diff --git a/algorithms/binarySearch.py b/algorithms/binarySearch.py
index 425fd77..f95efae 100644
--- a/algorithms/binarySearch.py
+++ b/algorithms/binarySearch.py
@@ -22,3 +22,21 @@ def binarySearch(sortedArray,target):
 
 a=[1,2,3,4,5,6,7,8,9,10,11,12]
 print(binarySearch(a,9))
+
+
+def search(sortedArray, v) -> bool:
+    m = len(sortedArray)
+    if m == 0:
+        return False
+    idx = m//2
+    print(f"a={sortedArray[idx]} and {sortedArray} and i:{idx}")
+    if sortedArray[idx] == v:
+        return True
+    elif sortedArray[idx] < v:
+        # search in [idx+1, m]
+        return search(sortedArray[idx+1:m],v)
+    else:
+        # search in [0, idx-1]
+        return search(sortedArray[0:idx],v)
+    
+print(search(a,9))
diff --git a/algorithms/duplicates_in.py b/algorithms/duplicates_in.py
new file mode 100644
index 0000000..99217c2
--- /dev/null
+++ b/algorithms/duplicates_in.py
@@ -0,0 +1,28 @@
+"""
+Contains Duplicate
+Given an integer array nums, return true if any value appears at least 
+twice in the array, and return false if every element is distinct.
+Input: nums = [1,2,3,1]
+Output: true
+
+Input: nums = [1,2,3,4]
+Output: false
+
+Input: nums = [1,1,1,3,3,4,3,2,4,2]
+Output: true
+"""
+
+def duplicate_in(nums)-> bool:
+    encounters = []
+    for i in nums:
+        if i not in encounters:
+            encounters.append(i)
+        else:
+            return True
+    return False
+
+assert duplicate_in([1,2,3,1])
+
+assert not duplicate_in([1,2,3,4])
+
+assert duplicate_in([1,1,1,3,3,4,3,2,4,2])
diff --git a/algorithms/max_subarray.py b/algorithms/max_subarray.py
new file mode 100644
index 0000000..1539ff2
--- /dev/null
+++ b/algorithms/max_subarray.py
@@ -0,0 +1,71 @@
+"""
+Given an integer array nums, find the 
+subarray with the largest sum, and return its sum.
+
+what is a subarray? it can be the array itself, or contiguous number from 1 to n elements
+n <= len(array)
+
+Given nums = [-2,1,-3,4,-1,2,1,-5,4]
+sub_array=[-2]  sum=-2
+sub_array=[-2,1]  sum=-1
+sub_array=[-2,1,-3]
+sub_array=[4,-1,2,1] sum=6 will be the biggest
+"""
+
+
+def sum_array(nums: []) -> int:
+    """
+    return the sum of the int within the given array
+    """
+    sum = 0
+    for i in nums:
+        sum+=i
+    return sum
+
+def build_sub_array(nums: [],i,j)-> []:
+    return nums[i:j]
+
+def max_subarray(nums: []) -> int:
+    """
+    brut force method, build the contiguous sub array, compute the sum of sub array and
+    compare to the current max
+    """
+    max = -10000
+    subarray=[]
+    for i in range(0,len(nums)):
+        for j in range(i+1,len(nums)+1):
+            s_a=build_sub_array(nums,i,j)
+            sum_s_a=sum_array(s_a)
+            if sum_s_a> max:
+                max = sum_s_a
+                subarray=s_a 
+    return (subarray,max)
+
+def better_sol(nums: []) -> int:
+    """
+    For O(n) we need one loop and when current sum is < 0 then we change sub array
+    """
+    max = -10000
+    current_sum =0
+    subarray=[]
+    new_idx=0
+    for i in range(0,len(nums)):
+        current_sum +=nums[i]
+        if current_sum < 0:
+            current_sum = 0
+            subarray=[]
+            new_idx=i+1
+        else:
+            if current_sum > max:
+                max=current_sum
+                subarray=nums[new_idx:i+1]
+
+    return (subarray,max)
+
+nums=[-2,1,-3,4,-1,2,1,-5,4]
+
+print(max_subarray(nums))
+assert ([4, -1, 2, 1], 6) == max_subarray(nums)
+print(max_subarray([1]))
+print(max_subarray([5,4,-1, 7, 8]))
+print(better_sol(nums))
\ No newline at end of file
diff --git a/algorithms/palindrome.py b/algorithms/palindrome.py
new file mode 100644
index 0000000..26cd1b0
--- /dev/null
+++ b/algorithms/palindrome.py
@@ -0,0 +1,77 @@
+"""
+Given an integer x, return true if x is a 
+palindrome, and false otherwise.
