Update mergesort.py

divide_and_conquer/mergesort.py

@@ -1,48 +1,109 @@
-def merge(arr, left, mid, right):
-    # overall array will divided into 2 array
-    # left_arr contains the left portion of array from left to mid
-    # right_arr contains the right portion of array from mid + 1 to right
-    left_arr = arr[left : mid + 1]
-    right_arr = arr[mid + 1 : right + 1]
-    k = left
-    i = 0
-    j = 0
-    while i < len(left_arr) and j < len(right_arr):
-        # change sign for Descending order
-        if left_arr[i] < right_arr[j]:
-            arr[k] = left_arr[i]
-            i += 1
-        else:
-            arr[k] = right_arr[j]
-            j += 1
-        k += 1
-    while i < len(left_arr):
-        arr[k] = left_arr[i]
-        i += 1
-        k += 1
-    while j < len(right_arr):
-        arr[k] = right_arr[j]
-        j += 1
-        k += 1
-    return arr
-
-
-def mergesort(arr, left, right):
+from typing import List
+
+
+def merge(left_half: List, right_half: List) -> List:
+    """Helper function for mergesort.
+
+    >>> left_half = [-2]
+    >>> right_half = [-1]
+    >>> merge(left_half, right_half)
+    [-2, -1]
+
+    >>> left_half = [1,2,3]
+    >>> right_half = [4,5,6]
+    >>> merge(left_half, right_half)
+    [1, 2, 3, 4, 5, 6]
+
+    >>> left_half = [-2]
+    >>> right_half = [-1]
+    >>> merge(left_half, right_half)
+    [-2, -1]
+
+    >>> left_half = [12, 15]
+    >>> right_half = [13, 14]
+    >>> merge(left_half, right_half)
+    [12, 13, 14, 15]
+
+    >>> left_half = []
+    >>> right_half = []
+    >>> merge(left_half, right_half)
+    []
     """
-    >>> mergesort([3, 2, 1], 0, 2)
-    [1, 2, 3]
-    >>> mergesort([3, 2, 1, 0, 1, 2, 3, 5, 4], 0, 8)
-    [0, 1, 1, 2, 2, 3, 3, 4, 5]
+    sorted_array = [None] * (len(right_half) + len(left_half))
+
+    pointer1 = 0  # pointer to current index for left Half
+    pointer2 = 0  # pointer to current index for the right Half
+    index = 0  # pointer to current index for the sorted array Half
+
+    while pointer1 < len(left_half) and pointer2 < len(right_half):
+        if left_half[pointer1] < right_half[pointer2]:
+            sorted_array[index] = left_half[pointer1]
+            pointer1 += 1
+            index += 1
+        else:
+            sorted_array[index] = right_half[pointer2]
+            pointer2 += 1
+            index += 1
+    while pointer1 < len(left_half):
+        sorted_array[index] = left_half[pointer1]
+        pointer1 += 1
+        index += 1
+
+    while pointer2 < len(right_half):
+        sorted_array[index] = right_half[pointer2]
+        pointer2 += 1
+        index += 1
+
+    return sorted_array
+
+
+def merge_sort(array: List) -> List:
+    """Returns a list of sorted array elements using merge sort.
+
+    >>> from random import shuffle
+    >>> array = [-2, 3, -10, 11, 99, 100000, 100, -200]
+    >>> shuffle(array)
+    >>> merge_sort(array)
+    [-200, -10, -2, 3, 11, 99, 100, 100000]
+
+    >>> shuffle(array)
+    >>> merge_sort(array)
+    [-200, -10, -2, 3, 11, 99, 100, 100000]
+
+    >>> array = [-200]
+    >>> merge_sort(array)
+    [-200]
+
+    >>> array = [-2, 3, -10, 11, 99, 100000, 100, -200]
+    >>> shuffle(array)
+    >>> sorted(array) == merge_sort(array)
+    True
+
+    >>> array = [-2]
+    >>> merge_sort(array)
+    [-2]
+
+    >>> array = []
+    >>> merge_sort(array)
+    []
+
+    >>> array = [10000000, 1, -1111111111, 101111111112, 9000002]
+    >>> sorted(array) == merge_sort(array)
+    True
     """
-    if left < right:
-        mid = (left + right) // 2
-        # print("ms1",a,b,m)
-        mergesort(arr, left, mid)
-        # print("ms2",a,m+1,e)
-        mergesort(arr, mid + 1, right)
-        # print("m",a,b,m,e)
-        merge(arr, left, mid, right)
-        return arr
+    if len(array) <= 1:
+        return array
+    # the actual formula to calculate the middle element = left + (right - left) // 2
+    # this avoids integer overflow in case of large N
+    middle = 0 + (len(array) - 0) // 2
+
+    # Split the array into halves till the array length becomes equal to One
+    # merge the arrays of single length returned by mergeSort function and
+    # pass them into the merge arrays function which merges the array
+    left_half = array[:middle]
+    right_half = array[middle:]
+
+    return merge(merge_sort(left_half), merge_sort(right_half))
 
 
 if __name__ == "__main__":