562.1715129644476], ['68618544', 864.77634951671], ['665788299030', 922.2836781459789], ['320482699384', 965.4538558086001]]}\n"
+    }
+   ],
+   "source": [
+    "# # print database\n",
+    "# for i in database.keys():\n",
+    "#     print(i,end=' ')\n",
+    "#     for j in database[i]:\n",
+    "#         print(j[0],end=' ')\n",
+    "#     for j in database[i]:\n",
+    "#         print(j[1],end=' ')\n",
+    "# print(database['0'])\n",
+    "print(database)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function to return time-intervals\n",
+    "def time_interval_itemsets(i,j):\n",
+    "    time_i=i[1]\n",
+    "    time_j=j[1]\n",
+    "    return abs(time_i-time_j)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# itemset pair generation\n",
+    "def itemset_pair_generator(seq):\n",
+    "    itemset_pairs=[]\n",
+    "    n=len(seq)\n",
+    "    for i in range(n):\n",
+    "        for j in range(i+1,n):\n",
+    "            itemset_pairs.append([seq[i],seq[j]])\n",
+    "    return(itemset_pairs)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function to generate the time intervals for a sequence\n",
+    "def time_interval_sequence(itemset_pairs):\n",
+    "    itemset_pairs_time=[]\n",
+    "    for i in itemset_pairs:\n",
+    "        time_interval=time_interval_itemsets(i[0],i[1])\n",
+    "        itemset_pairs_time.append(i+[time_interval])\n",
+    "    return(itemset_pairs_time)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function to obtain the strength of a pair of itemsets\n",
+    "def strength_pair(itemset_pairs_time):\n",
+    "    itemset_pairs_time_strength=[]\n",
+    "    for i in itemset_pairs_time:\n",
+    "        itemset1=i[0][0]\n",
+    "        itemset2=i[1][0]\n",
+    "        # strength= len(itemset1)*len(itemset2)\n",
+    "        strength= len(itemset1)*len(itemset2)/16    # because each item has 4 characters\n",
+    "        itemset_pairs_time_strength.append(i + [strength])\n",
+    "    return itemset_pairs_time_strength"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function to calculate the weighting function of the time interval\n",
+    "import math\n",
+    "\n",
+    "def weighting_function_1(time_interval, delta=0.9, u=1):\n",
+    "    w_TI=delta**(time_interval/u)\n",
+    "    return(w_TI)\n",
+    "\n",
+    "def weighting_function_2(time_interval, delta=0.9, u=1):\n",
+    "    w_TI=delta**math.log((1 + (time_interval/u)), 2)\n",
+    "    return(w_TI)\n",
+    "\n",
+    "def weighting_function_3(time_interval, delta=0.9, u=1):\n",
+    "    w_TI=delta**math.ceil(time_interval/u)\n",
+    "    return(w_TI)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function to calculate the time interval weight of the sequence\n",
+    "def TiW_sequence(itemset_pairs_time_strength, delta=0.9, u=1, wf = 1):\n",
+    "    if wf == 1:\n",
+    "        weighting_function = weighting_function_1\n",
+    "    elif wf == 2:\n",
+    "        weighting_function = weighting_function_2\n",
+    "    else:\n",
+    "        weighting_function = weighting_function_3\n",
+    "    total_strength=0\n",
+    "    weighted_strength=0\n",
+    "    for i in itemset_pairs_time_strength:\n",
+    "        w_TI=weighting_function(i[2], delta, u)\n",
+    "        # print(weighting_function_1(i[2], delta, u) < weighting_function_2(i[2], delta, u))\n",
+    "        weighted_strength+=w_TI*i[3]\n",
+    "        total_strength+=i[3]\n",
+    "    TiW=weighted_strength/total_strength\n",
+    "    return(TiW)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# function to check if a given sequence is a super sequence of the other \n",
+    "# checks if seq1 is a super sequence of seq2\n",
+    "def is_super_seq_test(seq1,seq2):\n",
+    "    i= 0\n",
+    "    j= 0\n",
+    "    while i<len(seq1) and j<len(seq2):\n",
+    "        if seq2[j][0] in seq1[i][0]:\n",
+    "            i+=1\n",
+    "            j+=1\n",
+    "        else:\n",
+    "            i+=1\n",
+    "    if j==len(seq2):\n",
+    "        return 1\n",
+    "    else:\n",
+    "        return 0\n",
+    "    \n",
+    "# testing function\n",
+    "def TiW_support_test():\n",
+    "    count=0\n",
+    "    for i in database.keys():\n",
+    "        seq1=database[i]\n",
+    "        seq2=[['ad'],['bc'],[]]\n",
+    "        count+=is_super_seq_test(seq1,seq2)\n",
+    "    \n",
+    "# print(count/len(database.keys()))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def chunkstring(string, length=4):\n",
+    "    return list(string[0+i:length+i] for i in range(0, len(string), length))\n",
+    "\n",
+    "def key(el):\n",
+    "    return len(el)    \n",
+    "    \n",
+    "def is_super_seq(s1, s2):\n",
+    "    seq_s1 = [chunkstring(s1[i][0]) for i in range(len(s1))]\n",
+    "    seq_s1.sort(key=key, reverse=True)\n",
+    "    seq_s2 = [chunkstring(s2[i][0]) for i in range(len(s2))]\n",
+    "    seq_s2.sort(key=key)\n",
+    "    super_seq_matrix = [0 for j in range(len(s2))]\n",
+    "    for ii in range(len(seq_s1)):\n",
+    "        for jj in range(len(seq_s2)):\n",
+    "            if not super_seq_matrix[jj]:\n",
+    "                count = 0\n",
+    "                for i in seq_s1[ii]:\n",
+    "                    if i in seq_s2[jj]:\n",
+    "                        count+=1\n",
+    "                if count == len(seq_s1[ii]):\n",
+    "                    super_seq_matrix[jj] = 1\n",
+    "    \n",
+    "    if sum(super_seq_matrix) == len(seq_s1):\n",
+    "        return True\n",
+    "    \n",
+    "    return False"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def TiW_support(TiWs, db):\n",
+    "    TiW_supports = dict()\n",
+    "    TiW_normalise = 0\n",
+    "    for x in db.keys():\n",
+    "        selected_sum = 0\n",
+    "        TiW_normalise += TiWs[x]\n",
+    "        for s in db.keys():\n",
+    "            if is_super_seq(db[x], db[s]):\n",
+    "                selected_sum += TiWs[s]\n",
+    "        TiW_supports[x] = (selected_sum)\n",
+    "\n",
+    "    for x in db.keys():\n",
+    "        TiW_supports[x] /= TiW_normalise\n",
+    "    return TiW_supports    \n",
+    "    "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def nominal(TiWs, db):\n",
+    "    n_supports = dict()\n",
+    "    n_normalise = 0\n",
+    "    for x in db.keys():\n",
+    "        selected_sum = 0\n",
+    "        n_normalise += 1\n",
+    "        for s in db.keys():\n",
+    "            if is_super_seq(db[x], db[s]):\n",
+    "                selected_sum += 1\n",
+    "        n_supports[x] = (selected_sum)\n",
+    "\n",
+    "    for x in db.keys():\n",
+    "        n_supports[x] /= n_normalise\n",
+    "    return n_supports"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# def main(): main function\n",
+    "def get_supports(delta, u, wf = 1):\n",
+    "    TiW_db = dict()\n",
+    "    for i in database.keys():\n",
+    "        itemset_pairs=itemset_pair_generator(database[i])\n",
+    "        itemset_pairs_time=time_interval_sequence(itemset_pairs)\n",
+    "        itemset_pairs_time_strength=strength_pair(itemset_pairs_time)\n",
+    "        TiW_db[i]=TiW_sequence(itemset_pairs_time_strength, delta, u, wf)\n",
+    "    sups = TiW_support(TiW_db,database)\n",
+    "    return [sups[k] for k in sups.keys()]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def get_support_modified(delta, u, wf = 1, x1 = 1, x2 = 0):\n",
+    "    TiW_db = dict()\n",
+    "    for i in database.keys():\n",
+    "        itemset_pairs=itemset_pair_generator(database[i])\n",
+    "        itemset_pairs_time=time_interval_sequence(itemset_pairs)\n",
+    "        itemset_pairs_time_strength=strength_pair(itemset_pairs_time)\n",
+    "        TiW_db[i]=TiW_sequence(itemset_pairs_time_strength, delta, u, wf)\n",
+    "    sups_TiW = TiW_support(TiW_db,database)\n",
+    "    sups_nominal = nominal(TiW_db,database)\n",
+    "    print(\"Hi\")\n",
+    "    assert len(sups_TiW.keys()), len(sups_nominal.keys())\n",
+    "    return [x1*sups_TiW[i] + x2*sups_nominal[i] for i in sups_TiW.keys()]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": "0.005656419848711377\n"
+    }
+   ],
+   "source": [
+    "# testing functions\n",
+    "itemset_pairs=itemset_pair_generator(database['0'])\n",
+    "itemset_pairs_time=time_interval_sequence(itemset_pairs)\n",
+    "itemset_pairs_time_strength=strength_pair(itemset_pairs_time)\n",
+    "TiW=TiW_sequence(itemset_pairs_time_strength)\n",
+    "# print(itemset_pairs)\n",
+    "print(TiW)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "def is_none(l, length):\n",
