diff --git a/book/book_second_edition.pdf b/book/book_second_edition.pdf
index 490f54d..60ca209 100644
Binary files a/book/book_second_edition.pdf and b/book/book_second_edition.pdf differ
diff --git a/src/searching_and_sorting/searching/binary_search.py b/src/searching_and_sorting/searching/binary_search.py
index 1ce26d6..79570cf 100644
--- a/src/searching_and_sorting/searching/binary_search.py
+++ b/src/searching_and_sorting/searching/binary_search.py
@@ -3,53 +3,63 @@
 __author__ = "bt3"
 
 
-
-def binary_search_rec(array, item, lo=0, hi = None):
+def binary_search(array, item, hi=None, lo=0):
     '''
-    >>> binary_search_rec([2,3,5,6,8,10,15,23], 15)
-    (True, 6)
-    >>> binary_search_rec([2,3,5,6,8,10,15,23], 4)
+    >>> binary_search([2,3,5,6,8,10,15,23], 15)
+    6
+    >>> binary_search([2,3,5,6,8,10,15,23], 4)
+    False
+    >>> binary_search([1,3,4,5,7,8 ,10,12,23], 10)
+    6
+    >>> binary_search([1,3,4,5,7,8 ,10,12,23], 22)
     False
     '''
+
     hi = hi or len(array)
-    if hi < lo :
+    if hi < lo:
         return False
 
     mid = (hi + lo)//2
-
-    if array[mid] == item:
-        return True, mid
-    elif array[mid] < item:
-        return binary_search_rec(array, item, mid + 1, hi)
+    if  item == array[mid]:
+        return mid
+    elif item < array[mid]:
+        return binary_search(array, item, hi=mid-1, lo=lo)
     else:
-        return binary_search_rec(array[:mid], item, lo, mid -1)
+        return binary_search(array, item, hi=hi, lo=mid+1)
+
 
 
 
 def binary_search_iter(array, item):
     '''
     >>> binary_search_iter([2,3,5,6,8,10,15,23], 15)
-    (True, 6)
+    6
     >>> binary_search_iter([2,3,5,6,8,10,15,23], 4)
     False
+    >>> binary_search_iter([1,3,4,5,7,8 ,10,12,23], 10)
+    6
+    >>> binary_search_iter([1,3,4,5,7,8 ,10,12,23], 22)
+    False
     '''
-    hi = len(array)
-    lo = 0
+    lo, hi = 0, len(array)
 
     while lo < hi:
         mid = (hi+lo)//2
         if array[mid] == item:
-            return True, mid
+            return mid
         elif array[mid] > item:
             hi = mid
         else:
-            lo  = mid + 1
+            lo=mid+1
     return False
 
 
 
 
 
+
+
+
 if __name__ == '__main__':
     import doctest
     doctest.testmod()
diff --git a/src/searching_and_sorting/sorting/merge_sort.py b/src/searching_and_sorting/sorting/merge_sort.py
index 8d7cfed..fd5ac54 100644
--- a/src/searching_and_sorting/sorting/merge_sort.py
+++ b/src/searching_and_sorting/sorting/merge_sort.py
@@ -3,62 +3,34 @@
 __author__ = "bt3"
 
 
-def merge_sort(seq):
+def merge_sort(array):
     '''
-    >>> seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
-    >>> merge_sort(seq)
-    [0, 1, 2, 2, 3, 3, 5, 5, 6, 6, 8]
+    >>> merge_sort([3 ,5, 1, 2, 10, 6])
+    [1, 2, 3, 5, 6, 10]
     '''
-    if len(seq) < 2:
-        return seq
-    mid = len(seq)//2
-    lft, rgt = seq[:mid], seq[mid:]
-    if len(lft)>1:
-        lft = merge_sort(lft)
-    if len(rgt)>1:
-        rgt = merge_sort(rgt)
+    if len(array) < 2:
+        return array
+
+    mid = len(array)//2
+    left = merge_sort(array[:mid])
+    right = merge_sort(array[mid:])
 
     res = []
-    while lft and rgt:
-        if lft [-1]>= rgt[-1]:
-            res.append(lft.pop())
-        else:
-            res.append(rgt.pop())
-    res.reverse()
-    return(lft or rgt) + res
-
-
-
-# separating the merge part in another function
-def merge_sort_sep(seq):
-    '''
-    >>> seq = [3, 5, 2, 6, 8, 1, 0, 3, 5, 6, 2]
-    >>> merge_sort_sep(seq)
-    [0, 1, 2, 2, 3, 3, 5, 5, 6, 6, 8]
-    '''
-    if len(seq) < 2 :
-        return seq
-    mid = len(seq)//2
-    left = merge_sort(seq[:mid])
-    right = merge_sort(seq[mid:])   # notice that mid is included!
-    return merge(left, right)      # merge iteratively
-
-
-def merge(left, right):
-    if not left or not right:
-        return left or right # nothing to be merged
-    result = []
     i, j = 0, 0
     while i < len(left) and j < len(right):
         if left[i] <= right[j]:
-            result.append(left[i])
+            res.append(left[i])
             i += 1
         else:
-            result.append(right[j])
+            res.append(right[j])
             j += 1
-    if left[i:] : result.extend(left[i:])   # REMEMBER TO EXTEND, NOT APPEND
-    if right[j:] : result.extend(right[j:])
-    return result
+
+    if left[i:]:
+       res.extend(left[i:])
+    if right[j:]:
+        res.extend(right[j:])
+    return res
+
 
 
 ''' Merge sort for files '''
diff --git a/src/searching_and_sorting/sorting/quick_sort.py b/src/searching_and_sorting/sorting/quick_sort.py
index e78ec38..5596d1a 100644
--- a/src/searching_and_sorting/sorting/quick_sort.py
+++ b/src/searching_and_sorting/sorting/quick_sort.py
@@ -18,11 +18,11 @@ def qs(array):
     left  = [a for a in new_array if a <= piv_element]
     right = [a for a in new_array if a > piv_element]
 
-
     return qs(left) + [array[piv]] + qs(right)
 
 
-""" we can also divide them into two functions """
+
+# we can also divide them into two functions
 def partition(seq):
     pi,seq = seq[0],seq[1:]
     lo = [x for x in seq if x <= pi]
@@ -41,9 +41,6 @@ def quick_sort_divided(seq):
 
 
 
-
-
-
 if __name__ == '__main__':
     import doctest
     doctest.testmod()
\ No newline at end of file