Merge Sort

Author: hashfx

DSA-Python/Algorithms/MergeSort.py

@@ -0,0 +1,84 @@
+"""
+Merge Sort
+    We have 2 unsorted arrays, we've to sort them and merge them in a way that merged array is also a sorted array
+    Traditional Method
+        Compare first element of each array
+            Insert the smallest element into sorted array
+        Compare greater element from previous array and 2nd element from 2nd array
+            Insert the smallest element into sorted array
+        Repeat until array is sorted
+
+
+                    9 - 2 - 1 - 7 - 5 - 3 - 4 - 6
+                  9 - 2 - 1 - 7       5 - 3 - 4 - 6
+               9 - 2    1 - 7           5 - 3    4 - 6
+             2 - 9    1 - 7               3 - 5    4 - 6
+           1 - 2  -  7 - 9                 3 - 4  -  5 - 6
+               1 - 2 - 7 - 9              3 - 4 - 5 - 6
+                      1 - 2 - 3 - 4 - 5 - 6 - 7 - 9
+
+
+Time Complexity: O(n log n)
+
+
+"""
+
+def Merge2SortedList(arr1, arr2):
+    """Input: 2 sorted lists"""
+    sortedList = []  # created an empty sorted list
+    len_arr1 = len(arr1)  # length of array1
+    len_arr2 = len(arr2)  # length of array2
+    i = j = 0  # pointers initialised
+    # iterate through both lists until end of any of them is reached
+    while i < len_arr1 and j < len_arr2:
+        if arr1[i] <= arr2[j]:  # compare elements between both the lists
+            sortedList.append(arr1[i])  # append to sorted list
+            i+=1  # i pointer is increased by 1 and j pointer is static
+        else:
+            sortedList.append(arr2[j])
+            j+=1
+    while i < len_arr1:
+        sortedList.append(arr1[i])
+        i+=1
+    while j < len_arr2:
+        sortedList.append(arr2[j])
+        j += 1
+    return sortedList  # sorted list returned
+
+
+def MergeSort(arr):
+    # if list is empty or contains 1 element only: return list
+    if len(arr) <= 1:
+        return arr
+    mid = len(arr) // 2  # get middle index of array to divide it into 2 parts: left and right
+    left = arr[:mid]  # dividing list into 2 parts: left and right
+    right = arr[mid:]  # dividing list into 2 parts: left and right
+
+    left = MergeSort(left)  # recursively call MergeSort function to sort left array
+    right = MergeSort(right)  # recursively call MergeSort function to sort right array
+    # MergeSort(left)  # recursively call MergeSort function to sort left array
+    # MergeSort(right)  # recursively call MergeSort function to sort right array
+
+    return Merge2SortedList(left, right)  # Merge Sort both sorted array
+    # Merge2SortedList(left, right)  # Merge Sort both sorted array
+
+
+if __name__ == '__main__':
+
+    """arr1 = [2, 4, 6, 8]
+    arr2 = [3, 6, 9, 12]
+    print(Merge2SortedList(arr1, arr2))"""
+    arr = [10, 3, 15, 7, 8, 23, 98, 29]
+    print(MergeSort(arr))
+
+    # test cases
+
+    tests = [
+        [20, 13, 5, 37, 8, 32, 98, 29],  # unsorted array
+        [],  # empty array
+        [5],  # array with single element
+        [10, 8, 6, 4, 2],  # reverse array
+        [1, 2, 3, 4, 5]  # sorted array
+    ]
+    for elements in tests:
+        print(MergeSort(elements))