+
+palindrome a number or string that can be read from both direction.
+
+Could you solve it without converting the integer to a string?
+"""
+import math
+def length(n: int) -> int:
+    l=1
+    if (n < 0):
+        n=-n
+    while n >= 10:
+        n=n//10
+        l+=1
+    return l
+
+def is_palindrome(n: int) -> bool:
+    if n < 0: 
+        return False
+    l = []
+    nb_digits : int = length(n)
+    z=n
+    e=nb_digits-1
+    while len(l) < nb_digits:
+        div = math.pow(10,e)
+        r = z % div
+        a = z // div
+        l.append(a)
+        z=r
+        e-=1
+        print(div, a, r) 
+    print(l)
+    i=0
+    j=nb_digits-1
+    while i<=j:
+        if l[i] != l[j]:
+            return False
+        i+=1
+        j-=1
+    return True
+
+def better_sol(n: int) -> bool:
+    """
+    reverse the number and reversed and n should be the same.
+    To reverse the number add the rest of div / 10 to current reversed number * 10
+    t=121  reversed = 1
+    t=12   reversed = 12
+    t=1    reversed = 121
+    """
+    if n < 0:
+        return False
+    reversed = 0
+    temp = n
+    while temp != 0:
+        r = temp % 10
+        reversed = reversed * 10 + r
+        temp //=10
+    return reversed == n
+
+assert length(1) == 1
+assert length(12) == 2
+assert length(212) == 3
+assert length(-212) == 3
+assert length(3142) == 4
+
+assert is_palindrome(1)
+assert is_palindrome(11)
+assert is_palindrome(121)
+assert not is_palindrome(-121)
+assert not is_palindrome(1341)
+assert is_palindrome(1234321)
+assert better_sol(1234321)
+
+
+
diff --git a/algorithms/remove_el.py b/algorithms/remove_el.py
new file mode 100644
index 0000000..7a7cd5a
--- /dev/null
+++ b/algorithms/remove_el.py
@@ -0,0 +1,65 @@
+"""
+Remove element
+
+Given an integer array nums and an integer val, remove all occurrences of val 
+in nums in-place.
+The order of the elements may be changed. Then return the number of elements 
+in nums which are not equal to val
+
+nums
+"""
+from typing import List
+
+def remove_element_1(nums: List[int],val: int) -> (int,List[int]):
+    c=0
+    for i in range(0,len(nums)):
+        if nums[i] == val:
+            nums[i]=None
+            c+=1
+    for k in range(0,len(nums)):
+        if nums[k] == None:
+            for j in range(k,len(nums)):
+                if nums[j] != None:
+                    nums[k] = nums[j]
+                    nums[j] = None
+                    break
+    return (len(nums)-c,nums)
+
+def remove_element(nums: List[int],val: int) -> (int,List[int]):
+    c=0
+    for i in range(0,len(nums)):
+        if nums[i] == val:
+            nums[i]= None
+            for k in range(len(nums)-1,i,-1):
+                if nums[k] != val and nums[k] != None:
+                    nums[i]=nums[k]
+                    nums[k]=None
+                    break
+            c+=1
+    return (len(nums)-c,nums)
+
+def better_sol(nums: List[int],val: int) -> (int,List[int]):
+    """
+    use index of the non target element
+    """
+    idx = 0
+    for i in range(len(nums)):
+        if nums[i] != val:
+            nums[idx]= nums[i]
+            idx+=1
+    return (idx,nums)
+
+nums=[3,2,2,3]
+val=3
+expected_num=[2,2,None,None]
+
+k,en = remove_element(nums,val)
+print(k,en)
+assert k == 2
+assert expected_num == en
+nums = [0,1,2,2,3,0,4,2]
+val = 2
+k,en = better_sol(nums,val)
+print(k,en)
+assert k == 5
+assert en[0:k] == [0,1,3,0,4]
diff --git a/algorithms/roman_to_int.py b/algorithms/roman_to_int.py
new file mode 100644
index 0000000..caedc3d
--- /dev/null
+++ b/algorithms/roman_to_int.py
@@ -0,0 +1,54 @@
+"""
+Roman numerals are represented by seven different symbols: I, V, X, L, C, D and M.
