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Data Structures in C

Merge Sort

Concept Overview

Merge Sort follows the divide and conquer approach:

  1. Divide → Split the array into two halves.
  2. Conquer → Recursively sort each half.
  3. Combine → Merge the two sorted halves into one sorted array.

Step-by-Step Example

Let’s sort:

[8, 3, 1, 7, 0, 10, 2]

Step 1: Divide →
Left: [8, 3, 1]
Right: [7, 0, 10, 2]

Step 2: Recursively divide until single elements remain.
Then, merge subarrays in sorted order:

[8, 3, 1] → [1, 3, 8]

[7, 0, 10, 2] → [0, 2, 7, 10]

Merge both → [0, 1, 2, 3, 7, 8, 10]

Final sorted array.

 

C Program: Merge Sort

C

#include <stdio.h>

 

// Function to merge two subarrays

void merge(int arr[], int left, int mid, int right) {

    int i, j, k;

    int n1 = mid - left + 1;

    int n2 = right - mid;

 

    // Temporary arrays

    int L[n1], R[n2];

 

    // Copy data to temp arrays

    for (i = 0; i < n1; i++)

        L[i] = arr[left + i];

    for (j = 0; j < n2; j++)

        R[j] = arr[mid + 1 + j];

 

    // Merge the temp arrays back into arr[left..right]

    i = 0;

    j = 0;

    k = left;

 

    while (i < n1 && j < n2) {

        if (L[i] <= R[j]) {

            arr[k] = L[i];

            i++;

        } else {

            arr[k] = R[j];

            j++;

        }

        k++;

    }

 

    // Copy remaining elements of L[], if any

    while (i < n1) {

        arr[k] = L[i];

        i++;

        k++;

    }

 

    // Copy remaining elements of R[], if any

    while (j < n2) {

        arr[k] = R[j];

        j++;

        k++;

    }

}

 

// Merge Sort function

void mergeSort(int arr[], int left, int right) {

    if (left < right) {

        int mid = left + (right - left) / 2;

 

        // Sort first and second halves

        mergeSort(arr, left, mid);

        mergeSort(arr, mid + 1, right);

 

        // Merge sorted halves

        merge(arr, left, mid, right);

    }

}

 

// Function to print array

void printArray(int arr[], int n) {

    for (int i = 0; i < n; i++)

        printf("%d ", arr[i]);

    printf("\n");

}

 

int main() {

    int n;

    printf("Enter number of elements: ");

    scanf("%d", &n);

 

    int arr[n];

    printf("Enter %d elements:\n", n);

    for (int i = 0; i < n; i++)

        scanf("%d", &arr[i]);

 

    printf("Original array: ");

    printArray(arr, n);

 

    mergeSort(arr, 0, n - 1);

 

    printf("Sorted array: ");

    printArray(arr, n);

 

    return 0;

}

Output

 
INPUT :
Enter number of elements: 7
Enter 7 elements:
8 3 1 7 0 10 2

OUTPUT :
Original array: 8 3 1 7 0 10 2 
Sorted array: 0 1 2 3 7 8 10

Complexity Analysis

Case

Time Complexity

Space Complexity

Best Case

O(n log n)

O(n)

Average Case

O(n log n)

O(n)

Worst Case

O(n log n)

O(n)

  • Stable sort (maintains order of equal elements).
  • Always O(n log n) — even in the worst case.
  • Requires extra memory (O(n)) for temporary arrays.

Key Takeaways

  • Divide and conquer approach.
  • Consistent O(n log n)
  • Stable sorting algorithm.
  • Good for linked lists and large datasets.
  • Uses additional memory → not in-place.

Comparison: Quick Sort vs Merge Sort

Feature

Quick Sort

Merge Sort

Type

Divide & Conquer

Divide & Conquer

Time (Best/Average)

O(n log n)

O(n log n)

Worst Case

O(n²)

O(n log n)

Space

O(log n)

O(n)

Stability

Not stable

Stable

Preferred For

In-memory data

Large / external data