What is Merge Sort Algorithm: How does it work, and More

What Is a Merge Sort Algorithm?

Merge sort is one of the most efficient sorting algorithms. It is based on the divide-and-conquer strategy. Merge sort continuously cuts down a list into multiple sublists until each has only one item, then merges those sublists into a sorted list.

What Is a Divide and Conquer Algorithm?

Divide-and-conquer recursively solves subproblems; each subproblem must be smaller than the original problem, and each must have a base case. A divide-and-conquer algorithm has three parts:

• Divide up the problem into a lot of smaller pieces of the same problem.
• Conquer the subproblems by recursively solving them. Solve the subproblems as base cases if they're small enough.
• To find the solutions to the original problem, combine the solutions of the subproblems.

How Does the Merge Sort Algorithm Work?

Merge sort algorithm can be executed in two ways:

• Top-down Approach

It starts at the top and works its way down, splitting the array in half, making a recursive call, and merging the results until it reaches the bottom of the array tree.

• Bottom-Up Approach 

The iterative technique is used in the Bottom-Up merge sort approach. It starts with a "single-element" array and then merges two nearby items while also sorting them. The combined-sorted arrays are merged and sorted again until only one single unit of the sorted array remains.

You have now explored two approaches to execute merge sort. Now, you will learn to implement one of the approaches in a code editor.

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How to Implement the Merge Sort Algorithm?

It splits the input array in half, calls itself for each half, and then combines the two sorted parts. Merging two halves is done with the merge() method. Merge (array[], left, mid, right) is a crucial process that assumes array[left..mid] and array[mid+1..right]  are both sorted sub-arrays and merges them into one.

Code:

// A C++ program to Sort an array using merge sort algorithm
#include <bits/stdc++.h>
using namespace std;
// Merges two subarrays of array[].
// First subarray is arr[begin..mid]
// Second subarray is arr[mid+1..end]
void merge(int array[], int const left, int const mid, int const right)
{
int const subarrayone = mid - left + 1;
int const subarraytwo = right - mid;
// Create temp arrays
int *leftarray = new int[subarrayone],
*rightarray = new int[subarraytwo];
// Copy data to temp arrays leftarray[] and rightarray[]
for (int i = 0; i < subarrayone; i++)
leftarray[i] = array[left + i];
for (int j = 0; j < subarraytwo; j++)
rightarray[j] = array[mid + 1 + j];
int indexofsubarrayone = 0, // Initial index of first sub-array
indexofsubarraytwo = 0; // Initial index of second sub-array
int indexofmergedarray = left; // Initial index of merged array
// Merge the temp arrays back into array[left..right]
while (indexofsubarrayone < subarrayone && indexofsubarraytwo < subarraytwo) {
if (leftarray[indexofsubarrayone] <= rightarray[indexofsubarraytwo]) {
array[indexofmergedarray] = leftarray[indexofsubarrayone];
indexofsubarrayone++;
}
else {
array[indexofmergedarray] = rightarray[indexofsubarraytwo];
indexofsubarraytwo++;
}
indexofmergedarray++;
}
// Copy the remaining elements of
// left[], if there are any
while (indexofsubarrayone < subarrayone) {
array[indexofmergedarray] = leftarray[indexofsubarrayone];
indexofsubarrayone++;
indexofmergedarray++;
}
// Copy the remaining elements of
// right[], if there are any
while (indexofsubarraytwo < subarraytwo) {
array[indexofmergedarray] = rightarray[indexofsubarraytwo];
indexofsubarraytwo++;
indexofmergedarray++;
}
}
// beg is for left index and end is
// right index of the sub-array
// of arr to be sorted */
void mergesort(int array[], int const beg, int const end)
{
if (beg >= end)
return; // Returns recursivly
int mid = beg + (end - beg) / 2;
mergesort(array, beg, mid);
mergesort(array, mid + 1, end);
merge(array, beg, mid, end);
}
// Function to print an array
void printarray(int arr[], int size)
{
for (int i = 0; i < size; i++)
cout << arr[i] << " ";
}
int main()
{
int arr[] = { 15, 9, 12, 2, 11, 18 };
int arrsize = sizeof(arr) / sizeof(arr[0]);
cout << "Array before sorting \n";
printarray(arr, arrsize);
mergesort(arr, 0, arrsize - 1);
cout << "\nArray after sorting \n";
printarray(arr, arrsize);
return 0;
}

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What Are the Advantages of the Merge Sort?

• Merge sort can efficiently sort a list in O(n*log(n)) time.
• Merge sort can be used with linked lists without taking up any more space.
• A merge sort algorithm is used to count the number of inversions in the list.
• Merge sort is employed in external sorting.

What Are the Drawbacks of the Merge Sort?

• For small datasets, merge sort is slower than other sorting algorithms.
• For the temporary array, mergesort requires an additional space of O(n).
• Even if the array is sorted, the merge sort goes through the entire process.

FAQs

1) What is the use of merge sort?

Merge sort is particularly beneficial when you need a stable sort. A stable sorting algorithm preserves the original order of equivalent elements in the sorted output. In other words, if two identical values appear in the unsorted input, they'll maintain their relative order in the sorted result. Thus, whenever data stability is a priority, consider using merge sort..

2) What is an example for merge sort?

Imagine merge sort as a process of merging two decks of cards that are sorted individually. To combine them into one sorted deck, you'd compare the top cards from each and place the smaller card on a new pile. For a simple example, let's merge two lists:

List A: [12, 25],  List B: [8, 31]

• Start by comparing the first numbers: 12 (from List A) and 8 (from List B). 8 is smaller, so you put it in the new list. New List: [8]
• Next, compare 12 (from List A) and 31 (from List B). 12 is smaller, so you add it next in the new list. New List: [8, 12]
• List A has 25 left. Compare 25 and 31. 25 is smaller, so you add it. New List: [8, 12, 25]
• Now, only 31 remain. Add it to the new list. Final List: [8, 12, 25, 31]

This demonstrates a single merge operation of merge sort.

3) Can Merge Sort be used for sorting linked lists?

Absolutely! Merge sort is a go-to choice for sorting linked lists. Since linked lists don't support fast random access like arrays, some sorting algorithms like quicksort become inefficient, while others like heapsort are not feasible at all. In contrast, merge sort capitalizes on the sequential access nature of linked lists, making it an optimal choice..

4) What is the difference between Merge Sort and Quick Sort?

Merge Sort splits the list in half, sorts each part, and then merges them. It keeps the order of equal elements. Quick Sort picks a 'pivot' and arranges the list based on whether elements are smaller or larger than this pivot. Quick Sort is usually faster for arrays, but can sometimes take longer in worst-case scenarios. Plus, unlike Merge Sort, Quick Sort doesn't always maintain the original order of equal elements.

Next Steps

Your next stop in mastering data structures should be the Insertion Sort Algorithm. Insertion sort is a basic sorting algorithm in which each item in the final sorted array (or list) is sorted one at a time.

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