+    "\tif l is None:\n",
+    "\t\treturn [None for ii in range(length)]\n",
+    "\telse:\n",
+    "\t\tassert len(l), length\n",
+    "\t\treturn l\n",
+    "\n",
+    "# no. pattern vs threshold for delta = 0.5 0.7 0.9\n",
+    "def plt_graphs(xss, yss, labels=None, colors=None, markers=None, x_label=\"x - axis\", y_label=\"y - axis\"):\n",
+    "    l = len(xss)\n",
+    "    assert l, len(yss)\n",
+    "    labels = is_none(labels, l)\n",
+    "    markers = is_none(markers, l)\n",
+    "    colors = is_none(colors, l)\n",
+    "    for ll in range(l):\n",
+    "        plt.plot(xss[ll], yss[ll], label=labels[ll], color=colors[ll], marker=markers[ll])\n",
+    "    plt.xlabel(x_label)\n",
+    "    plt.ylabel(y_label)\n",
+    "    plt.legend()\n",
+    "    plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": "<Figure size 432x288 with 1 Axes>"
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# For graph 1\n",
+    "gs = []\n",
+    "dels = [0.5, 0.7, 0.9]\n",
+    "pers = [[0.2, 0.3, 0.5, 0.7, 1] for _ in range(len(dels))]\n",
+    "counts = [[0, 0, 0, 0, 0] for _ in range(len(dels))]\n",
+    "for ds in dels:\n",
+    "    gs.append(get_supports(ds, 0.5))\n",
+    "\n",
+    "# print(get_supports(0.9, 0.5))\n",
+    "\n",
+    "for i in range(3):\n",
+    "    for j in range(5):\n",
+    "        percent = pers[i][j]/100\n",
+    "        for k in gs[i]:\n",
+    "            if k > percent:\n",
+    "                counts[i][j] += 1\n",
+    "\n",
+    "plt_graphs(pers, counts, labels=[\"del 0.5\", \"del 0.7\", \"del 0.9\"], colors=[\"b\", \"g\", \"r\"], markers=['.', 'o', '^'], x_label=\"Support threshold (%)\", y_label= \"Number of patterns (k)\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": "Hi\nHi\nHi\n"
+    },
+    {
+     "data": {
+      "image/png": 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HXRw5At99F/j4AkRi6ux+/frRtm1bLrnkEsaOHUutWrWKFPuxwj51tog0BmYDbVX1sIi8C3wB9AE+VNVJIvIisExVXwh2roo6dXZ+jh51c+ElJ8OUqRmcOPZEqsVXY/GQxcSIX/7PyIBu3eDHH2HFClvb2ZQLNnV2YGVl6uxYoIqIxAKJwHbgbOB9b/8E4LIIxVZmVaoEt90GM2fC9yviGNlzJMt2LOPDVR/mPtCqnY0x+Qh7UlDVrcBjwGZcMtgPLAL2qWqmd9gWIODXVxEZLCILRWThrl27whFymTJokJta+5lnoH/7/pxY90QenP4gR7OO5j7whBOs2tkYk0fYk4KI1AIuBVKARkBV4MIAhwa8r6Wq41S1i6p2qVevXukFWkbVqgUDBsBbb8Ge3ZV4qOdDrPp1FZNWTsp7sFU7m3KmLK8kWRqK8nlE4vbROcAGVd2lqhnAh8AfgCTvdhJAE2BbBGIrF26/3d0Zeukl6Ne2Hx3qd2DkzJFkZmXmPtCqnU05kpCQwO7duy0xeFSV3bt3k5CQUKj3RaKj+XTgVeBU4DDwOrAQ6A584NfRvFxVnw92Lutozt8FF8Dy5W400pfrP+Gydy7jlb6vcOMpN+Y9ePJkV+18zz3wz3+GPVZjSkJGRgZbtmwhLS0t0qFEjYSEBJo0aUJcXFyu7cE6moMmBRFJAC4GzsLd6jkMrAQ+V9XvixqoiDwEXANkAkuAv+D6ECYBtb1t16tq0NI/Swr5+/JLV7g8cSL076+c9vJp7Pp9F2uHrSW+UoDRvjfdBK+8AjNmWLWzMeVckZKCiIwELgFm4DqCdwIJwAlAL+/531R1ecmHHBpLCvnLyoITT4SkJJg3D7768SsunHghz/d5nltOvSXvGw4edHO7ZGZatbMx5VxRh6QuUNXOqvo3VX1LVf+nqp+p6hOqeglwHWAFZlEqJsb1LcyfD3PnwvnHn0+3pt0YPWs0aZkBmtfVqrlhqlbtbEyFlm9SUNXPAUQk+dh9InKqqu5UVfuaHsUGDHBf+J9+2s3LMqrXKLYe2MpLC18K/Ab/auf33w98jDGmXAtl9NGHXhUyACLSA9dRbKJctWqubuH9990yzb1SetEruRePzH6E34/8HvhNDzwAp57q5uPeZgPAjKloQkkKQ4CPRaSBiPQBnsZNSWHKgNtuc/0Lz3vjuEb1GsXO33cydsHYwG/wVTunpcHAgVbtbEwFU2BSUNUFwO3A18BI4FxV/bmU4zIlJCXFLaXw0ktw+DB0a9aNC1pewKPfPspv6b8FftMJJ8Djj1u1szEVUL5JQUQ+FZHJIjIZuBc3R1E68Iq3zZQRqamwe7ercgbXWthzeA9Pz306/zcNGQIXXWTVzsZUMMGGpPYI9kZVnVkqERWCDUkNjaobbarqRpuKwGWTLmPGxhlsSN1ArSr5TLm7YwecdJKbRXXevOBLFRpjyoyiDkn9RlVn5vfwTpx35QcTdURca2HFClebBvBwr4fZn76fx+c8nv8bfWs7L10KI0aEJVZjTGQFSwrTRWSYiDTz3ygi8SJytohMAAaUbnimpFx7LdSt64anAnSo34Gr213N0/OeZtfvQWab7dsX/vIXePRRmDUrPMEaYyImWFK4ADgKvC0i20TkBxFZD6wD+gNPqurrYYjRlICEBNdNMHky/PST2zayx0gOZRziX9/+K/ibn3zSrWd7ww2wf3/pB2uMiZhgxWtpqvq8qnYDmgO9gU6q2lxVb1LV0FeiNlFh6FC3EI9vQNGJ9U7k2pOuZeyCsfxy8Jf83+hb2/nnn63a2ZhyLqSps1U1Q1W3q+q+0g7IlJ5GjeCqq+DVV+HAAbdtRI8RHDl6hH/OKmB21K5drdrZmAogUstxmghJTYXffoPXX3evW9ZuycCOA3lx0Yv8vL+A8pPhw63a2ZhyzpJCBXP66e7x7LM5xcrDuw9HVRk9a3TwN/tXO9vazsaUSwUmBRGpKiIx3vMTRKSviMQV9D4TvVJTYd06t+YCQPOk5tzU6SZeWfIK6/euD/5mX7Xz11/D2HymyjDGlFmhtBS+ARK8SfGmAn/GrZZWJCLSWkSW+j1+E5E7RKS2iEwRkXXez3wqqkxxXXml61942q+g+b6z7qOSVGLUN6MKPoGv2vmuu6za2ZhyJpSkIKp6CLgCeFZVLwfaFvWCqrpGVTuqakegM3AI+Ai4B5iqqq1wyeeeol7DBBcX50YiTZmS8ze9cY3GDD11KG8se4O1u9cGP4Fvbedq1WxtZ2PKmZCSgoh0xS2q87m3LbaErt8b+ElVNwGXAhO87ROAy0roGiaAwYOhcmV45pmcbfeceQ8JsQmMnDGy4BM0aGDVzsaUQ6EkhVTchHgfqer3ItICmF5C1/8j8Lb3vL6qbgfwfh4X6A0iMlhEForIwl27glTimqDq1XNf8t94A/bscduOq3oct592O5NWTmLlzpUFn+TSS63a2ZhyJt8J8Ur9wiLxwDagnaruEJF9qprkt3+vqgbtV7AJ8Ypn+XI4+WT3N/2uu9y23Yd2k/J0Cucdfx7vXx1CPYL/2s7Ll0ONGqUbtDGm2Io6IZ7vzSeIyDgR+VpEpvkeJRDXhcBiVd3hvd4hIg29azYEdpbANUwQHTpAr16uwjkz022rk1iHO8+4kw9WfcCS7UsKPolVOxtTroRy++g9YAnwAPB/fo/i6k/OrSOAyeRMsDcA+KQErmEKkJrq/p5//HHOtju73kmthFo8OOPB0E7iq3aeMMGqnY0p4wq8feQ1MzqX6EVFEoGfgRaqut/bVgd4F2gGbAauUtU9wc5jt4+K7+hRaNXKLZng3y3wyKxHuH/a/cwZNIczmpxR8IkyMqBbNzfb3ooVbsyrMSYqFev2EfCpiAwVkYZeLUFtEaldnIBU9ZCq1vElBG/bblXtraqtvJ9BE4IpGZUqwbBhMHs2LF6cs/3202+nbmJdHpweYmshLs7dRjp82KqdjSnDQkkKA3C3i74DFnkP+3pejtx4o+sa8C9mqxZfjXu63cOU9VP4ZtM3oZ2odWt44gmrdjamDAuaFLzpLa5X1ZRjHi3CFJ8Jg5o1YeBAmDTJrcDpc8upt9CgWgOGT3dzI4XEqp2NKdOCJgVVzQIeC1MsJoKGDXOFyS++mLMtMS6R+8+6n282fcPUDVNDO5F/tfP111u1szFlTCi3j74WkX62HnP5dsIJ0KcPvPACpKfnbL+p0000rdGUB6Y9EHprwVftvGQJjBxZKvEaY0pHKEnhr7hhqUe8yesOiMhvpRyXiYDUVHf76N13c7ZVjq3M8O7Dmbd1Hl+s+yL0k116KQwaBGPGWLWzMWVIxCqaS4INSS1ZqtCuHSQmwoIF7k4QQMbRDNqMbUPNyjVZNHgRITcaDxxw1c5Hj1q1szFRpLgVzSIi14vIcO91UxE5raSDNJEn4oqSFy2C777L2R5XKY4Huz/Ikl+W8NHqj0I/YfXqblEeq3Y2pswI5fbR80BX4Frv9UHAxhuWUzfcAElJuYenAlzX4Tpa12nNiBkjyNJC1CD4Vzt/8EHJBmuMKXGhJIXTVfVWIA1AVfcC8aUalYmYqlXhppvgww/dF3yf2JhYRvYcycqdK3n3+3fzP0EgvrWdBw+2tZ2NiXKhJIUMEakEKICI1AOsXLUcu/VW179wbP3Z1e2upv1x7RkxYwSZWZmhn9CqnY0pM0JJCs/gVkY7TkRGA7OBf5ZqVCaimjeHyy+HcePg0KGc7TESw8M9H2bt7rVMXD6xcCdt3drWdjamDAhp9JGItMGtkia4JTNXlXZgobDRR6Vn1izo3h1eesnd9fFRVbqM78Lew3tZc9sa4irFhX5SVbj4Ypg2zfVmty3yqq7GmGIo7uij/6jqalUdq6rPqeoqEflPyYdposmZZ8Ipp7gOZ//vDSLCqF6j2LBvA68tfa1wJxWBV16xamdjolgot4/a+b/w+hdKdCptE31EXDHbDz/A//6Xe9+FLS/kjCZnMOqbUaRlphXuxFbtbExUyzcpiMi9InIA6OBVMv/mvd6JWxDHlHN//CMcd1ze4am+1sKW37YwftH4wp/YV+386KNuzm5jTNTINymo6j9VtTrwb1Wt4T2qe+sg3BPGGE2EVK4MN98Mn38O69bl3tc7pTc9mvfgkdmPcCjjUOATBPPkk5Cc7AojfrNZU4yJFqHcPspTvSwiIU6ZGZiIJInI+yKyWkRWiUhXb/GeKSKyzvtZqzjXMCXjllvciNJnn8293dda+OXgLzy/4PnCn9hX7bx5s1U7GxNFgt0+SvCWyKwrIrX8Vl1LBoq71uLTwFeq2gY4GVgF3IMb2dQKmOq9NhHWoAFccw289hrs359731nNz+K848/j0W8f5UD6gcKfvGtXuO8+q3Y2JooEaykMwa2w1oacFdcWAZ9QjGkuRKQG0B14BUBVj6jqPuBSYIJ32ATgsqJew5Ss1FQ4eNAlhmON6jWKXw/9yrPzn827MxQPPghduli1szFRosA6BREZpqpF/D8+4Pk6AuOAH3CthEVAKrBVVZP8jturqnluIYnIYGAwQLNmzTpv2rSppEIzQXTrBr/8AmvXunWd/V3y9iXM3jybDakbSEpICnyCYNasceNfu3eHL7/MmZ7VGFMqilWnoKrPikh7EblaRP7kexQjnligE/CCqp4C/E4hbhWp6jhV7aKqXerVq1eMMExhpKbC+vWu0/lYD/d8mH1p+3hyzpNFO7mv2vm//7VqZ2MiLJTitRHAs96jF/AvoG8xrrkF2KKq87zX7+OSxA4RaehdsyFu6KuJEpdfDk2a5B2eCnBKw1Pod2I/npz7JLsP7S7aBW6+2S399n//B6uiomDemAoplNFHV+KmuPhFVf+Mu+VTuagXVNVfgJ9FpLW3qTfuVtJkYIC3bQCu78JEibg4N1HetGmwYkXe/Q/1fIiDRw7y7+/+XbQL+Fc7X3edVTsbEyGhJIXDqpoFZHqdxDuBFsW87jBgoogsBzoCjwBjgHNFZB1wrvfaRJGbboIqVeCZZ/Lua3dcO/qf1J9n5z/LjoM7inaBBg1g/HirdjYmgkJJCgtFJAkYj+sUXgzML85FVXWp1y/QQVUvU9W9qrpbVXuraivv557iXMOUvDp13JRFb74Jv/6ad/+IHiNIy0xjzOxi5PPLLoMbb7RqZ2MiJJSO5qGquk9VX8R9gx/g3UYyFdDtt0NamvtCf6wT6pzAgJMH8MLCF9j629aiX+Spp6za2ZgICaWlgIhcISJP4G77HF+6IZlo1r49nHOOGySUkZF3//DuwzmqR3lk1iNFv4h/tXNqatHPY4wptFBGHz0P3AysAFYCQ0TExg1WYKmpsHWrW7LzWCm1UvjLKX9h/OLxbNpXjBoSX7Xz669btbMxYRRK8dr3QHv1DhSRGGCFqrYL+sYwsEV2IiMry5UW1KsH332Xd/+W37bQ8pmWXN/hel7u+3LRL5SRAX/4gyuQWLECGhV3dhVjDBSzeA1YAzTze90UWF4SgZmyKSYGhg2DOXNgwYK8+5vUaMKQzkN4fenr/Ljnx6JfKC7O3UY6fNh1PoewSqAxpnhCSQp1gFUiMkNEZuBqCuqJyGQRsXUVKqiBA92t/0DFbAD3nnUv8ZXieWjmQ8W7UOvW8NhjVu1sTJiEcvuoR7D9qjqzRCMqBLt9FFl33AHPPw+bNkHDhnn33zXlLh777jFWDl1J23rFWI9ZFS66CKZPh8WL4cQTi34uY0yx5z6aGexR8uGasmLYMMjMhBdeCLz/rm53UTW+KiNnjCzehUTg1VdtbWdjwiCkIanGBHL88XDxxfDii6524Vh1E+tyx+l38N4P77Hsl2XFu5iv2nnxYniomLekjDH5sqRgiiU1FXbtgkmTAu//a9e/UrNyTUbMGFH8i/mqnceMsWpnY0pJsJXXpno/Hw1fOKasOftsV9D29NOBBwfVqlKLv//h73yy5hMWbA0wVKmwrNrZmFIVrKXQ0Otk7isip4hIJ/9HuAI00U3ETX2xdCnMmhX4mNTTU6lTpQ4Pzniw+BesXh3+8x9X7XzTTdCjh1v9xxhTIoIlhQdxi980AZ4AHvd7PFb6oZmy4rrroHbt/IenVq9cnbu63cVXP37Ft5u/Lf4F//AHV+387hAxyKcAACAASURBVLsuE40aVfxzGmOA0IakDlfVqPy/zoakRo9774V//Qt++snd3TnW70d+5/hnjqdtvbZMGzCt+BfcvNldSNUVuc2b55b0NMYUqLhDUkeJSF8Recx7XFzyIZqybuhQdyspv/qyqvFVuffMe5m+cTrTNpRAUhgzBmJj3fOMDOjUCXr3dkNX9+8v/vmNqaBCmRDvn0AqrpL5ByDV22ZMtqZNoV8/ePllOHgw8DFDugyhcfXGDJ8+nIJaqEFt3w6vvZZ7mtbYWNdMGTQI6teHq66Cjz+G9PSiX8eYCiiUIakXAeeq6quq+ipwgbetyERko4isEJGlIrLQ21ZbRKaIyDrvZ63iXMOEX2oq7NsHb7wReH9CbAIPdH+A737+jv/+9N+iX2jUKDcrn7+YGLfG89y5rgN65ky3sHTDhjBkiOt7OPY9xpg8Qq1TSPJ7XrOErt1LVTv63de6B5iqqq2Aqd5rU4Z07QpdurjlOvP7+3vjKTeSnJRcvNbCnDl5q5qPHHHbTz8dnn3Wze39+edw4YVuUr3u3SElxXVQf/990a5rTAUQSlL4J7BERF4XkQm4JTmLsYJKvi4FJnjPJwCXlcI1TCkSca2FNWvg668DHxNfKZ4Huz/Iwm0LmbymiPMpLlniOpiPfSxZknNMXJxrOUycCDt2uGGsbdu6ZT7bt3ed0o895pKHMSZbgaOPAESkIXAqIMA8VS3WwHAR2QDsBRR4SVXHicg+VU3yO2avqua5hSQig4HBAM2aNeu8aVMxFnIxJe7IEWjeHDp2hC+/DHxMZlYmbce2pUpcFZYMWUKMhLGwfscOeOcd13pYsMBlsl693Ljafv2gZkk1hI2JXsVdTwFV3a6qk1X1k+ImBE83Ve0EXAjcKiLdQ32jqo5T1S6q2qVevXolEIopSfHxcMst8NVXsHp14GNiY2IZ2XMky3cs5/0f3g9vgPXru2q7+fNdk2b4cDfNq38H9Sef2KR7psKKyNxHqrrN+7kT+Ag4DdjhtUh8LZOdkYjNFN+QIS45PPts/sdc0+4a2tZry4gZIziadTR8wfk74QQ3ud66dbk7qC+7zE3Ad/PN1kFtKpywJwURqSoi1X3PgfNwaz9PBgZ4hw0APgl3bKZk1K8P/fvDhAluNFIglWIq8VDPh1j962reWvFWeAM8lkjgDuo33nAd1C1aWAe1qTCC9il46zEvV9X2JXZBkRa41gFALPCWqo4WkTrAu7ilPzcDV6nqnmDnsorm6LVkiasne+wx+NvfAh+TpVl0HteZA+kHWHXrKuIqxYU3yIIcPOhqHd58E6ZMcS2Gjh1d/0P//tC4caQjNKZIgvUphDLNxUTgXlXdXBrBFYclhejWvTv8/DP8+CNUqhT4mE/XfErfSX15+ZKXGdRpUHgDLIz8Oqivvx6uuMI6qE2ZUtyO5obA9yIy1bcus63NbEKRmgobN8LkIP9aLj7hYk5rfBoPf/Mw6ZlRXH2cXwf1jTe6fVdfbR3Uplwo8hrN0bAUp7UUoltmpludLSUFZszI/7ivf/qa8988n7F9xjL01KFhi6/YVN1EfBMnulWGfv3VTRd71VWuBfGHP7hKa2OiTLHXaAY2AnHe8wXA4hKN0JRLsbFw221uQM/Spfkfd26Lczmz2ZmMnjWawxmHwxdgcYnAGWe4Dupt21wH9QUXuA7qs87K6aD+4YdIR2pMyEKZEO8m4H3gJW9TY+Dj0gzKlB9/+QskJrqpL/IjIvyj1z/YdmAbLy58MXzBlST/CuqdO10FdZs2roK6XTtXQf344y55GBPFQmnb3gp0A34DUNV1wHGlGZQpP2rVgj/9Cd56y63lnJ8eyT3ondKbMd+O4eCRfKZZLSuqVXO3j776yg1xfeoplzT+/ndo0gTOOcfN8mpTfJsoFEpSSFfV7N4zEYnFTU9hTEhuv93NYP3SS8GPG9VrFDt/38lz858LT2Dh0KCB63H376DeuNF1UDdo4DqoJ0+2DmoTNUJJCjNF5D6gioicC7wHfFq6YZny5MQT4bzz4Pnng//t69q0K31a9eHf3/2b39J/C1+A4eJfQT1njru3Nn06XHqpm+L7lltg9myroDYRFUpSuAfYBawAhgBfAA+UZlCm/LnjDrc2zvsFTHX0cM+H2XN4D0/NfSo8gUVCoA7q8893JeC+Dur777cOahMRoc6SGg+0wd02WuN/OymSbEhq2ZGV5VoMSUluFGcwV7xzBVM3TGVD6gZqV6kdngCjwYEDroJ64sScCupTTsmpoG7UKNIRmnKiWENSReQi4CfgGeA54EcRubBkQzTlXUxMTu3X3LnBj32o50McSD/A4989Hp7gokX16nDDDbk7qGNjc3dQv/46/FYOb62ZqBFK8dpq4GJV/dF7fTzwuaq2CUN8QVlLoWw5eND9bbvwQnj77eDH/vH9P/LZ2s/YkLqBelUr+BTpa9e61sPEiW4d6oQE6NvXtSAuuMBNSWtMIRR3moudvoTgWY9Na22KoFo1t2zB++8XvODZyJ4jOZx5mEe/fTQ8wUWzQB3U06ZZB7UpFfkmBRG5QkSuwM179IWIDBSRAbiRRwvCFqEpV267zf3tev754Me1qduG6ztcz9gFY9l+YHt4got2BXVQH3+8dVCbYgvWUrjEeyQAO4AeQE/cSKQ8y2QaE4qUFHfn46WX4HABM1o82P1BMrMyeWRWaSwJXsb5KqjfesvN4PrGG9C6NYwZ4yqoO3WCJ57IW0G9fTv06AG/lMQCiqZcUtUy++jcubOasmf6dFVQffnlgo+9afJNGj8qXjft21TqcZUL27erPvWU6qmnug9ZRLV3b9XXXlPdv1/1lltUY2JUhw6NdKQmgoCFms/f1VA6mlOAYUAyblEcXzLpW5xkJCKVgIXAVlW92LvOJKA2bsK9G7SAoa/W0Vw2qbq1alRh2TJ3VyQ/m/dvptWzrRh48kBeuqSAkmiT25o1riXx5puwfj1UrgwZGe7+XXw8fP21ux1VuXKkIzVhVtyO5o9xs6Q+Czzu9yiuVGCV3+tHgSdVtRWwF4jiFVdMcYi4mR9WrAg+pTZAs5rNGNxpMK8ufZX1e9eHJb5yo3Vr10H944+ug7pVq5zO6CNHoGdPN1vh8ce7W1F33gkvvug6sbdudVnbVDihtBTmqerpJXpRkSbABGA08Fdc38UuoIGqZopIV2Ckqp4f7DzWUii70tKgaVPo1s3VawWz/cB2WjzTgmvaXcPrl70elvjKne3bXaV0WlrOtrg41/O/dasb9rp2LRw6lLO/WjU38ql165yfvufVqoX/dzAlJlhLITbQxmM8LSIjgK+B7KWxVLU4ayo8BdwFVPde1wH2qWqm93oLbopuU04lJMCQIfDII+7ORosW+R/bsHpDbj31Vp6c+yT3nHkPbepGvESm7Bk1Ku+QVRE3U+E777jXWVkuQaxZ4x5r17qfc+a4RYT8v0A2bpw7UfgezZvnv/aqKRNCaSn8E7gBV9Xs+1elqnp2kS4ocjHQR1WHikhP4O/An4E5qtrSO6Yp8IWqnhTg/YOBwQDNmjXrvGnTpqKEYaLAtm3ub8iwYW6gTDC7ft9FytMpXNL6Et7uV0Dlm8nrlFMCr3TUsSMsWVLw+w8fdoVzvoTh/9i3L+e4+Hho2TJ3ovAljzp1Su73McUSrKUQakVzh4I6fQsRjC/JZOKGu9YAPgLOx24fVTjXXuuG22/Z4mZ5COa+qfcxZvYYlt28jJPq5/m+YCJB1S1D6p8kfC2Mn35yHds+derkTRStW7s+DevsDqviJoV3gGGqWuJVzL6Wgjf66D3gA1WdJCIvAstVNWiJkyWFsm/ePDcA5plnXIshmD2H95DydAq9U3rz4TUfhidAU3SZmbBhQ06S8H/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+      "text/plain": "<Figure size 432x288 with 1 Axes>"
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "gs = []\n",
+    "dels = [0.5, 0.7, 0.9]\n",
+    "pers = [[0.2, 0.3, 0.5, 0.7, 1] for _ in range(len(dels))]\n",
+    "counts = [[0, 0, 0, 0, 0] for _ in range(len(dels))]\n",
+    "for ds in dels:\n",
+    "    gs.append(get_support_modified(ds, 0.5, 1, 0.7, 0.3))\n",
+    "\n",
+    "# print(get_supports(0.9, 0.5))\n",
+    "\n",
+    "for i in range(3):\n",
+    "    for j in range(5):\n",
+    "        percent = pers[i][j]/100\n",
+    "        for k in gs[i]:\n",
+    "            if k > percent:\n",
+    "                counts[i][j] += 1\n",
+    "\n",
+    "plt_graphs(pers, counts, labels=[\"del 0.5\", \"del 0.7\", \"del 0.9\"], colors=[\"b\", \"g\", \"r\"], markers=['.', 'o', '^'], x_label=\"Support threshold (%)\", y_label= \"Number of patterns (k)\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": "Hi\nHi\nHi\n"
+    },
+    {
+     "data": {
+      "image/png": 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h4sSJdbLtoUOHsnv30R1gTZw4kSlT6qasuj/1+NOAB3CS/XbgMlW1J3eHkd7H9eaCLhcwbdk0Dh466HU4xniqQYMGzJkzhx07dtT5tt977z2aNWtW59utLX/q8b+mql+r6nRVfUZV14vIa/URnKk/EwZPYPu+7fxzzT+9DsWYWsnIgD//2XmtCzExMYwePZqpU6ce8V52djZDhgyhV69eDBkyhM2bNwMwatQoxowZw3nnnUeXLl345JNPuOWWW+jevTujRo0qW79Tp07s2LGDTZs20b17d2677TZ69OjBhRdeyIEDBwB44YUXGDBgAL179+bKK68kPz+/br6Y73f0Y5kevhNue3//Oo/EeOoXXX5B77a9mZIxhZF9RhIl/rQCGhM448bBypXVL5OXB6tXQ0kJREVBr17QtGnVy/fpA089VfNn33XXXfTq1YsHHnig3Py7776bm266iZEjR/LSSy9x7733MnfuXAB27drFRx99xLx58xg+fDifffYZL774IgMGDGDlypX06dOn3LaysrKYPXs2L7zwAldffTX//ve/ueGGG7jiiiu47bbbAPjd737HzJkzueeee2oOuhaq/N8tIg+LyF6gl9tjd487/TNOJywTRkSE1MGprMtZxwfffeB1OMb4JS/PSfrgvObV0WMmmjRpwk033cS0adPKzc/IyOC665w722+88UaWLFlS9t7w4cMREXr27Enbtm3p2bMnUVFR9OjRg02bNh3xGZ07dy7bGfTv379smbVr13LWWWfRs2dP0tLS+Oqrr+rmS/mo8ohfVf8M/FlE/qyqD9f5J5ug8+sev+bhhQ8zOX0yQ7sO9TocE+H8OTLPyIAhQ6CwEOLiIC0NUlLq5vPHjRtHv379uPnmm6tcxvc2ygYNGgAQFRVVNl46fejQoSPW9V0mOjq6rKln1KhRzJ07l969e/PKK6+waNGiY/0qR/DnfP70ijNEZGGdR2I8Fxsdy7iB41i0aRGZP1hPaRP8UlJg4UKYNMl5raukD9CiRQuuvvpqZs6cWTZv8ODBvP66U848LS2NM888s+4+0LV3717atWtHUVERaWmB6VFfXVNPvFteoZWINPd5+lYn4PiARGM8d1v/22jSoAlT0uvmtjFjAi0lBR5+uG6Tfqnx48eXu7tn2rRpvPzyy/Tq1YvXXnuNp5+u+46PkyZNYuDAgVxwwQWccsopdb59qKZWj4iMBcbhJPltQOk5zR7gBVV9JiARVcJq9dSvBxY8wBMZT/DdPd/RuXnnmlcwpo6sX7+e7t27ex1GSKrst6t1rR5VfVpVOwOpqtrF5+lbvesz6Zv6N3bgWKIlmqeW+tHIaowJOf504PqbiJwmIleLyE2lQ30EZ7zRvkl7rut5HS+ueJGdB6yGnjHhxp8OXI8Cf3OH84C/4jxRy4Sx8SnjyS/KtzIOxoQhf+7quQrnYek/qurNQG+gQfWrmFDXs21PLjrpIqYtm0bBIXsohjHhxJ/Ef8B96PohEWmC04GrS2DDMsEgNSWVn/b/xD9W/8PrUIwxdcifxJ8pIs2AF4AvgeVAjU/fMqHv/M7n0/e4vjyR8QQlapW4jQkX/lzcvVNVd6vq88AFwEi3yceEORFhwuAJfL3ja+Z/O9/rcIypFyLCjTfeWDZ96NAhWrduzSWXXFKr7ZQWZAOn41epCRMm0KNHDyZMmMDzzz/Pq6++WqvtNmrUqFbLV8afIm2IyBXAmTgPY1kCrD7mTzYh4apTr+KhhQ8xJWMKw7sN9zocY8pJW5PGbxf+ls15m+nQtAOPDXmM63tef0zbbNiwIWvXruXAgQMkJCSwYMEC2rdvf0zbTE9PLxv/+9//Tk5OTrmSDfXNn7t6ngXuANYAa4HbRcSvZ+6KSDMReUtEvhaR9SKS4vb+XSAiWe5r82P7CiaQYqNjuW/QfSzOXszn26yFzwSPtDVpjH53NNl52ShKdl42o98dTdqaYy9zcPHFFzN/vnOWO3v2bK699tqy93bu3Mlll11Gr169GDRoEKtXO8fBubm5XHjhhfTt25fbb78d386xpUfpI0aMYP/+/QwcOJA33nij3MNVNmzYwEUXXUT//v0566yz+PrrrwHnAfQpKSkMGDCA3//+98f83cC/I/5zgNPU/RYiMgtnJ+CPp4EPVPUqEYkDEoH/Axaq6uMi8hDwEPBg7UM39eXWvrcycdFEJqdP5s1fvel1OCZCjPtgHCt/rLou89KtSzlYXP7BQflF+dz6zq288OULla7T57g+PHVRzR0Tr7nmGv74xz9yySWXsHr1am655RY+/fRTAB599FH69u3L3Llz+eijj7jppptYuXIlf/jDHzjzzDN55JFHmD9/PjNmzDhiu/PmzaNRo0asdOtN+z7Za/To0Tz//PN07dqVZcuWceedd/LRRx8xduxYxowZw0033cT06X4dc9fIn4u73wAdfKZPwI+mHvcOoLOBmQCqWqiqu4FLgVnuYrOAy2oTsKl/jRs0ZkzyGOasn8OGnRu8DscYgCOSfk3za6NXr15s2rSJ2bNnM3Ro+Uq1S5YsKbsGcP7555Obm0teXh6LFy/mhhtuAGDYsGE0b+5/Y8a+fftIT0/nV7/6FX369OH2229n+/btAHz22WdlZxy+1x6OhT9H/C2B9SJSep4/AMgQkXkAqlpVZ64uQA7wsoj0xrkjaCzQVlW3u+tuF5E2la0sIqOB0QAdOnSobBFTj+4deC9PZDzB1KVTeWaoVewwgVfTkXmnpzqRnZd9xPyOTTuyaNSiY/78ESNGkJqayqJFi8jNzS2bX1l9s9LyzL5lmmujpKSEZs2alZ0JVLX9uuLPEf8jwMXAo+4wFJgEPOEOVYkB+gHPqWpfYD9Os45fVHWGqiaranLr1q39Xc0ESLvG7bih1w28tOIlduTX/bNIjamtx4Y8RmJsYrl5ibGJPDbksTrZ/i233MIjjzxCz549y80/++yzy8olL1q0iFatWtGkSZNy899//3127drl92c1adKEzp078+abTlOqqrJq1SoAzjjjjHKloOuCP7dzflLdUM2qW4GtqrrMnX4LZ0fwk4i0A3Bffz7WL2Hqx/iU8Rw4dIDnvnjO61CM4fqe1zNj+Aw6Nu2IIHRs2pEZw2cc8109pZKSkhg7duwR8ydOnEhmZia9evXioYceYtYsp+X60UcfZfHixfTr148PP/yw1i0VaWlpzJw5k969e9OjRw/eeecdAJ5++mmmT5/OgAEDyKujR4xVWZa5TjYu8inwG1X9RkQmAg3dt3J9Lu62UNUHqtwIVpY5mAz75zC+2PYF2eOySYhN8DocE2asLPPRq5OyzHXkHiBNRFYDfYD/BzwOXCAiWTgdwh4PcAymDk0YPIGc/BxeW/2a16EYY45SdU/gWui+/uVoN66qK912+l6qepmq7lLVXFUdoqpd3Ver+xtCzul4DsnHJ1sZB2NCWHVH/O1E5BxghIj0FZF+vkN9BWiCi4iQmpLKt7nfMu+beV6HY4w5CtXdzvkIzl04ScCTFd5T4PxABWWC25WnXkmnhZ2Ykj6Fy06xbhjGhJrqHr34lqpeDPxVVc+rMFjSj2AxUTHcN+g+PtvyGRlbMrwOxxhTS/7czjlJREaIyBR3qF2JOhOWbul7C83jmzMlY4rXoRhjasmfIm1/xulxu84dxrrzTARrFNeIOwfcydvr3yYrN8vrcIypE7m5ufTp04c+ffpw3HHH0b59+7Lp0tLKl19+OXPnzi1bp1u3bvzpT38qm77yyiuZM2dOvcdeG/7czjkMuEBVX1LVl4CL3Hkmwt19+t3ERsfyZEbFS0DG1KPt2+Gcc+DHH495Uy1btmTlypWsXLmSO+64g/vuu69surS08uDBg8vGc3NzadSoERkZh5s8MzIyytXfD0b+3sffzGe8aSACMaHnuEbHcVOvm3hl1Svk7M/xOhwTqSZNgiVLnNcAKi2tfMYZZ5Ql/vT0dC655BJycnJQVb7//nsSEhI47rjjAhrLsfKnSNufgRUi8jEgOBU3Hw5oVCZkjB88nhdXvMj0L6Yz8dyJXodjwsm4cVBF0bIyBw/C559DSQk8/zysWAFxcVUv36cPPFVzWebq9O/fn7Vr11JYWEh6ejrnnHMOGzduZP369axYsYIzzjjjmLZfH/y5uDsbGATMcYcUVX090IGZ0HBKq1MYfvJwpn8xnfyifK/DMZEmOxtKy86oOtMB1qBBA3r06MHy5ctZunQpAwcOJCUlhfT0dNLT04O+mQf8fPSiW0bZeuuYSk0YPIGzXzmbWStnMWbAGK/DMeGipiPz7duhS5fyiX/XLnj9dQhwU8vgwYNZvHgxe/fupXnz5gwaNIhnnnmGFStWcMcddwT0s+tCoGv1mAhwZoczOb396TyR8QTFJcVeh2MixaRJThOPr+LigLf1g9PO//e//53evXsDzoNbli5dyubNm+nRo0fAP/9YWeI3x0xEmDB4Aht2beCdb97xOhwTKTIyoLCw/LzCQvB5sHmgDB48mI0bN5KSkgJATEwMbdq0ITk5maio4E+r1ZZlFpEoYLWqnlZ/IR3JyjIHv+KSYk5+5mTaNGxD+i3pdf7EIBMZrCzz0auzssyqWgKsEhF79qGpVnRUNPcPup+lW5fy2ZbPvA7HGFMNf85J2gFfichCEZlXOgQ6MBN6bu57My0TWjIl3co4GBPM/Lmr5w8Bj8KEhcTYRO4ccCd/WvwnvtnxDd1adfM6JBOCVNWaCmuptk9S9OuZu8AmINYd/wJYfjTBmfB39+l30yCmgZVxMEclPj6e3NzcWieySKaq5ObmEh8f7/c6NR7xi8htwGigBXAi0B54HhhylHGaMNamYRtG9h7JKytf4Y/n/ZG2jdp6HZIJIUlJSWzdupWcHCsBUhvx8fEkJSX5vbw/TT13AacDywBUNUtE2hxdeCYS3J9yPzO+nMEznz/DpPMDf0+1CR+xsbF07tzZ6zDCnj8Xdw+qatnNsiISg/MErhqJyCYRWSMiK0U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+      "text/plain": "<Figure size 432x288 with 1 Axes>"
