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Merge Sort in Python - GeeksforGeeks

Last Updated : 23 Jul, 2025

Merge Sort is a Divide and Conquer algorithm. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves. The merge() function is used for merging two halves. The merge(arr, l, m, r) is key process that assumes that arr[l..m] and arr[m+1..r] are sorted and merges the two sorted sub-arrays into one. 

Merge sort is a popular sorting algorithm known for its efficiency and stability. It follows the divide-and-conquer approach to sort a given array of elements.
Here’s a step-by-step explanation of how merge sort works:

1. Divide: Divide the list or array recursively into two halves until it can no more be divided.
2. Conquer: Each subarray is sorted individually using the merge sort algorithm.
3. Merge: The sorted subarrays are merged back together in sorted order. The process continues until all elements from both subarrays have been merged.

Let’s sort the array or list [38, 27, 43, 10] using Merge Sort

Let’s look at the working of above example:

Divide:

• [38, 27, 43, 10] is divided into [38, 27 ] and [43, 10] .
• [38, 27] is divided into [38] and [27] .
• [43, 10] is divided into [43] and [10] .

Conquer:

• [38] is already sorted.
• [27] is already sorted.
• [43] is already sorted.
• [10] is already sorted.

Merge:

• Merge [38] and [27] to get [27, 38] .
• Merge [43] and [10] to get [10,43] .
• Merge [27, 38] and [10,43] to get the final sorted list [10, 27, 38, 43]

Therefore, the sorted list is [10, 27, 38, 43] .

The provided Python code implements the Merge Sort algorithm, a divide-and-conquer sorting technique. It breaks down an array into smaller subarrays, sorts them individually, and then merges them back together to create a sorted array. The code includes two main functions:

• merge, responsible for merging two subarrays, and mergeSort, which recursively divides and sorts the array. The merge function combines two sorted subarrays into a single sorted array.
• The mergeSort function recursively splits the array in half until each subarray has a single element, then merges them to achieve the final sorted result. The example sorts an array using Merge Sort and prints both the initial and sorted arrays.

def merge(arr, l, m, r):
    n1 = m - l + 1
    n2 = r - m

    # create temp arrays
    L = [0] * (n1)
    R = [0] * (n2)

    # Copy data to temp arrays L[] and R[]
    for i in range(0, n1):
        L[i] = arr[l + i]

    for j in range(0, n2):
        R[j] = arr[m + 1 + j]

    # Merge the temp arrays back into arr[l..r]
    i = 0     # Initial index of first subarray
    j = 0     # Initial index of second subarray
    k = l     # Initial index of merged subarray

    while i < n1 and j < n2:
        if L[i] <= R[j]:
            arr[k] = L[i]
            i += 1
        else:
            arr[k] = R[j]
            j += 1
        k += 1

    # Copy the remaining elements of L[], if there
    # are any
    while i < n1:
        arr[k] = L[i]
        i += 1
        k += 1

    # Copy the remaining elements of R[], if there
    # are any
    while j < n2:
        arr[k] = R[j]
        j += 1
        k += 1

# l is for left index and r is right index of the
# sub-array of arr to be sorted


def mergeSort(arr, l, r):
    if l < r:

        # Same as (l+r)//2, but avoids overflow for
        # large l and h
        m = l+(r-l)//2

        # Sort first and second halves
        mergeSort(arr, l, m)
        mergeSort(arr, m+1, r)
        merge(arr, l, m, r)


# Driver code to test above
arr = [12, 11, 13, 5, 6, 7]
n = len(arr)
print("Given array is")
for i in range(n):
    print("%d" % arr[i],end=" ")

mergeSort(arr, 0, n-1)
print("\n\nSorted array is")
for i in range(n):
    print("%d" % arr[i],end=" ")

Given array is
12 11 13 5 6 7 

Sorted array is
5 6 7 11 12 13 

Time Complexity: O(n*log(n))

Auxiliary Space: O(n)

Please refer complete article on Merge Sort for more details!

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