Merge Sort vs Quick Sort – Complete Explanation with Examples and Time Complexity

Merge Sort and Quick Sort are two of the most important and widely used sorting algorithms in computer science. They are much faster than basic sorting algorithms and are commonly asked in technical interviews.

What is Merge Sort?

Merge Sort is a Divide and Conquer algorithm. It divides the array into two halves, sorts each half, and then merges them into a single sorted array.

How Merge Sort Works

• Divide the array into two halves
• Recursively sort both halves
• Merge the sorted halves

void merge(int arr[], int l, int m, int r) {
    int i = l, j = m+1;
    while(i <= m && j <= r) {
        if(arr[i] <= arr[j]) i++;
        else j++;
    }
}

What is Quick Sort?

Quick Sort is also a Divide and Conquer algorithm. It selects a pivot element and arranges all smaller elements on one side and larger elements on the other.

How Quick Sort Works

• Select a pivot element
• Partition the array around the pivot
• Recursively sort left and right parts

int partition(int arr[], int low, int high) {
    int pivot = arr[high];
    int i = low - 1;
    for(int j = low; j < high; j++) {
        if(arr[j] < pivot) {
            i++;
            swap(arr[i], arr[j]);
        }
    }
    swap(arr[i+1], arr[high]);
    return i+1;
}

Time Complexity Comparison

Algorithm	Best	Average	Worst
Merge Sort	O(n log n)	O(n log n)	O(n log n)
Quick Sort	O(n log n)	O(n log n)	O(n²)

Merge Sort vs Quick Sort

• Merge Sort uses extra memory, Quick Sort works in-place.
• Merge Sort has guaranteed O(n log n) time.
• Quick Sort is faster in practice but worst-case is O(n²).

Interview Importance

Companies often ask about these two algorithms to test your understanding of recursion, partitioning, and divide-and-conquer strategies.

Conclusion

Merge Sort is stable and reliable, while Quick Sort is fast and memory efficient. Knowing both gives you a strong foundation in advanced sorting techniques.

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