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Graph 5 modified vs\n",
+    "gs = []\n",
+    "x1s = [0, 0.7, 1]\n",
+    "pers = [[0.2, 0.3, 0.5, 0.7, 1] for _ in range(len(dels))]\n",
+    "counts = [[0, 0, 0, 0, 0] for _ in range(len(dels))]\n",
+    "for x1 in x1s:\n",
+    "    gs.append(get_support_modified(0.7, 0.5, 1, x1, 1-x1))\n",
+    "\n",
+    "# print(get_supports(0.9, 0.5))\n",
+    "\n",
+    "for i in range(3):\n",
+    "    for j in range(5):\n",
+    "        percent = pers[i][j]/100\n",
+    "        for k in gs[i]:\n",
+    "            if k > percent:\n",
+    "                counts[i][j] += 1\n",
+    "\n",
+    "plt_graphs(pers, counts, labels=[\"Nominal\", \"Modified\", \"TiW\"], colors=[\"b\", \"g\", \"r\"], markers=['.', 'o', '^'], x_label=\"Support threshold (%)\", y_label= \"Number of patterns (k)\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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Hjh3b7rTM1113HSeddBLZ2dksXrwYcNMyf+lLX+LFF19k//79gcXV6+vr+exnPxuyEOmsiE/L3BP6y7TMba32MzJ9JL++9NcUlxRTVFJEcUkxB6sOApDgS2Dq8KmBgmDmyJlMHjqZeF/fKbPLy92qY40FwfbtbvuYMc2rhbKyejdO0z/YtMxN2pqWuV8n/t7om9uexhHFbfU2aqTqRhsXlxRTtLeI4tJiikuKA11Qk+OTmZ47ncJcVxAU5hVycs7JfaZ30fbtTdVCy5e79gKfD2bObCoIZs2ChITejtT0RZb4mwzIxL9lyy2Uli4kL+/mbvfN7Sld7dXjVz/bDm9zBUFJMcWlxbxT+k6gEElPTOeMvDOa7gzyZlIwuCDmxx/U18PbbzfdDaxe7VYdS0+HCy5whcDQobB1q6smarmOgTEtWeJvMuASf01NKatWjQbqgXgmTlzE0KFXEheX0tGhfUa9v573D75P0d6iQBXR+v3rA72GcpJzKMwrbNZmMDIj5CzYMePoUTdtxNKl8PLLEDyKPS4O7rsPbrkFBg/utRBNjLPE32TAJf4tW75CaenjuMTviCSSmXkO2dnzycqaT1raVKSPVI+Eq7ahlo37NwYKgqKSIjYd2ESDNgCQm5bbrCAozCtkaOrQXo46NFW31sCDDzafTdTnc1VBjdVCZ54J8X2nycNEmCX+JgMq8Tf2zfX7m/rPiiQyYsQXqah4k8pKt6BtQsIwsrLmeQXBPAYN6p8L2lbVVbFu3zpXReQVBlsObgn0MBqTOca1FXhtBmfknkFmUmYvR+2sWuUafmtrXVfQBx90i88sXQpFRa5aKDOzqVpo/nwYN663oza9yRJ/ky6tuSsiScBlwDlAHnACeBd4QVU39VjEPSxU31wAER8zZ26gpqaUI0eWceTIMg4fXsqBA2665tTUKWRlzSc7ez6ZmecQF9c/Jm5LSUhhzqg5zBk1J7CtoqaCd0rfCRQERXuLWPLeksD7J+ec3OzOYPqI6b0yxmD2bNcA3HJx+h/8AA4fbl4t9PTT7r3x45sKgfPPdwWDMaZJm1f8InIvcDluVs01wAEgCTgZON97fruqboh0kJ294i8qmk5lZev5OVJTpzFz5tpm21T9VFZu5PDhpRw5spSjR/+Jag0igxg8+NxAQZCaOiXmG0q761DVIdaUrgn0JCraW8TeY3sB8ImPyUMnN2s8jqUxBqquAbixkfiVV6Cy0rULnHVWU0FQWGjVQv1dX7nir6mp4fOf/zxr1qwhJyeHP/3pTxQUFLTa74tf/CLPP/88w4YNC0z8FkqPVPWIyKWq+kJbJxGRYcBoVY14B/to9uNvaKiivPyfgYKgstJ90YmJI8jKmkdW1nyysi6Kie6h0VB6rLRZFVFRSVGrMQbBDciTh04mIa73+2HW1sJbbzUVBMXFrnAYPNhVHTUWBCH+n5k+rlOJf/p0dxv53e9CbnSren/961+zYcMGHnvsMRYvXszTTz8dclrm119/nbS0ND7/+c9HPvEHHVigqjtbbJupqkXtHtiDenMAV03NXg4fXsaRI0s5cmQZdXUu6aWmnh5oJM7M/AhxcQNjQVtV5cPyD5sNNisuKaa8phyApPgkpo+Y3qya6JQhp/T6GINDh1yVUWO10J49bvuECc2rhdLTezVM0wM6lfhFXOORzwdf+EKPFADhTst88cUXc++99zJ79mzq6+sZMWIEZWVlIWsWWn5mKD1Wx+/5m4hcrqp7vQ86D/gVMCWMY/u8QYNGkpt7A7m5N6Dq5/jxdYG7gT17HmL37p/g8yWRmXleoCBITT2131YLiQhjBo9hzOAxfHLyJwE3xmD74e3NehI9sfYJfvn2LwE3xmBG7gxm5s0MDDgbO3hsVL+jnBz41KfcQxW2bGm6G/j97+GRR1wV0OzZTQXBGWe4qiLTh912G6xrf1pmar0pGx57DH7zG7ck3ZgxMKiNasxp09ySdt0U7rTMkRBO4r8J+LuIXA7MAH4IfKyjg7yG4deBQd55lqjq90TkSeA8oNzb9QZV7eAvExtEfKSnzyA9fQZjxtxJQ0MlR4++5hUEy9i+/XYAEhNzA20DWVkXkZg4rNnnxNqI4u7yiY8JOROYkDOBz075LAAN/gY2H9zcbPTxw28/HBhjkJ2c7aqIgkYfj0wf2aowiMQ01iIwcaJ7fP3rbqnJVauaCoLvftc9srLcwjONBcHo0d06rYl1qu5RWgpVVS7BR/R04U3LHAkdJn5VLRKRrwNLgWpgnqqWhfHZNcAFqnpcRBKAN0TkJe+9/6eqS9o5tk+Ii0slJ+dj5OS4crC6eo/XW2gphw49z/79iwBIS5se1Fvo7B5d7SdWxfniAlNb3zDtBsCNMXj3wLuB0cdFJUU88OYDgTEGI9JGNKsi+vDoh9y+7PbA6ORITWM9aJDrMTR3Lvzwh1BW1rxa6C9/cfudckpTITB3rpt0zsS4jq7MgxNtYqK7xWus8hkRG9MyR0KbiV9EnoNmU0mm4K7SnxARVPWK9j5YXXHWODl9gveI/UED3ZCUlE9u7hfIzf2CVy20lsOHl3L48Mvs2fMgu3c/gEiSNxugn337fseYMd/tF1f94UiMS2RG7gxm5M7gJm4C4ETdicAYg8aqohf+9ULIWUzBjUm4e/ndEV2/YOhQ+Mxn3EMVNm9uuhv47W/hl7908wjNmdNUEMyY4aqJTR/UQwm/UU9Oyxwp7fXqOa+9A1X1tQ4/XCQO1xX0JOARVb3Dq+qZjbsjWA7cqao1IY5dACwAGD169Bm7drWe1bIvqa8/Tnn5a+zYcVdgABlAcvJEJk36AxkZrdpfBqyKmgrWlq5l7qK5be7z5MefZN74eeSl50UvMKC6Gt58s6kgaKw+zslpXi2Unx/VsEyQTvfqmTOnRxJ+sIcffpiHH36YsWPHMnLkSAoKClo17lZXV3Pdddexdu3awLTM48aNazYtM8A111zDihUrOHjwIMOHD+f73/8+N954Y6tz9lR3TtEOuvyEs4+332DgaeBW4BCwD0gEFgLbVfUH7R3fX6ZlDjWiuFF6eiF5ebcwbNhn+tV8Qt3R1jTWPvHh9wbonTbsNOaPm8/88fM5Z8w5pCRE97vbvx/+8Y+mgmDfPrd90qSmQuC889wSlSY6+ko//p7WmcTf3s3pqyJyq4g0a9ISkUQRuUBEFgHXhxOQqh7FDQS7RFVL1akBfg+cGc5n9AehRhQ3zh/U0FDFli03smrVSLZuvY3Kyvd7KcrYcf+F97dK5CkJKSy6chFrb1rLAxc9wPDU4fyq6Fdc8tQlZD+Qzbw/zOMnb/6E9fvWh2w862nDh8O118KiRW4qiQ0b4Kc/dQ3Bv/kNXHopZGe7sQMPPABr17ppJozpTe1d8ScBXwSuBcYCR3GjdeNwDb2PtNcbR0SGAnWqelREkr1jHgDWqGqpuMqsnwPVqnpne0H2lyv+9kYUFxa+Q3n5PykpeZSysr+iWsfgweeTl3cLQ4Zcic/X+4OiekM4vXqq6qp4fdfrLN2+lKXbl7KpzM0mMjx1OPPGz2P+uPnMGz+PEWnRbUuproY33mi6G1i/3m0fOrSpWmjePBgZ2xOm9jl2xd+kW5O0eb1yhgAnvKv3cI6ZCizCFRQ+4M+q+gMReQUYCgiwDrhZVY+3/Un9J/GHq7Z2P6Wlv6Ok5DfU1OwiMXEEublfIjd3AUlJo3o7vJi3t2Ivy3YsY+n2pSzbsSww0njq8KmBaqGPjP4IyQnRnYtp376mBWiWLXPVRACnntpULXTuuZBiNX3dsnnzZiZOnNhvx9KEoqq8//77A3t2zv5CtYHDh/+PvXsf5fDhFwEhJ+cy8vJuITt7fr+bUjoS/Opn3b51gbuBNz58gzp/HUnxSZw75txAQXDasNOimij8fti4selu4J//dOMJEhPhnHOaCoKpU623UGd98MEHpKenk5OTMyCSv6py6NAhjh07xtixY5u9Z4m/jztxYielpQspLX2CuroDJCWNIy/vZkaM+AKJiZEf6ddfVNZW8tqu1wIFweaDmwG3TsG88fO4ePzFXDTuIoalDuvgk3pWVZVL/o0FQePI/GHDXHXQxRe76qEoTyfTJ9XV1bFnz542+8/3R0lJSeTn55PQYr1SS/z9hN9fS1nZ3ygpeZTy8tcRSWTo0H9j5MhbyMiYMyCucHrS7vLdzaqFDp84DMD0EdOZP97dDZw96uyoz0JaUtK8WqjMGzI5ZUrT3cA550By/5g53ERIdyZpS8XV7ftF5GRgIvCSqtZFJtTWLPGHVlm5iZKSx9i3779paKggNXUKeXm3MHz454iPt9nGOqvB38DafWsDdwMrd6+kzl9HcnwycwvmBgqCSUMmRb1aaP36pruBN95w08sMGuTaBBoLgilTmg9ENaY7iX8NbiGWLOAtoBioUtXIDZ1swRJ/++rrj3PgwB8pKXmU48fXEheXxvDhnyMv7xbS0qb2dnh91rGaY82qhbYc2gLAyPSRzB8/n3nj5nHRuIuivnRlZSW8/npTQfDee277iBGuWmjsWFcwXHYZnH12VEMzMaY7if8dVZ0hIrcCyar6XyKyVlWnRyrYlizxh0dVOXbsbfbufZSysj/h91eTkTGHvLxbGDr06gEzdXSk7Dq6K1At9I8d/+BI9REAZuTOCDQSzxk1J+rVQnv2NFULvfgiVFQ0vZeTA6NGuUJh+HD3CPU8O9sakfuj7iT+tcBXcH3ub1TVTSKyUVWjNi2zJf7Oq6s7zL59T1JS8hgnTmwlIWEII0Z8gby8m0hOHt/b4fV5Df4G1pSuCdwNrNqzinp/PakJqc2qhU7JOSWq1UI//KGbfcDvd9U+M2a45L5/v+tOun8/1IWopI2Pdw3J7RUOwYWEVSn1Dd1J/OcC/w68qaoPiMg44DZV/XpkQm3NEn/Xqfo5cuQVSkoe5eDBZ4AGsrIuZuTIW8jOvhSfz9Yh7AkVNRWs2LkiUBBsPbwVgFEZowKFwIVjLyQnJSeicbRcnH758qZ1isFNOnf0aFMhEFwgtHzeXiHRWCi0LCRavrZCondZrx5DTc1eSkt/S0nJQmprSxg0aBS5uQvIzf3SgJkhNFo+OPJBoFpo+QfLOVp9FEEozCsMFARn5Z9FYlxij5971arWi9N3hSocOdJ+4RD8vL6+9WckJDTdSXRU3ZSVZYVET+vOFf/JuCv+AoKmcVbVC3o4xjZZ4u9Zfn89hw49R0nJoxw5sgyReIYMuYq8vFsYPHiudQntYfX+eopLigN3A2/teYsGbSAtMY3zC84PFAQTsif02e/e728qJDoqKA4caLuQaOvOoeXzwYOtkAhHdxL/euAx3PTKDY3bVXVNTwfZFkv8kVNVtZWSkt+wb9/vqa8/TErKRPLybmb48OtJSBjc2+H1S+XV5by689VAQbD9yHYAxmSOCRQCF4y9gOzk6CzKEW2NhUS41U0NDa0/IzHR3Ul0dBcxfPjALiS61Z1TVc+IWGRhsMQfeQ0NJygr+wslJY9SUfEWPl8yw4ZdQ17ezWRkzOzt8Pq17Ye3N6sWqqipwCc+ZubNDBQEs0bOIiFu4E3U5/fD4cPhVTcdONB2IRHOXcTw4ZCZ2b8Kie4k/nuBA7j59AMLpqjq4R6OsU2W+KPr2LF1lJQ8yv79T+H3V5KWdgYjR97CsGHX2FoBEVbvr6dobxEvb3+ZpduXsnrvavzqJz0xnQvGXhAoCMZnje+z1UKR4vfDoUPhVTeVlYUuJAYNCr+6KSMj9guJ7iT+D0JsVlUd11PBdcQSf++ory9n//7/Ye/eR6mq2kRcXCYjRlxPXt4tpKZO7O3wBoSj1Ud55YNXWLp9KS9vf5mdR3cCMHbw2GbVQoOTXLVcJBan748aC4lwqpsOHAi9hkJjIRFOdVNvFRJdSvzipn+crapvRjK4jlji712qSnn5G95aAUu8tQLmkpf3lQG9VkC0qSrbj2wPtA288sErHKs9hk98zBo5i9y0XF7Y+gI1DU0rmaYkpLDw8oWW/LuhoSH8QqKsLHQhkZQUfnVTenpTIdHdHlrdueJfpard6BTWfZb4Y0dt7QFKS39HaelvqK7eaWsF9KK6hjpW710dKAhW710dcr/RGaPZ9c2+vWZ1X9HQAFx4heAAAB8xSURBVAcPhtcmUVbmusy2lJTkCoGUFHjfW4hv0KDWYzLC0Z3E/31gA/C3cNbXjQRL/LHHrRXwMiUlj3Lo0AvYWgG9z/d9H0ro/6Jnjzqbs0edzZxRc5g9anbUp502rdXXNxUSoQqHt96C7a7DF3FxcN99cNddnTtHdxL/MSAV15XzBG7lLFXVjM6F0HWW+GNbdfUuSkoWUlr626C1Am7y1gqI7gRmA1lbi9NnJGZw6rBTWVO6htqGWgAmZE9gzqg5zBk1h7NHnc2koZPwWWEdUzoahR2OqI/c9dbsfR0YhBv4tURVvyciY4HFQDbwDnCdqta291mW+PsGv7+WgwefZu/eRykvf83WCoiypzY+xYLnFlBVVxXYFlzHX11fzTul7/Dmh2+ycs9K3vzwTcqq3ET/mYMymT1qduCu4MyRZ5KWmNZbv4rx9GYdv+AtuK6q94nIKCBXVd8O47hUVT3urdn7BvAN4Fu4aqPFIvIYsF5VH23vsyzx9z2Vle95awUssrUCoqgzvXoaG4tX7l7Jyt0reXP3m2w6sAlFiZM4Th9xOnPyvbuC0WczKmOUFd59THcS/6OAH7hAVSeJSBawVFXDHtUjIim4xH8L8AIwQlXrRWQ2cK+qXtze8Zb4+66Ghkr27/9fWyugjzhafZTVe1bz5u43