mnoziny.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Množiny -- set()\n",
    "\n",
    "\n",
    "Množina je **neuspořádaná** kolekce jedinečných prvků. Přidání duplicitních prvků\n",
    "je bezpečné, ale bezúčelné. Tento datový typ je **měnitelný**. Počet prvků v\n",
    "množině určíme pomocí funkce `len()`.\n",
    "\n",
    "Vytváří se pomocí složených závorek a/nebo pomocí funkce `set()`. Prázdná\n",
    "množina se vytváří výhradně pomocí funkce `set()` -- prázdné složené závorky by\n",
    "vedly k vytvoření prázdného [slovníku](#slovnky----dict)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hruska', 'jablko', 'merunka'}"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set({'jablko','hruska', 'merunka', 'jablko','merunka'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hruska', 'jablko', 'merunka'}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{'jablko','hruska', 'merunka'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "set()"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "ovoce = {'jablko','hruska', 'merunka', 'jablko','merunka'}\n",
    "zelenina=set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "set"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(ovoce)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "set"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(zelenina)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'a', 'e', 'k', 'l', 'n'}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set('alenka')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Některé metody\n",
    "\n",
    "metoda |\n",
    ":------|:-------\n",
    "`s.add(x)` | Přidá prvek `x` do množiny `s`.\n",
    "`s.update(t)` | Přidá do množiny `s` prvky z množiny `t`.\n",
    "`s.pop()` | Odstraní z množiny `s` **náhodný** prvek a vydá ho jako svou návratovou hodnotu.\n",
    "`s.remove(x)` | Odstraní z množiny `s` prvek `x`.\n",
    "`s.clear()` | Odstraní všechny prvky z množiny `s`.\n",
    "`s.copy()` | Vrátí **mělkou** kopii množiny `s`.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hruska', 'jablko', 'merunka'}"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hruska', 'jablko', 'merunka', 'tresne'}"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce.add('tresne')\n",
    "ovoce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'tresne'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'merunka'"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce.pop()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hruska', 'jablko'}"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hruska'}"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce.remove('jablko')\n",
    "ovoce"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'hruska', 'jablko', 'merunka'}"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce.update({'hruska', 'jablko', 'merunka'})\n",
    "ovoce"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Operace s množinami\n",
    "\n",
    "operace |\n",
    ":------|:-------\n",
    "`a`&nbsp;&#124;&nbsp;`b` | Sjednocení -- vrátí všechny prvky množiny `a` i `b`.\n",
    "`a`&nbsp;`&`&nbsp;`b` | Průnik -- vrátí všechny prvky společné množině `a` a `b`.\n",
    "`a`&nbsp;`-`&nbsp;`b` | Rozdíl -- vrátí množinu `a` zbavenou všech prvků, které byly obsaženy v `b`\n",
    "`a`&nbsp;`^`&nbsp;`b` | Symetrický rozdíl -- vrátí množinu obsahující prvky množiny `a` i `b`, ale bez prvků, které jsou v&nbsp;obou množinách.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A', 'C', 'I', 'K', 'N', 'O', 'V'}"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set(\"KVOCNA\") | set('NOCI')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'C', 'N', 'O'}"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set(\"KVOCNA\") & set('NOCI')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A', 'K', 'V'}"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set(\"KVOCNA\") - set('NOCI')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'A', 'I', 'K', 'V'}"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set(\"KVOCNA\") ^ set('NOCI')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Množiny lze také procházet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "merunka\n",
      "hruska\n",
      "jablko\n"
     ]
    }
   ],
   "source": [
    "ovoce = {'hruska', 'jablko', 'merunka'}\n",
    "\n",
    "for o in ovoce:\n",
    "    print(o)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pravdivostní operátory\n",
    "\n",
    "operator |\n",
    ":------|:-------\n",
    "`==` | Testuje shodnost množin\n",
    "`in` | Testuje příslušnost prvku v množině\n",
    "`a.isdisjoint(b)`  | Vrátí `True` pokud `a` a `b` nemají žádný společný prvek.\n",
    "`a`&nbsp;`<`&nbsp;`b` | `a` je podmnožinou `b`.\n",
    "`a`&nbsp;`<=`&nbsp;`b` | `a` je podmnožinou nebo ekvivalentem `b`.\n",
    "`a`&nbsp;`>`&nbsp;`b` | `a` je nadmnožinou `b`.\n",
    "`a`&nbsp;`>=`&nbsp;`b` | `a` je nadmnožinou nebo ekvivalentem `b`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{'hruska', 'jablko', 'merunka'} == {'jablko', 'merunka', 'hruska'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'merunka' in {'jablko', 'merunka', 'hruska'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'datel' in {'jablko', 'merunka', 'hruska'}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ovoce.isdisjoint({'datel', 'zeli'})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set('KOSTNI DREN') > set ('DREN')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set('KOSTNI DREN') > set ('ODRENINA')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set('KOSTNI DREN') > set ('ODRENINA')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set('KOSTNI DREN') >= set ('DREN')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set('KOSTNI DREN') >= set ('KOSTNI DREN')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "set('KOSTNI DREN') > set ('KOSTNI DREN')"
   ]
  }
 ],
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