# Java Sorting Algorithms: Merge Sort Today we are going to analyze one of the most used sorting algorithms: the Merge Sort. It is part of the Divide and Conquer family, just like the  Quick SortMerge Sort offers a better performance despite of the Quick Sort since its complexity remains O(n log n) keeping performances. It is also called "algorithm by fusion"

The main defect of the Merge Sort is that it needs auxiliary data structures in order to execute its tasks. We can say that it is a stable and adaptive algorithm, but it is not in-place.

### How does it work?

Let's start looking at an image that explains very well how the algorithm works. If someone has already had to deal with large collections of data to order, the way of working of the algorithm may be already known. The basic idea is the one of dividing the array into small groups and sort them. Once the sorting operation of every subset is completed the minimum element among the elements is taken and it is put into the final array. The process is repeated until every subset contains at least one element.

The foundamental problem is the fusion process.

#### Fusion algorithm

• The left half of the array is copied on an auxiliary array;
• The minimum element between the auxiliary array and the right half of the array is chosen and the value is copied on the final array;
• The process ends when every element of the auxiliary array has been copied;

### Implementation

```public class MergeSort
{
// Merge the two half of arr[].
// The first subset of the array is arr[l..m]
// The second subset of the array is arr[m+1..r]
public static void merge(int arr[], int l, int m, int r) {
// Find the size of the two subarrays to merge
int n1 = m - l + 1;
int n2 = r - m;

/* Create auxiliary arrays */
int L[] = new int [n1];
int R[] = new int [n2];

/*Copy data to auxiliary arrays*/
for (int index=0; index<n1; ++index)
L[index] = arr[l + i];
for (int j=0; j<n2; ++j)
R[j] = arr[m + 1+ j];

/* Merge the auxiliary arrays */

// Starting indexes of the two arrays
int index = 0, j = 0;

// Starting index of the final array
int k = l;
while (index < n1 && j < n2){
if (L[index] <= R[j]) {
arr[k] = L[index];
index++;
} else{
arr[k] = R[j];
j++;
}
k++;
}
/* Copy the remaining elements of L[] if any */
while (i < n1) {
arr[k] = L[i];
index++;
k++;
}

/* Copy the remaining elements of R[] if any */
while (j < n2) {
arr[k] = R[j];
j++;
k++;
}
}

// Main function that sorts arr[l..r] using
// merge()
public static void sort(int arr[], int l, int r) {
if (l < r) {
// Find the middle point
int m = (l+r)/2;

// Sort the first and the second half
sort(arr, l, m);
sort(arr , m+1, r);

// Merge the two halves
merge(arr, l, m, r);
}
}

public static void main(String args[]) {
int arr[] = {12, 11, 13, 5, 6, 7};

System.out.println("Unsorted array");
System.out.println(Arrays.toString(arr));

MergeSort.sort(arr, 0, arr.length-1);

System.out.println("Sorted array");
System.out.println(Arrays.toString(arr));
}
}
```

### Let's understand the code

First of all, some precisation. When we write a for cicle we can omit the curly brackets if the body of the cicle contains only one instruction. In this case, in the two for cicles written above the curly brackets can be omitted since there is a single instruction and there will not be any problem about the extension of the code.

Like in the example about Quick Sort I made static methods since I think that it is useless using non-static methods. Non-static methods would need an object that would call them and this object would have to be created and managed.

• Merge method:

The two halves' sizes are calculated and then the arrays are created. After that, the two subsets of the starting array are copied to the auxiliary structures. At the end the elements are sorted and copied to the original array again.

• Sort method

In this method the medium point of the array is calculated. This point is used to make the division into subarrays. Using the middle point is important in order to balance the complexity of each call. Then the two halves, respectively of indexes (l, m) and (m+1, r) are sorted.
At the end the two parts are merged.
The most important thing is the check on l and r. These two indexer represent the two limits of the array to sort. L stands for the left limit while R stands for the right limit. The problem is that, under particular conditions, l could become greater then r. This could create inconsistent situations so the necessary condition for the execution of the entire procedure is l < r, thus avoiding errors in passing parameters and inconsistencies in situations.