Wbl7JW/teYvKukrArUPQWDU0Z9Qcpo2YNiAHlfUlPTEff2AOfhFZr6qnh3HSONxUDycBjwA/Ad5S1ZO890fhVvM6LcSxC4AFAKNHjz5j1y7rldCX2VoBfVO9v56N+ze6uwKveqixHSE5PpkzR54ZaCuYnT874rOPms7pTuJfDcwBirwCYCjuij/shVhEZDBu5O89wO9bJP4XO5rb3674+5eWawXEx+eQm/tFWyugj9hbsZdVe1YF2greKX2Her+bdW3ikInMyXdVQ3NGzYn6egSmue4k/muBTwMzgEXA1cB3VfXPnQzge0AVcAdW1WMIf62AmppS3nvvM0ye/CebPjoGVdVVUVxSHGgnWLl7ZWDR+uzkbHdH4LUVzBw5k5QEm/YjWrrVq0dEJgIX4rpyLlfVzWEcMxSoU9WjIpIMLAUeAK4H/hrUuLtBVX/d3mdZ4u//3FoBT3hrBexl0KD8wFoBO3feR2npb8jLu5mTT36kt0M1HVBV/nXoX4FCYOXulWw+6FJGvC+e6SOmN2srGJkxspcj7r+6c8X/B1W9rqNtIY6birtDiAN8wJ9V9QfeCl6N3TnXAp9T1Zq2P8kS/0Di1gp43lsrYCnun48Cfny+JGbN+sCu+vugQ1WHeGvPW4G7grf3vs2J+hMAjM4cHSgE5oyaw9ThU4m3leF6RLcbd4NexwEbVXVyz4cZmiX+gamqahubNl1NZeX6wLa4uEyGDLmc9PRC0tNnkpY2zWYM7YPqGupYv399szEFe4/tBSA1IZVZ+bMCbQVn5Z8VmITOdE6nE7+I3AV8G0jG1c2Dq+qpBR5X1TsjFGsrlvgHppqaUlavHoffXx201UdCwlDq6vZ7r+NITT01UBCkpxeSljYVn6/nlzQ0kfVh+YfNxhSs37eeBm1AECYPndzsruCk7JOs0TgM3bni/5GqdnKGiJ5liX9g2rLlK+zb9wTBA7tFEsnN/RJjxtzNsWPF3qOIiooi6usPBfZJS5saKAjS02eSkjLJFpbvY47XHqdob1GgrWDVnlUcrT4KwNCUoc2mnDgj7wyS4q1LcEvdSfzLVfXCjrZFkiX+gamoaDqVletabU9NncbMmWubbVNVqqt3BQqCxkKhoaECAJ8vhbS06aSnF5KR4QqE5OQJNplcH+JXP5vLNjcbU7D18FYAEnwJnJF3RrO7ghFp1hbUlaqeJNzkbK8Ac3HVPAAZuEFXkyITamuW+E1XqPo5cWJboCCoqCji+PF38Ptdo2JcXAbp6Wc0uzNIShpjVQh9SFllWbMxBUV7iwLrEYzLGhfoSnr26LM5deipxPniejni6OpK4v8GcBuQB+ylKfFX4Or4fxWhWFuxxG96it9fT1XV5mZ3BsePrw9UJyUkDPEKgaY2g0GD8no5ahOu2oZa3il9p1lbwb7j+wBIT0znrPyzAncFs/JnkTEoapMM94ruVPXcqqq/jFhkYbDEbyLJ76+hsvJdKiqKAgVCZeUm3EzkkJiY16wgSE8vJDFxSO8GbcKiquw8urPZ4LKNBzbiVz8+8TFl2JRmbQUFgwv61R1fdwdwnQZMBgKtJ6r63z0aYTss8Ztoa2io4vjxdc2qiU6c2BJ4PympoFlBkJ5+BvHxmb0YsQlXRU0Fq/esDrQVrNq9imO1xwAYkTai2eCyGbkzSIzruz3EunPF/z1cHf9k4EXgo8Abqnp1BOIMyRK/iQX19RUcO7amWTVRdfUHgfeTk08OFAYZGTNJS5tuYwz6gAZ/A5vKNjW7K9hxZAcAg+IGMXPkzMCUE3NGzWFoat9ZXKg7iX8jcDqwVlVPF5HhwG9V9fLIhNqaJX4Tq2prD3L8+Jpm1US1tSXeuz5vjMHMoAFnU/D5BvVqzKZj+47vC7QTrNy9kuKSYur8dUDT6mWNdwWxvHpZdxL/26p6poisAc4HjgHvquqpkQm1NUv8pi+pqSlpZ4xBAmlppzdrQE5JmWxjDGJcdX01a0rWNJt/qHH1ssFJg5mdPztwRxBLq5d1J/H/GjeC9zPA7cBxYJ2qfiESgYZiid/0ZR2PMUgOjDFovDtISTnZxhjEMFVl2+FtTXcFe1aGXL2scXrq0ZmjeyXOHllzV0QKgAxV3dBzoXXMEr/pb8IfY9BUGCQl9a8eJ/3N0eqjvLXnrcCYgtV7VgdWL8vPyG82puD04adHZfWy7vbq+QTwEdw0iW+o6tM9H2LbLPGbgaCjMQbx8TmBKqLG0ceDBrWe0tjWL4gN9f56Nuzf0KytoOXqZY3tBLNHzSY7ObvZ8Z1ZP7kt3a3qOQn4o7fp08B2Vf1qpyLoBkv8ZqDqeIxBbosxBjP54IN7bP2CGLWnYg+rdq8KtBWs3be22epljQXB4ROH+d6K71FVVxU4NiUhhYWXL+xU8u9O4t8EnKbejuIqHjda464xvaOjMQZukL0CcQwffh2JicOIi0vzHqlBz5u/9vlSvZ+DrEopSqrqqijaWxRoJwhevSyUMZlj2HnbzrA/v63EH05Xgi3AaKBxtfNRQFTr+I0xTeLiUsjMnENm5pzAtsYxBjt2fJtjx97GJf4GDhxwN+odrHXU8gwtCojQzxsLivb2CX4ukmgFSgspCSmcV3Ae5xWcB7iJ6P516F9MeiT0VGgfln/YI+cNJ/HnAJtF5G3v9UxglYg8C6CqV/RIJMaYLouPzyAlZaI3m6k/sF3Ex6xZO0hIyKGhoRK/v5KGhuPeo+PnwfvX1R2kunpns32Cp8zuWFynCopwC5b+VKD4xMfEIRMZkzkm0B4QrKd6B4WT+O/pygeLyCjgv4ERuH+JC1X1FyJyL/BloMzb9duq+mJXzmGMabJz532o+pttU21g1677OPnkR/D5BgM9u5KV31/XotA43unCpa6ujOrqD4K2H0O1PuwYROK7dAfS0f69uZjP/Rfez4LnFpAkVXx3EvzgPaghhfsvvL9HPr/DxK+qr3Xxs+uB21X1HRFJB9aIyDLvvZ+r6k+7+LnGmBAqKla1ugJXraW8fGXEzunzJeDzDSYhoacLlNqw7kLaK1hqa/fT0LC92f6dK1ASulW11db+Pl/H3TgbG3Df33IzUzOP89WT05h4ymOd7tXTlogNF1TVUqDUe35MRDYDrfueGWN6RMvFafoyny8Rny+RhISsHv1cV6CEX70Vap/a2tJW7zX2sgqHK1A6LijOTIL8odWowrxhDcw6uefWvorKOHF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+      "text/plain": "<Figure size 432x288 with 1 Axes>"
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# For graph 2\n",
+    "gs = []\n",
+    "us = [1, 0.7, 0.5, 0.1]\n",
+    "pers = [[0.2, 0.3, 0.5, 0.7, 1] for _ in range(len(us))]\n",
+    "counts = [[0, 0, 0, 0, 0] for _ in range(len(us))]\n",
+    "\n",
+    "for u in us:\n",
+    "    gs.append(get_supports(0.7, u))\n",
+    "\n",
+    "for i in range(4):\n",
+    "    for j in range(5):\n",
+    "        percent = pers[i][j]/100\n",
+    "        for k in gs[i]:\n",
+    "            if k > percent:\n",
+    "                counts[i][j] += 1\n",
+    "\n",
+    "plt_graphs(pers, counts, labels=[\"u 1\", \"u 0.7\", \"u 0.5\", \"u 0.1\"], colors=[\"b\", \"g\", \"y\", \"r\"], markers=['.', 'o', '^', \">\"], x_label=\"Support threshold (%)\", y_label= \"Number of patterns (k)\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": "<Figure size 432x288 with 1 Axes>"
+     },
+     "metadata": {
+      "needs_background": "light"
+     },
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# For graph 3\n",
+    "gs = []\n",
+    "WF = [1, 2, 3]\n",
+    "dels = [[0.3, 0.5, 0.7, 0.9] for _ in range(3)]\n",
+    "counts = [[0, 0, 0, 0] for _ in range(3)]\n",
+    "for wf in WF:\n",
+    "    for dl in dels[0]:\n",
+    "        gs.append(get_supports(dl, 0.5, wf))\n",
+    "\n",
+    "for i in range(3):\n",
+    "    for j in range(4):\n",
+    "        for k in gs[4*i + j]:\n",
+    "            if k > 0.003:\n",
+    "                counts[i][j] += 1\n",
+    "\n",
+    "plt_graphs(dels, counts, labels=[\"WF_1\", \"WF_2\", \"WF_3\"], colors=[\"b\", \"g\", \"r\"], markers=['.', 'o', '^'], x_label=\"delta\", y_label= \"Number of patterns (k)\")"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.6.5"
+  },
+  "pycharm": {
+   "stem_cell": {
+    "cell_type": "raw",
+    "source": [],
+    "metadata": {
+     "collapsed": false
+    }
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
\ No newline at end of file
diff --git a/DWDM_dataset_Extraction.py b/DWDM_dataset_Extraction.py
new file mode 100644
index 0000000..3c35170
--- /dev/null
+++ b/DWDM_dataset_Extraction.py
@@ -0,0 +1,108 @@
+# create database
+
+# database = dict()
+# database['sid']=[10,20,30,40]
+# database['sequence']=[['a','abc','ac','d'],['ad','c','bc','ae'],['ad','bc','df'],['a','abc','d']]
+# database['timestamp']=[[0,1,2,3],[1,2,3,4],[1,3,5],[2,3,4]]
+#
+# database['10'] = [['a', 0], ['abc', 1], ['ac', 2], ['d', 3]]
+# database['20'] = [['ad', 1], ['c', 2], ['bc', 3], ['ae', 4]]
+# database['30'] = [['ad', 1], ['bc', 3], ['df', 5]]
+# database['cd40'] = [['a', 2], ['abc', 3], ['d', 4]]
+#
+# # print database
+#
+# for i in database.keys():
+# 	print(i, end=' ')
+# 	for j in database[i]:
+# 		print(j[0], end=' ')
+# 	for j in database[i]:
+# 		print(j[1], end=' ')
+# 	print()
+
+import random
+
+# lower = 111; upper = 999
+# random_float = random.uniform(lower, upper)
+# print(random_float)
+def Randlist(start, end, num):
+	res = []
+
+	for j in range(num):
+		val=(random.uniform(start, end))
+	#	val=int(val)
+		res.append(val)
+
+	res.sort()
+	return res
+
+
+text_file= open("sample.data","r")
+lines= text_file.readlines()
+# line1= lines[0]
+undelted_lines= lines
+print("\nInput :\n")
+print(lines)
+x = dict()
+for i in range(len(lines)):
+	line1 = list(lines[i].split(" "))
+	# print(line1)
+	line1.pop()
+	length = int(line1[0])
+	# print(length)
+	line1.pop(0)
+	# x= dict()
+	# print(line1)
+	lst = []
+
+	for j in range(length):
+		sizeoflistoftime= int(line1[0])
+		# print(sizeoflistoftime)
+		line1.pop(0)
+		# print(line1)
+
+		listoftime=Randlist(0,1000,sizeoflistoftime)
+		for k in range(sizeoflistoftime):
+			line1.pop(0)
+		# print(listoftime)
+
+		lst.append(listoftime)
+	# print("The list is :")
+	# print(lst)
+	x[i]=lst
+
+
+# print(x)
+
+# print(undelted_lines)
+x2= dict()
+
+for i in range(len(undelted_lines)):
+	line1 = list(undelted_lines[i].split(" "))
+	# print(line1)
+	line1.pop()
+	length = int(line1[0])
+	# print(length)
+	line1.pop(0)
+	# print(line1)
+	listoftime=[]
+	for j in range(length):
+		sizeoflistoftime= int(line1[0])
+		# print(sizeoflistoftime)
+		line1.pop(0)
+		# print(line1)
+		temp=""
+		# listoftime=Randlist(0,1000,sizeoflistoftime)
+		for k in range(sizeoflistoftime):
+			temp=temp+line1[0]
+			line1.pop(0)
+
+
+		listoftime.append(temp)
+	# print(listoftime)
+	x2[i]=listoftime
+
+print("\n\nTime stamp\n")
+print(x)
+print("\n\nSequence\n")
+print(x2)
\ No newline at end of file
diff --git a/Datasets/eighty.data b/Datasets/eighty.data
new file mode 100644
index 0000000..d95ff2f
--- /dev/null
+++ b/Datasets/eighty.data
@@ -0,0 +1,77 @@
+9 1 2479 2 2154 5477 4 440 2276 6036 9838 4 6639 7926 9054 9748 1 1247 1 1992 1 2535 3 5095 7744 9337 6 2343 4737 7188 8518 9241 9486 
+9 3 765 1542 7203 3 5854 7309 8827 1 5993 4 991 4956 6376 7993 3 606 1798 8964 3 606 1091 2787 2 4023 5242 3 2451 6392 8259 5 703 3355 5892 7169 9239 
+6 1 9033 3 1845 7713 8778 3 1285 1705 7890 3 4049 6908 7443 2 765 1739 2 3627 9693 
+1 2 269 4701 
+2 2 6273 7655 1 2654 
+6 1 149 2 3533 9471 1 5758 1 1491 1 5024 1 3812 
+8 3 3404 4764 6487 3 5210 7637 7771 3 1405 5501 9708 3 3572 3875 7705 3 2709 4167 5713 7 886 2870 6918 7963 8571 9125 9795 2 723 6970 2 625 5975 
+4 1 7851 1 2053 2 5826 8595 1 1734 