+matching values 1,5,10,50,100,500,1000
+Roman numerals are usually written largest to smallest from left to right.
+
+Some rules to respect:
+I can be placed before V (5) and X (10) to make 4 and 9. 
+X can be placed before L (50) and C (100) to make 40 and 90. 
+C can be placed before D (500) and M (1000) to make 400 and 900.
+
+Approach: parse roman number representation char by char and match the char read
+to a k in a dict to get matching value.
+"""
+
+symbols = { 'I':1, 'V':5, 'X':10, 'L':50, 'C':100, 'D':500, 'M':1000}
+
+
+def roman_to_int(roman: str) -> int:
+    n=0
+    i = 0
+    previous = ''
+    while i < len(roman):
+        c = roman[i]
+        if (c == 'V' or c == 'X') and previous == 'I':
+            n=n+symbols[c]-2
+        elif (c == 'L' or c == 'C') and previous == 'X':
+            n=n+symbols[c]-20
+        elif (c == 'D' or c == 'M') and previous == 'C':
+            n=n+symbols[c]-200
+        else:
+            n=n+symbols[c]
+        previous=c
+        i+=1
+    return n
+
+
+def better_sol(roman: str) -> int:
+    ans = 0
+    
+    for i in range(len(roman)):
+        if i < len(roman) - 1 and symbols[roman[i]] < symbols[roman[i+1]]:
+            ans -= symbols[roman[i]]
+        else:
+            ans += symbols[roman[i]]
+    
+    return ans
+
+assert roman_to_int("III") == 3
+assert roman_to_int("IV") == 4
+assert roman_to_int("IX") == 9
+assert roman_to_int("XL") == 40
+assert roman_to_int("XC") == 90
+assert roman_to_int("LVII") == 57
+assert better_sol("MCMXCIV") == 1994
diff --git a/algorithms/two_sum.py b/algorithms/two_sum.py
new file mode 100644
index 0000000..9e3b197
--- /dev/null
+++ b/algorithms/two_sum.py
@@ -0,0 +1,54 @@
+"""
+Given an array of integers nums and an integer target, return indices 
+of the two numbers such that they add up to target.
+
+numbers are > 0, nums is not sorted, we can have the same number multiple times in nums
+
+Input: nums = [2,7,11,15], target = 9
+Output: [0,1]
+
+Input: nums = [3,2,4], target = 6
+Output: [1,2]
+
+O(log N)
+"""
+from typing import List
+
+def two_sum_O2(nums, target) -> (int, int):
+    """
+    brute force is to loop over the array and look at the numbers above to find
+    the complement and return the first match 
+    """
+    for i in range(0,len(nums)-1):
+        for j in range(i+1,len(nums)):
+            if nums[i] + nums[j] == target:
+                return (i,j)
+    return (-1,-1)
+    
+
+def two_sum(nums: List[int], target: int) -> (int, int):
+    """
+    loop over the list in one shot. 
+    use a list of complement from current number to the target if there is no 
+    one existing in the complements already
+    O(log(n))
+    """
+    complements=[]
+    for i in range(0,len(nums)):
+        # do we have a complement
+        comp = target-nums[i]
+        for j in range(0,len(complements)):
+            p_i, c = complements[j]
+            if nums[i] == c:
+                return (p_i,i)
+        if nums[i] < target:
+            complements.append((i,comp))
+    return (-1,-1)
+
+a,b= two_sum([2,7,11,15],9)
+
+print(a,b)
+
+print(two_sum([3,2,4],6))
+print(two_sum([3,2,4],8))
+print(two_sum([3,3],6))