• Main

This main is quite easy. The collection to sort is created (in this case the collection is an array composed of integer numbers). The sort methodo is then called passing the array to sort, 0 and n-1 (where n-1 stands for the array's length) as parameters.
The right extreme is the index of the last element of the array because the algorithm iterates in a range of the type [ 0 ; array.length ), that can be written equivalently as  [ 0 ; array.length-1 ], simplifying the controls in the various cycles.

#### Complexity of the fusion process

The complexity of the merging process has a linear growth, in fact at each iteration the final array's size always grows by 1. So it is O(N).

There is starting cost of O(N) for the copy of the auxiliary array.

#### Algorithm cost

T(n) = 2T(n/2) + Through suitable algebraic passages it is possible to reach the conclusion that the complexity of the algorithm is equal to .

### When can Merge Sort be useful?

Merge Sort can be useful expecially when we deal with Linked Lists just because the insertion process has linear complexity. Because the nodes of the list are not adjacent, it is particularly convenient to use this algorithm. This is the most significant situations, but this is not the only one.

by Alessio Mungelli Date: 14-12-2019 java jdk jre developement source code educational explanation merge sort algorithm sorting sortmethod hits : 1327 #### Alessio Mungelli

Computer Science student at UniTo (University of Turin), Network specializtion, blogger and writer. I am a kind of expert in Java desktop developement with interests in AI and web developement. Unix lover (but not Windows hater). I am interested in Linux scripting. I am very inquisitive and I love learning new stuffs.

### Related Posts

#### A Java approach: condtional structures

Hello everyone and welcome back! The previous times we have introduced the concept of variable, trying to define some basic concepts about it.  However, some situations suggest that the concept of…

#### Hashmap: hashing, collisions and first functions

Today we are going to study some concepts closely related to hashmaps. The concepts we are going to see are hashing and collisions. Hashing The idea of hashing with chaining is to…

#### Hashmap: Overflow Lists

In this short series of articles we will go to see how it is possible to create the Hashmap data structure in C. In the implementation we're going to use the…

#### Javascript: what are callbacks and how to use them.

Today we are going to learn about a concept that is widely used in javascript and that is used quite a lot by today's frameworks, libraries, especially NodeJS. This is…

#### Data structures in Java - Linked Lists

With 2020 we are going to look at a new aspect of programming: data structures. It is often the case that everyone uses structures provided by the various programming languages.…

#### A Java approach: variables - use case

Hello all friends and welcome back! After the introduction made on the variables, we try to analyse some critical issues that may arise in quite common situations. Let's start by analysing…

#### Introduction to REGEX - Regular Expression

Today we are going to write about Regular Expressions known as regex or shortened  regexp, a very useful concept of using search patterns. Surely you were in a situation when you…

#### A Java approach: variables

Hello everyone and welcome back! Today we will begin a journey that will lead us to study, and possibly review, what are the basics of programming. We will start by talking…

#### HTTP Cookies: how they work and how to use them

Today we are going to write about the way to store data in a browser, why websites use cookies and how they work in detail. Continue reading to find out how…

#### The most popular Array Sorting Algorithms In PHP

There are many ways to sort an array in PHP, the easiest being to use the sort() function built into PHP. This sort function is quick but has it's limitations,…

#### The package managers npm and yarn: main differences

Npm and yarn are package managers that help to manage a project’s dependencies. A dependency is, as it sounds, something that a project depends on, a piece of code that…

#### The Javascript asign() method to merge and clone objects

In this article, we will be covering Object.assign()method in javascript in detail with examples. A javascript object is a collection of key-value pairs. Keys are also known as properties of object. Keys…

ALL USERSUSER