+6 2 7213 7771 1 5510 2 4652 9373 1 9928 2 6771 7774 2 3113 8769 
+5 2 765 6075 1 5735 1 3541 1 2715 1 2104 
+3 1 1956 1 7093 2 298 2017 
+7 1 3297 3 5577 5612 8526 3 3337 3692 8210 2 3279 8497 2 6052 7708 1 1258 1 6150 
+9 1 4632 3 7612 8099 9393 4 1327 2055 5783 7642 5 4581 5060 6055 6901 8900 1 116 3 1510 3768 4435 1 140 4 4464 4664 6228 8283 3 2575 4565 6039 
+8 7 2123 3096 3235 5029 8444 8567 8708 3 5550 5553 8445 4 3560 4804 7879 8034 2 4204 9124 4 327 3315 7615 7832 5 959 3023 6318 7616 8665 4 157 646 5661 8723 4 46 2051 2729 6037 
+10 3 5869 5872 8093 2 312 4650 2 5783 6558 1 6116 3 494 2540 6711 1 3278 2 5193 5852 3 1917 4144 4474 4 1788 3629 4386 9542 4 2958 6708 7960 8983 
+8 2 148 689 2 8663 9840 2 5675 7421 3 281 4646 5886 1 7924 3 1186 3023 7960 1 876 1 9731 
+11 1 6201 1 3928 2 1345 4035 2 3811 9780 4 2177 5436 6150 7741 2 1710 8789 2 3708 6654 1 2702 2 3400 6061 4 2343 4627 4737 9487 1 4861 
+4 1 1483 1 7835 1 8185 1 7218 
+13 1 2217 3 5116 7988 9601 1 7211 3 1146 5819 9517 1 5724 1 611 1 9715 3 3441 8566 9551 2 7953 8373 2 1714 2410 1 9916 2 4149 7187 3 767 2285 3023 
+7 2 617 9118 1 8204 3 1258 3825 7991 2 9387 9928 3 1504 6771 9845 2 8 381 1 7960 
+6 4 2431 6365 9355 9567 1 4548 2 3592 4688 2 5309 6481 2 1805 3691 3 70 3613 4895 
+7 1 5089 2 4177 7067 1 1051 2 3973 8280 3 1323 3697 9049 1 5982 2 3812 9296 
+14 3 764 5329 5899 2 3386 6186 4 3342 5945 9075 9293 3 3143 5937 6944 3 2756 3331 4049 2 6034 9023 2 1098 5561 3 2375 8785 9983 5 1367 3927 4549 8724 9799 2 1279 5759 2 6376 7759 2 715 9674 2 765 2155 4 1521 3162 6392 8381 
+6 3 3819 7192 9827 2 2547 2839 1 6529 3 3473 5357 7927 3 33 2341 5907 1 6537 
+10 6 3428 3592 8911 9195 9238 9752 7 666 1767 4316 5598 7472 8404 9841 4 449 3923 5089 5535 4 1040 2634 5728 6674 3 173 1638 6305 4 647 4838 4901 6712 5 1464 5591 5710 7379 8258 3 2573 5777 8303 5 743 814 3586 4274 6773 5 70 3117 3125 4375 5689 
+11 2 1060 6944 4 281 2991 6775 9198 5 188 1829 5649 5724 9114 2 3927 7455 4 1190 1513 3122 7450 4 619 1759 5779 7721 3 827 4252 7786 3 1566 3154 3342 5 562 1074 1386 5470 8625 3 365 6337 6672 3 2500 4613 4905 
+8 3 2712 6256 8279 2 4085 5280 2 5885 6534 2 1018 5171 1 6640 2 7960 8774 1 5193 1 8865 
+9 3 210 6045 8259 4 2967 3872 6147 7804 2 1779 8605 1 8457 4 1011 1038 4905 5052 3 3026 4488 9400 1 5365 4 647 2063 4642 8763 5 365 1826 2155 5278 9566 
+6 5 514 833 1127 3789 6495 3 6244 6293 9128 6 1269 3790 5216 6564 8671 8773 6 3018 3292 4213 7661 8332 8492 4 249 2874 4098 5146 3 4770 5724 7379 
+11 4 407 3874 4419 6962 4 3264 5843 6195 7269 6 91 145 276 6063 8096 9556 4 3795 3927 5199 8698 6 1704 3195 3461 4282 6503 7962 2 6317 8440 1 3559 2 1991 7101 7 8 738 3910 4626 4895 7524 8356 3 1146 3334 5199 3 62 4828 7516 
+5 2 7146 7354 1 1610 1 3781 1 5478 1 2191 
+9 2 2991 9841 2 2123 8567 2 2573 8068 1 7832 3 1759 7879 8278 2 5031 5974 2 3342 5329 2 4438 7980 2 5748 6086 
+15 3 68 3696 5111 3 872 1709 8372 5 318 502 5427 5967 6990 6 1813 1985 2190 3665 3889 4751 4 881 2117 2979 9562 3 1767 4066 5907 2 1334 9952 5 1006 2938 4777 6784 9556 5 1038 2429 4905 5687 8825 2 3188 6754 3 986 1630 7313 3 841 1369 2599 5 253 5312 6084 9257 9575 3 1355 1725 4741 4 7827 8126 9482 9845 
+5 2 7389 9657 2 2991 6225 2 1387 7938 1 2636 1 3696 
+13 7 1367 2233 3099 5502 5854 8827 9184 5 244 4135 4464 7715 9863 5 2997 6393 7145 7804 9842 4 1500 5278 7309 7669 7 751 5851 6179 8052 8732 8990 9916 2 3064 5877 5 899 1339 1746 2019 3922 3 7867 9100 9475 8 430 767 1274 4654 6397 6513 7826 8512 5 2051 2769 3718 4333 6355 6 5964 6657 7293 7342 7985 9867 4 872 1338 6043 7909 6 624 3130 3270 3600 5889 9928 
+5 3 1269 1692 8512 2 5759 8540 1 8578 3 1629 6286 7124 2 1216 8573 
+5 1 551 2 1507 7615 3 2250 3045 9363 3 447 710 9982 2 4552 7920 
+11 3 1724 7594 7696 3 1620 2928 6195 1 962 3 4588 5693 8785 1 2980 2 510 7510 3 2 6640 7537 4 469 2731 3879 6513 2 4555 6032 3 1404 5697 6106 2 744 5322 
+16 2 2967 6147 4 1490 3010 7744 8303 1 1255 3 1011 4115 4459 2 4135 7613 1 3467 1 6711 2 1537 6643 2 3629 9542 1 6734 2 2132 7396 3 4508 5573 9488 2 3246 7317 2 3711 7635 1 4876 2 3812 9296 
+10 2 5835 6804 2 5650 8723 1 7080 2 4246 8760 2 341 1805 4 827 3300 4976 7473 2 3771 4432 3 467 2485 6353 2 1067 4047 2 4056 5461 
+10 2 3134 9119 3 4533 5261 5619 3 198 2988 6879 3 5559 6356 7534 3 3577 8032 9614 2 1669 7090 1 4001 2 6084 7220 2 7698 9662 1 229 
+10 1 2963 5 1065 3331 4897 8285 8618 4 467 1304 2272 5479 4 127 5162 5308 7572 4 3093 3284 3627 7406 5 414 2065 6668 6914 9300 5 138 735 3345 4197 4594 4 2117 4085 5679 6508 4 45 1199 2654 9845 5 1816 2393 2977 7938 8080 
+7 2 6962 9448 1 3726 2 8096 9556 1 1981 2 3927 5321 3 1704 2424 3461 3 3398 3559 6241 
+6 1 7705 1 744 1 70 1 75 2 9705 9978 1 5270 
+5 3 3491 3572 6810 3 1844 4570 9402 2 1339 5096 1 1801 1 1397 
+13 3 6495 7101 8273 2 6228 8341 6 2505 2998 3212 5449 6131 7455 4 1312 3351 4098 7101 3 3790 4922 7375 4 4213 4654 5110 6771 8 1334 2031 2375 7227 7622 7708 8905 9463 4 5893 6092 8672 8837 4 681 1537 2082 3491 5 163 414 2182 3390 9229 8 138 272 3093 3279 4372 7455 8578 9062 5 117 293 1781 5893 8274 4 1563 5605 6879 7958 
+12 5 1279 1792 3467 3986 9728 4 684 1397 1591 4953 3 7548 7823 8375 4 1917 5004 6119 8436 4 1831 2817 3851 5928 6 946 1338 2774 4386 5605 9764 3 2264 6150 7671 4 6918 7796 9288 9591 4 57 1345 4497 6725 4 1079 1491 2117 6804 6 303 2880 6228 8026 8181 8672 4 1005 2211 5499 7353 
+7 2 6758 7101 2 2512 2998 4 1880 2880 3279 7930 2 3576 3661 3 3338 6614 8905 2 1844 2155 2 8274 8783 
+6 3 6674 9287 9623 2 6761 7192 4 3315 4328 9193 9627 6 27 2395 3204 4534 6840 7926 1 6220 2 6804 9066 
+8 1 9527 2 7440 7845 1 4908 2 1998 7269 1 1816 2 6092 8169 1 4477 1 6749 
+10 6 1979 2421 6315 7594 7598 9913 6 212 294 845 3122 3934 7031 7 155 1276 2066 4737 4871 5024 9461 3 966 4961 7528 5 745 2164 3282 3668 5862 5 3022 3298 3341 5938 6045 5 271 1813 3226 3826 4929 6 1327 2052 4168 6924 8196 9532 4 116 2961 5787 6640 5 265 687 5729 7189 8488 
+7 2 207 8595 3 2431 9355 9567 2 606 6960 2 265 8447 2 1304 2424 1 3613 1 8279 
+16 2 6011 9364 3 3134 9119 9548 3 1337 5271 9752 2 1767 9695 1 4901 2 4905 8982 2 6499 7175 1 3577 1 4001 4 1301 1491 2903 3441 1 6919 2 3281 7220 1 6042 2 4419 9662 1 70 1 9054 
+6 1 874 1 9934 1 3984 1 8285 1 1877 1 5471 
+2 1 1362 1 8404 
+11 5 1345 2766 7696 8617 9511 5 2967 4734 5826 6147 6195 9 542 1011 1859 3066 3134 4773 6241 8605 9119 5 2980 4463 6886 7136 9000 4 1150 5311 6743 8788 5 872 2181 4533 6225 7510 8 365 2071 3289 3577 3708 5422 6654 7771 4 2 1867 4001 9889 5 1828 3899 6106 6818 7123 3 5935 7392 9153 6 34 1294 4469 5378 6718 7220 
+11 1 7203 1 3461 3 139 4423 9448 3 1709 3726 7653 2 229 4181 3 2451 3665 5321 3 2424 5309 8825 1 3355 1 790 1 7827 1 6241 
+13 5 619 3592 4202 6782 7986 7 430 1146 1798 6111 6674 7183 9517 5 304 1880 4252 8279 8732 4 2370 6042 9170 9431 5 6376 6771 8274 8289 9043 5 3338 3835 6437 6795 7396 3 1609 4669 6775 7 44 1714 2410 6629 7560 8351 8440 7 1018 1092 1731 1991 4664 5171 6474 8 188 1504 1806 1954 7192 8902 9852 9916 10 183 210 548 738 1234 3551 4149 5924 8393 9954 5 2073 2658 5226 5724 7443 3 2285 5249 6953 
+7 4 606 2766 5441 7145 7 1638 3188 3606 4024 4626 6531 9668 5 3311 4296 5373 7170 7823 5 1274 7098 7683 8071 9836 5 950 7146 7420 7721 9613 8 1918 1930 3680 3889 4751 5928 6899 7002 5 3334 4876 5366 5479 7379 
+4 1 5511 1 1023 1 8534 1 3342 
+10 2 6178 6961 2 6516 8685 2 6883 7406 2 269 5350 1 5088 3 1868 2254 5825 3 662 1630 7379 2 6353 9593 2 397 8944 1 6742 
+8 2 3018 4900 4 198 2072 2988 7721 2 1801 9195 5 2815 7774 8015 9044 9229 8 645 1920 4372 4876 5562 7876 8764 9338 3 1146 2361 5437 3 2956 3039 4469 3 1669 5893 7316 
+13 1 3212 1 5317 2 645 9338 1 8498 2 3039 3278 3 1290 4578 5783 3 681 4734 6626 1 3066 2 163 476 1 4463 3 272 1828 2890 3 727 5343 8982 1 6045 
+6 1 8384 2 61 7285 1 2797 1 9950 1 8181 1 1187 
+12 4 2077 2132 3667 6365 4 173 3364 3491 4688 5 1186 1453 3270 7189 8911 3 7597 8261 9954 2 1970 5098 4 651 1743 5886 6261 2 4033 4603 5 3277 4135 6075 7421 9574 4 3592 6910 7354 7528 3 3405 4665 5993 6 3916 5309 7210 7993 9780 9897 4 1662 1805 5991 6750 
+15 1 5483 2 1861 8069 2 2800 6344 1 3337 2 147 9377 2 269 7167 1 5622 3 5 7099 8074 4 1038 1526 4905 8199 2 1938 7121 3 5436 8351 8816 2 6201 8636 3 3835 8896 9034 1 5812 3 5079 7138 7457 
+6 2 5354 9363 3 242 9916 9943 2 4971 8444 4 4177 7982 9522 9559 1 173 1 8053 
+7 4 5854 6516 7528 8723 3 269 5350 5800 3 1845 8887 9128 3 4463 5094 6144 1 397 3 5479 6742 9637 3 4432 4905 8479 
+12 3 3404 4636 9023 2 1092 1731 2 681 3706 2 2234 6399 1 2487 3 3029 3572 5177 1 6186 3 1127 2709 9407 5 886 3772 6564 8773 8790 2 6970 7989 2 2731 6235 1 2447 
