> For the complete documentation index, see [llms.txt](https://tanias-workspace.gitbook.io/tanias-little-corner/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://tanias-workspace.gitbook.io/tanias-little-corner/algorithms/merge-sort.md).

# Merge Sort

Merge Sort is a divide-and-conquer algorithm that divides the array into halves, sorts each half, and then merges the sorted halves.

**Steps**:

1. Divide the array into two halves.
2. Recursively sort each half.
3. Merge the two sorted halves into a single sorted array.

<figure><img src="/files/oK7TzhO6SNhIxofVdYf5" alt="" width="375"><figcaption></figcaption></figure>

```cpp
#include <vector>
#include <iostream>

void merge(std::vector<int> &arr, int left, int mid, int right) {
    int n1 = mid - left + 1;
    int n2 = right - mid;
    
    std::vector<int> L(n1), R(n2);
    
    for (int i = 0; i < n1; i++)
        L[i] = arr[left + i];
    for (int j = 0; j < n2; j++)
        R[j] = arr[mid + 1 + j];
    
    int i = 0, j = 0, k = left;
    while (i < n1 && j < n2) {
        if (L[i] <= R[j]) {
            arr[k++] = L[i++];
        } else {
            arr[k++] = R[j++];
        }
    }
    
    while (i < n1) {
        arr[k++] = L[i++];
    }
    
    while (j < n2) {
        arr[k++] = R[j++];
    }
}

void mergeSort(std::vector<int> &arr, int left, int right) {
    if (left < right) {
        int mid = left + (right - left) / 2;
        mergeSort(arr, left, mid);
        mergeSort(arr, mid + 1, right);
        merge(arr, left, mid, right);
    }
}

int main() {
    std::vector<int> arr = {64, 34, 25, 12, 22, 11, 90};
    mergeSort(arr, 0, arr.size() - 1);
    for (int num : arr) std::cout << num << " ";
    return 0;
}

```

**Merge Sort**: Efficient and stable, with a time complexity of O(nlog⁡n).