+11 3 1954 8381 9364 2 2594 8727 2 3080 9269 3 2713 6512 9548 5 1692 3433 6134 8356 8669 2 1898 9204 4 5645 7124 7372 7972 3 2154 2741 5271 2 1566 1759 3 2779 3080 4630 1 1504 
+8 7 1187 2683 6174 7805 8947 9250 9843 4 2726 3736 4256 8356 4 466 1665 3023 6318 4 4093 7099 7774 9987 5 210 1663 4734 8929 9287 2 306 4449 3 927 8731 8822 6 1938 2232 3613 4665 8145 8515 
+6 2 3466 7616 2 2871 5998 2 5319 6495 1 1463 3 2494 4336 7868 2 4096 5724 
+8 4 244 1956 4060 9060 2 3345 7801 1 9008 5 2267 2481 3266 6018 8293 4 624 3139 7376 9068 5 466 3278 5093 5284 8735 2 1687 8906 3 1187 4517 9722 
+7 2 267 440 4 1724 1767 2580 8696 3 127 161 3022 7 4649 5938 6376 6804 7759 8515 8901 2 6822 7379 3 1879 7926 8731 5 3639 4145 4650 5193 5380 
+7 1 3004 6 448 2123 4112 4167 7736 8567 4 1822 3293 6662 8285 5 6044 6392 7879 7971 9195 8 313 906 1268 2512 3587 8691 8816 9790 6 3130 6040 6488 7435 7472 7855 5 3039 3066 6326 9463 9841 
+7 1 5282 1 7077 1 7101 1 2998 3 2837 4922 7375 2 1257 8905 2 8274 9469 
+9 2 3732 7810 3 4920 5934 8488 2 1798 8964 1 7905 2 765 6662 1 237 2 3845 4177 1 7406 1 9739 
diff --git a/Datasets/eighty.pat b/Datasets/eighty.pat
new file mode 100644
index 0000000..8544aec
--- /dev/null
+++ b/Datasets/eighty.pat
@@ -0,0 +1,19 @@
+Number of customers in database = 80
+Average sequence length = 10
+Average transaction length = 2.5
+Number of items = 10000
+Repetition-level = 0
+Variation in repetition-level = 0.1
+Large Itemsets:
+	Number of patterns = 25000
+	Average length of pattern = 1.25
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+Large Sequences:
+	Number of patterns = 5000
+	Average length of pattern = 4
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+
diff --git a/Datasets/fourty.data b/Datasets/fourty.data
new file mode 100644
index 0000000..c6cbf6f
--- /dev/null
+++ b/Datasets/fourty.data
@@ -0,0 +1,39 @@
+9 1 2479 2 2154 5477 4 440 2276 6036 9838 4 6639 7926 9054 9748 1 1247 1 1992 1 2535 3 5095 7744 9337 6 2343 4737 7188 8518 9241 9486 
+9 3 765 1542 7203 3 5854 7309 8827 1 5993 4 991 4956 6376 7993 3 606 1798 8964 3 606 1091 2787 2 4023 5242 3 2451 6392 8259 5 703 3355 5892 7169 9239 
+6 1 9033 3 1845 7713 8778 3 1285 1705 7890 3 4049 6908 7443 2 765 1739 2 3627 9693 
+1 2 269 4701 
+2 2 6273 7655 1 2654 
+6 1 149 2 3533 9471 1 5758 1 1491 1 5024 1 3812 
+8 3 3404 4764 6487 3 5210 7637 7771 3 1405 5501 9708 3 3572 3875 7705 3 2709 4167 5713 7 886 2870 6918 7963 8571 9125 9795 2 723 6970 2 625 5975 
+4 1 7851 1 2053 2 5826 8595 1 1734 
+6 2 7213 7771 1 5510 2 4652 9373 1 9928 2 6771 7774 2 3113 8769 
+5 2 765 6075 1 5735 1 3541 1 2715 1 2104 
+3 1 1956 1 7093 2 298 2017 
+7 1 3297 3 5577 5612 8526 3 3337 3692 8210 2 3279 8497 2 6052 7708 1 1258 1 6150 
+9 1 4632 3 7612 8099 9393 4 1327 2055 5783 7642 5 4581 5060 6055 6901 8900 1 116 3 1510 3768 4435 1 140 4 4464 4664 6228 8283 3 2575 4565 6039 
+8 7 2123 3096 3235 5029 8444 8567 8708 3 5550 5553 8445 4 3560 4804 7879 8034 2 4204 9124 4 327 3315 7615 7832 5 959 3023 6318 7616 8665 4 157 646 5661 8723 4 46 2051 2729 6037 
+10 3 5869 5872 8093 2 312 4650 2 5783 6558 1 6116 3 494 2540 6711 1 3278 2 5193 5852 3 1917 4144 4474 4 1788 3629 4386 9542 4 2958 6708 7960 8983 
+8 2 148 689 2 8663 9840 2 5675 7421 3 281 4646 5886 1 7924 3 1186 3023 7960 1 876 1 9731 
+11 1 6201 1 3928 2 1345 4035 2 3811 9780 4 2177 5436 6150 7741 2 1710 8789 2 3708 6654 1 2702 2 3400 6061 4 2343 4627 4737 9487 1 4861 
+4 1 1483 1 7835 1 8185 1 7218 
+13 1 2217 3 5116 7988 9601 1 7211 3 1146 5819 9517 1 5724 1 611 1 9715 3 3441 8566 9551 2 7953 8373 2 1714 2410 1 9916 2 4149 7187 3 767 2285 3023 
+7 2 617 9118 1 8204 3 1258 3825 7991 2 9387 9928 3 1504 6771 9845 2 8 381 1 7960 
+6 4 2431 6365 9355 9567 1 4548 2 3592 4688 2 5309 6481 2 1805 3691 3 70 3613 4895 
+7 1 5089 2 4177 7067 1 1051 2 3973 8280 3 1323 3697 9049 1 5982 2 3812 9296 
+14 3 764 5329 5899 2 3386 6186 4 3342 5945 9075 9293 3 3143 5937 6944 3 2756 3331 4049 2 6034 9023 2 1098 5561 3 2375 8785 9983 5 1367 3927 4549 8724 9799 2 1279 5759 2 6376 7759 2 715 9674 2 765 2155 4 1521 3162 6392 8381 
+6 3 3819 7192 9827 2 2547 2839 1 6529 3 3473 5357 7927 3 33 2341 5907 1 6537 
+10 6 3428 3592 8911 9195 9238 9752 7 666 1767 4316 5598 7472 8404 9841 4 449 3923 5089 5535 4 1040 2634 5728 6674 3 173 1638 6305 4 647 4838 4901 6712 5 1464 5591 5710 7379 8258 3 2573 5777 8303 5 743 814 3586 4274 6773 5 70 3117 3125 4375 5689 
+11 2 1060 6944 4 281 2991 6775 9198 5 188 1829 5649 5724 9114 2 3927 7455 4 1190 1513 3122 7450 4 619 1759 5779 7721 3 827 4252 7786 3 1566 3154 3342 5 562 1074 1386 5470 8625 3 365 6337 6672 3 2500 4613 4905 
+8 3 2712 6256 8279 2 4085 5280 2 5885 6534 2 1018 5171 1 6640 2 7960 8774 1 5193 1 8865 
+9 3 210 6045 8259 4 2967 3872 6147 7804 2 1779 8605 1 8457 4 1011 1038 4905 5052 3 3026 4488 9400 1 5365 4 647 2063 4642 8763 5 365 1826 2155 5278 9566 
+6 5 514 833 1127 3789 6495 3 6244 6293 9128 6 1269 3790 5216 6564 8671 8773 6 3018 3292 4213 7661 8332 8492 4 249 2874 4098 5146 3 4770 5724 7379 
+11 4 407 3874 4419 6962 4 3264 5843 6195 7269 6 91 145 276 6063 8096 9556 4 3795 3927 5199 8698 6 1704 3195 3461 4282 6503 7962 2 6317 8440 1 3559 2 1991 7101 7 8 738 3910 4626 4895 7524 8356 3 1146 3334 5199 3 62 4828 7516 
+5 2 7146 7354 1 1610 1 3781 1 5478 1 2191 
+9 2 2991 9841 2 2123 8567 2 2573 8068 1 7832 3 1759 7879 8278 2 5031 5974 2 3342 5329 2 4438 7980 2 5748 6086 
+15 3 68 3696 5111 3 872 1709 8372 5 318 502 5427 5967 6990 6 1813 1985 2190 3665 3889 4751 4 881 2117 2979 9562 3 1767 4066 5907 2 1334 9952 5 1006 2938 4777 6784 9556 5 1038 2429 4905 5687 8825 2 3188 6754 3 986 1630 7313 3 841 1369 2599 5 253 5312 6084 9257 9575 3 1355 1725 4741 4 7827 8126 9482 9845 
+5 2 7389 9657 2 2991 6225 2 1387 7938 1 2636 1 3696 
+13 7 1367 2233 3099 5502 5854 8827 9184 5 244 4135 4464 7715 9863 5 2997 6393 7145 7804 9842 4 1500 5278 7309 7669 7 751 5851 6179 8052 8732 8990 9916 2 3064 5877 5 899 1339 1746 2019 3922 3 7867 9100 9475 8 430 767 1274 4654 6397 6513 7826 8512 5 2051 2769 3718 4333 6355 6 5964 6657 7293 7342 7985 9867 4 872 1338 6043 7909 6 624 3130 3270 3600 5889 9928 
+5 3 1269 1692 8512 2 5759 8540 1 8578 3 1629 6286 7124 2 1216 8573 
+5 1 551 2 1507 7615 3 2250 3045 9363 3 447 710 9982 2 4552 7920 
+11 3 1724 7594 7696 3 1620 2928 6195 1 962 3 4588 5693 8785 1 2980 2 510 7510 3 2 6640 7537 4 469 2731 3879 6513 2 4555 6032 3 1404 5697 6106 2 744 5322 
+16 2 2967 6147 4 1490 3010 7744 8303 1 1255 3 1011 4115 4459 2 4135 7613 1 3467 1 6711 2 1537 6643 2 3629 9542 1 6734 2 2132 7396 3 4508 5573 9488 2 3246 7317 2 3711 7635 1 4876 2 3812 9296 
diff --git a/Datasets/fourty.pat b/Datasets/fourty.pat
new file mode 100644
index 0000000..d5d8005
--- /dev/null
+++ b/Datasets/fourty.pat
@@ -0,0 +1,19 @@
+Number of customers in database = 40
+Average sequence length = 10
+Average transaction length = 2.5
+Number of items = 10000
+Repetition-level = 0
+Variation in repetition-level = 0.1
+Large Itemsets:
+	Number of patterns = 25000
+	Average length of pattern = 1.25
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+Large Sequences:
+	Number of patterns = 5000
+	Average length of pattern = 4
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+
diff --git a/Datasets/hundred.data b/Datasets/hundred.data
new file mode 100644
index 0000000..d213030
--- /dev/null
+++ b/Datasets/hundred.data
@@ -0,0 +1,97 @@
+9 1 2479 2 2154 5477 4 440 2276 6036 9838 4 6639 7926 9054 9748 1 1247 1 1992 1 2535 3 5095 7744 9337 6 2343 4737 7188 8518 9241 9486 
+9 3 765 1542 7203 3 5854 7309 8827 1 5993 4 991 4956 6376 7993 3 606 1798 8964 3 606 1091 2787 2 4023 5242 3 2451 6392 8259 5 703 3355 5892 7169 9239 
+6 1 9033 3 1845 7713 8778 3 1285 1705 7890 3 4049 6908 7443 2 765 1739 2 3627 9693 
+1 2 269 4701 
+2 2 6273 7655 1 2654 
+6 1 149 2 3533 9471 1 5758 1 1491 1 5024 1 3812 
+8 3 3404 4764 6487 3 5210 7637 7771 3 1405 5501 9708 3 3572 3875 7705 3 2709 4167 5713 7 886 2870 6918 7963 8571 9125 9795 2 723 6970 2 625 5975 
+4 1 7851 1 2053 2 5826 8595 1 1734 
+6 2 7213 7771 1 5510 2 4652 9373 1 9928 2 6771 7774 2 3113 8769 
+5 2 765 6075 1 5735 1 3541 1 2715 1 2104 
+3 1 1956 1 7093 2 298 2017 
+7 1 3297 3 5577 5612 8526 3 3337 3692 8210 2 3279 8497 2 6052 7708 1 1258 1 6150 
+9 1 4632 3 7612 8099 9393 4 1327 2055 5783 7642 5 4581 5060 6055 6901 8900 1 116 3 1510 3768 4435 1 140 4 4464 4664 6228 8283 3 2575 4565 6039 
+8 7 2123 3096 3235 5029 8444 8567 8708 3 5550 5553 8445 4 3560 4804 7879 8034 2 4204 9124 4 327 3315 7615 7832 5 959 3023 6318 7616 8665 4 157 646 5661 8723 4 46 2051 2729 6037 
+10 3 5869 5872 8093 2 312 4650 2 5783 6558 1 6116 3 494 2540 6711 1 3278 2 5193 5852 3 1917 4144 4474 4 1788 3629 4386 9542 4 2958 6708 7960 8983 
+8 2 148 689 2 8663 9840 2 5675 7421 3 281 4646 5886 1 7924 3 1186 3023 7960 1 876 1 9731 
+11 1 6201 1 3928 2 1345 4035 2 3811 9780 4 2177 5436 6150 7741 2 1710 8789 2 3708 6654 1 2702 2 3400 6061 4 2343 4627 4737 9487 1 4861 
+4 1 1483 1 7835 1 8185 1 7218 
+13 1 2217 3 5116 7988 9601 1 7211 3 1146 5819 9517 1 5724 1 611 1 9715 3 3441 8566 9551 2 7953 8373 2 1714 2410 1 9916 2 4149 7187 3 767 2285 3023 
+7 2 617 9118 1 8204 3 1258 3825 7991 2 9387 9928 3 1504 6771 9845 2 8 381 1 7960 
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diff --git a/Datasets/hundred.pat b/Datasets/hundred.pat
new file mode 100644
index 0000000..e9af54f
--- /dev/null
+++ b/Datasets/hundred.pat
@@ -0,0 +1,19 @@
+Number of customers in database = 100
+Average sequence length = 10
+Average transaction length = 2.5
+Number of items = 10000
+Repetition-level = 0
+Variation in repetition-level = 0.1
+Large Itemsets:
+	Number of patterns = 25000
+	Average length of pattern = 1.25
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+Large Sequences:
+	Number of patterns = 5000
+	Average length of pattern = 4
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+
diff --git a/Datasets/sixty.data b/Datasets/sixty.data
new file mode 100644
index 0000000..f96c83e
--- /dev/null
+++ b/Datasets/sixty.data
@@ -0,0 +1,59 @@
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+6 1 874 1 9934 1 3984 1 8285 1 1877 1 5471 
+2 1 1362 1 8404 
+11 5 1345 2766 7696 8617 9511 5 2967 4734 5826 6147 6195 9 542 1011 1859 3066 3134 4773 6241 8605 9119 5 2980 4463 6886 7136 9000 4 1150 5311 6743 8788 5 872 2181 4533 6225 7510 8 365 2071 3289 3577 3708 5422 6654 7771 4 2 1867 4001 9889 5 1828 3899 6106 6818 7123 3 5935 7392 9153 6 34 1294 4469 5378 6718 7220 
+11 1 7203 1 3461 3 139 4423 9448 3 1709 3726 7653 2 229 4181 3 2451 3665 5321 3 2424 5309 8825 1 3355 1 790 1 7827 1 6241 
+13 5 619 3592 4202 6782 7986 7 430 1146 1798 6111 6674 7183 9517 5 304 1880 4252 8279 8732 4 2370 6042 9170 9431 5 6376 6771 8274 8289 9043 5 3338 3835 6437 6795 7396 3 1609 4669 6775 7 44 1714 2410 6629 7560 8351 8440 7 1018 1092 1731 1991 4664 5171 6474 8 188 1504 1806 1954 7192 8902 9852 9916 10 183 210 548 738 1234 3551 4149 5924 8393 9954 5 2073 2658 5226 5724 7443 3 2285 5249 6953 
+7 4 606 2766 5441 7145 7 1638 3188 3606 4024 4626 6531 9668 5 3311 4296 5373 7170 7823 5 1274 7098 7683 8071 9836 5 950 7146 7420 7721 9613 8 1918 1930 3680 3889 4751 5928 6899 7002 5 3334 4876 5366 5479 7379 
diff --git a/Datasets/sixty.pat b/Datasets/sixty.pat
new file mode 100644
index 0000000..84bd12c
--- /dev/null
+++ b/Datasets/sixty.pat
@@ -0,0 +1,19 @@
+Number of customers in database = 60
+Average sequence length = 10
+Average transaction length = 2.5
+Number of items = 10000
+Repetition-level = 0
+Variation in repetition-level = 0.1
+Large Itemsets:
+	Number of patterns = 25000
+	Average length of pattern = 1.25
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+Large Sequences:
+	Number of patterns = 5000
+	Average length of pattern = 4
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+
diff --git a/Datasets/ten.data b/Datasets/ten.data
new file mode 100644
index 0000000..e0c435a
--- /dev/null
+++ b/Datasets/ten.data
@@ -0,0 +1,10 @@
+9 1 2479 2 2154 5477 4 440 2276 6036 9838 4 6639 7926 9054 9748 1 1247 1 1992 1 2535 3 5095 7744 9337 6 2343 4737 7188 8518 9241 9486 
+9 3 765 1542 7203 3 5854 7309 8827 1 5993 4 991 4956 6376 7993 3 606 1798 8964 3 606 1091 2787 2 4023 5242 3 2451 6392 8259 5 703 3355 5892 7169 9239 
+6 1 9033 3 1845 7713 8778 3 1285 1705 7890 3 4049 6908 7443 2 765 1739 2 3627 9693 
+1 2 269 4701 
+2 2 6273 7655 1 2654 
+6 1 149 2 3533 9471 1 5758 1 1491 1 5024 1 3812 
+8 3 3404 4764 6487 3 5210 7637 7771 3 1405 5501 9708 3 3572 3875 7705 3 2709 4167 5713 7 886 2870 6918 7963 8571 9125 9795 2 723 6970 2 625 5975 
+4 1 7851 1 2053 2 5826 8595 1 1734 
+6 2 7213 7771 1 5510 2 4652 9373 1 9928 2 6771 7774 2 3113 8769 
+5 2 765 6075 1 5735 1 3541 1 2715 1 2104 
diff --git a/Datasets/ten.pat b/Datasets/ten.pat
new file mode 100644
index 0000000..4a2be20
--- /dev/null
+++ b/Datasets/ten.pat
@@ -0,0 +1,19 @@
+Number of customers in database = 10
+Average sequence length = 10
+Average transaction length = 2.5
+Number of items = 10000
+Repetition-level = 0
+Variation in repetition-level = 0.1
+Large Itemsets:
+	Number of patterns = 25000
+	Average length of pattern = 1.25
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+Large Sequences:
+	Number of patterns = 5000
+	Average length of pattern = 4
+	Correlation between consecutive patterns = 0.25
+	Average confidence in a rule = 0.75
+	Variation in the confidence = 0.1
+
diff --git a/README.md b/README.md
deleted file mode 100644
index 76047a7..0000000
--- a/README.md
+++ /dev/null
@@ -1,2 +0,0 @@
-# Sequential-Pattern-mining-using-TiW
-Implementation of Sequential Pattern mining using Time interval weights
diff --git a/final.py.ipynb b/final.py.ipynb
new file mode 100644
index 0000000..c97cfef
--- /dev/null
+++ b/final.py.ipynb
@@ -0,0 +1,132 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {
+    "collapsed": true,
+    "pycharm": {
+     "name": "#%%",
+     "is_executing": false
+    }
+   },
+   "outputs": [],
+   "source": [
+    "import random\n",
+    "\n",
+    "def Randlist(start, end, num):\n",
+    "\tres = []\n",
+    "\n",
+    "\tfor j in range(num):\n",
+    "\t\tval=(random.uniform(start, end))\n",
+    "\t#\tval=int(val)\n",
+    "\t\tres.append(val)\n",
+    "\n",
+    "\tres.sort()\n",
+    "\treturn res"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "outputs": [
+    {
+     "name": "stdout",
+     "text": [
+      "\nInput :\n\n1 2 269 4701 \n\ndict_keys(['0', '1', '2', '4', '5', '6', '7', '8', '9'])\n"
+     ],
+     "output_type": "stream"
+    }
+   ],
+   "source": [
+    "text_file= open(\"sample.data\",\"r\")\n",
+    "lines= text_file.readlines()\n",
+    "undelted_lines= lines\n",
+    "print(\"\\nInput :\\n\")\n",
+    "print(lines[3])\n",
+    "x = dict()\n",
+    "for i in range(len(lines)):\n",
+    "\tline1 = list(lines[i].split(\" \"))\n",
+    "\tline1.pop()\n",
+    "\tlength = int(line1[0])\n",
+    "\tline1.pop(0)\n",
+    "\tlst = []\n",
+    "\n",
+    "\tfor j in range(length):\n",
+    "\t\tsizeoflistoftime= int(line1[0])\n",
+    "\t\tline1.pop(0)\n",
+    "\t\tlistoftime=Randlist(0,1000,1)\n",
+    "\t\tfor k in range(sizeoflistoftime):\n",
+    "\t\t\tline1.pop(0)\n",
+    "\t\tlst.append(listoftime[0])\n",
+    "\tlst.sort()\n",
+    "\tx[i]=lst[:]\n",
+    "\n",
+    "x2 = dict()\n",
+    "\n",
+    "for i in range(len(undelted_lines)):\n",
+    "\tline1 = list(undelted_lines[i].split(\" \"))\n",
+    "\tline1.pop()\n",
+    "\tlength = int(line1[0])\n",
+    "\tline1.pop(0)\n",
+    "\tlistoftime=[]\n",
+    "\tfor j in range(length):\n",
+    "\t\tsizeoflistoftime= int(line1[0])\n",
+    "\t\tline1.pop(0)\n",
+    "\t\ttemp=\"\"\n",
+    "\t\tfor k in range(sizeoflistoftime):\n",
+    "\t\t\ttemp=temp+line1[0].zfill(4)\n",
+    "\t\t\tline1.pop(0)\n",
+    "\t\tlistoftime.append(temp)\n",
+    "\tx2[i]=listoftime\n",
+    "\n",
+    "database=dict()\n",
+    "for i in x.keys():\n",
+    "    if len(x[i])>1:\n",
+    "        database[str(i)]=[]\n",
+    "        for j in range(len(x[i])):\n",
+    "            database[str(i)].append([x2[i][j],x[i][j]])\n",
+    "        \n",
+    "print(database.keys())\n",
+    "    "
+   ],
+   "metadata": {
+    "collapsed": false,
+    "pycharm": {
+     "name": "#%%s\n",
+     "is_executing": false
+    }
+   }
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  },
+  "pycharm": {
+   "stem_cell": {
+    "cell_type": "raw",
+    "source": [],
+    "metadata": {
+     "collapsed": false
+    }
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}
\ No newline at end of file
diff --git a/plotting.py b/plotting.py
new file mode 100644
index 0000000..2e6dd0f
--- /dev/null
+++ b/plotting.py
@@ -0,0 +1,25 @@
+import matplotlib.pyplot as plt
+
+def is_none(l, length):
+	if l is None:
+		return [None for ii in range(length)]
+	else:
+		assert len(l), length
+		return l
+
+# no. pattern vs threshold for delta = 0.5 0.7 0.9
+def plt_graphs(xss, yss, labels=None, colors=None, markers=None, x_label="x - axis", y_label="y - axis"):
+	l = len(xss)
+	assert l, len(yss)
+
+	labels = is_none(labels, l)
+	markers = is_none(markers, l)
+	colors = is_none(colors, l)
+
+	for ll in range(l):
+		plt.plot(xss[ll], yss[ll], label=labels[ll], color=colors[ll], marker=markers[ll])
+	plt.legend()
+	plt.show()
+
+
+plt_graphs([[1, 2]], [[2, 2]])