If you want to become an expert in data structures and algorithms, then you should learn how to sort algorithms with your full concentration. Among many other sorting algorithms, you should consider “Merge Sort in Java” as one of the most important methods.
In this article, we are going to first discuss the Merge Sort Algorithm. Later, we will describe the Pseudo-Code along with a Sample Java Program to demonstrate the implementation process. So, let us start our journey with the basics of Merge Sort.
TL;DR: Merge Sort In Java
Aspect | Summary |
Core Concept | Merge Sort uses the Divide and Conquer method, which splits the array, sorts the subarrays, and then merges them back into a sorted result. |
Pseudo-Code Logic | The algorithm will recursively divide the array using the mid index. Then, it will call the MergeSort on the left & right parts. Later, both halves will combine. |
Implementation Process |
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Time And Space Complexity |
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Pros And Cons |
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What Is Merge Sort Algorithm In Java? Read Below
Merge Sort is one of the best sorting algorithms that most developers use for working on large external datasets. It is considered one of the Stable and Efficient Algorithms. Merge Sort is one of the algorithms that follows the Divide and Conquer Strategy to sort any array.
In Merge Sort, a large array is first divided into some smaller pieces. Later, the sorting of those smaller pieces is done, which is known as the Conquer. And in the end, all of the small pieces are combined to get the Sorted Array. We will discuss this theory elaborately in the following section.
Historical Evolution Of Merge Sort Algorithm:
- 1940s: The Merge Sort Algorithm was first introduced in 1945 by John von Neumann.
- 19 60s: The Merge Sort was started using early computer systems for sorting large datasets.
- 1980s: The improved version of the Merge Sort appeared where the Memory Usage is optimized.
- 1990s: Merge Sort was widely used in databases and external sorting techniques.
- 2000s: The Parallel and Multi-threaded versions of Merge Sort became available.
Understanding Merge Sort Algorithm With Flowchart:
Now, it is time to understand the Merge Sort Algorithm theory with the proper flowchart. Here, we will describe the flowchart or diagram in a step-by-step format for better understanding.
Let us assume that there is an array with some random elements like 4, 3, 2, 1. In this array, we want to implement the Merge Sort that will make the array sorted in Ascending Order. So, let us start with the Step 1.
Step 1: First Division
In this step, the complete array will become smaller. Here, two new arrays will be created by dividing the large array, where each new array will have the 2 Elements.
So, one new array will have the Element 4 and the Element 3. And another new array will have the Element 2 and the Element 1. Now, let us move on to the Step 2.
Step 2: Second Division
In this step, creating 2 new arrays will become smaller. Here, 4 new arrays will be created by dividing the existing 2 arrays. Newly created, each array will have a Single Element.
So, the First Array will have the Element 4. The Second Array will have the Element 3. The Third Array will have Element 2 and the Last and Fourth Array will have Element 1.
Step 3: Conquer And Combine Arrays
The last step is to Conquer and Combine the arrays. The newly created four arrays will be sorted in Ascending Order. So, the array with Element 1 will be the first, and the array with Element 4 will be the last.
Later, all of these arrays will be combined, and the new fully sorted array will surface. Hence, we have done sorting of the array with the help of the Merge Sort Algorithm.
What Is The Pseudo-Code Of The Java Merge Sort Algorithm?
After discussing the steps of Merge Sort with the flowchart, we can move towards its practical implementation process. However, before that, we would like to discuss the Pseudo-code of Merge Sort.
Pseudocode is the blueprint for the programming implementation process. They are implemented using a simple language that helps to understand the workflow.
So, let us have a look at the following Pseudo-code.
Function-Mergesort(array, first element, last element)
get middle = (first + last)/2
call again Function-Mergesort(array, first element, middle)
call again Function-Mergesort(array, middle, last element)
combine both results & print
How To Implement Merge Sort Algorithm With Java Recursion?
We hope that the Pseudo-Code for Merge Sorting has become clear to you. Now, it is time to implement Merge Sorting in practice using the Java Programming Language. To do so, we will use Array and Recursion Concepts.
So, we will advise you to clear your basic understanding of the Array and Recursion to get the implementation process. Now, let us check the following code.
import java.util.*;
public class Main
{
public static int[] merge(int[] a, int f, int l)
{
if(f == l) //Base Case To Terminate The Recursion Function
{
int [] r = new int[1];
r[0]= a[f];
return r;
}
int m = (f + l)/2; // Getting The Middle Part Of The Array
int [] ls = merge(a,f,m); // Recursion Calling For The Left Subarray
int[] rs = merge(a,m+1,l); // Recursion Calling For The Right Subarray
int [] an = result(ls,rs); // Calling Function For Getting The Final Array Result
return an;
}
public static int[] result(int[] x1, int[] x2)
{
int a1 = 0, a2 =0, a3 = 0;
int[] x3 = new int[x1.length + x2.length]; // Creation Of Array Which Contains Merged Sorted Elements
while(a1 < x1.length && a2 < x2.length) // Implementation Of While Loop For Merging
{
if(x1[a1] <= x2[a2])
{
x3[a3] = x1[a1];
a1++;
a3++;
}
else
{
x3[a3] = x2[a2];
a2++;
a3++;
}
}
while(a1 < x1.length) // Implementation Of While loop For First Part
{
x3[a3] = x1[a1];
a3++;
a1++;
}
while(a2 < x2.length) // Implementation Of While loop For Second Part
{
x3[a3] = x2[a2];
a3++;
a2++;
}
return x3;
}
public static void data(int[] x) // Function For Printing The Array
{
for (int i = 0; i < x.length; i++)
{
System.out.print(x[i] + " ");
}
System.out.println();
}
public static void main(String[] args)
{
int[] a = {8,7,11,15}; // Assigning The Unsorted Array Value
System.out.print("Original Array Before Merge Sort: ");
data(a);
int[] b = merge(a,0,a.length - 1); // Calling The Function For Merge Sorting
System.out.print("Sorted Array After Merge Sort: ");
data(b);
}
}
Steps Of The Program:
- Here, we will first import the Java utility package into the program.
- Inside the main function, the unsorted data will be assigned. The function will be called where the complete operation will be executed.
- While calling the function, we should share the array along with its first & last index numbers. The first index number will be zero & the last index will be the end length of the array.
- The terminating condition will be developed in that faction. It will check the left and right elements of the array. If they are the same, the program will terminate. In other cases, it will find the middle of the array.
- Based upon that middle element, the left & right sub-arrays will be formed. And those sub-arrays will be called using the recursion function.
- For calling the recursion function, we should follow some conditions.
- The left sub-array will stretch from the beginning index to the middle index number. So, while recursively calling the function, we need to change the index number.
- The same method will be followed for the right sub-array, but with a different index number. The right sub-arrays will stretch from the next middle element to the last index number.
- After sorting all the data and the sub-arrays, the work will be combined. For that purpose, one separate function is being declared.
Output:
How To Implement Merge Sort In Java Using An Iterative Method?
The Java Merge Sort Algorithm can’t only be implemented with the Recursive Method, but it can also be implemented using the Iterative Method, where the Java Loops are highly used to get the result.
This version is also known as the Bottom-Up Sort. Let us check the following code for full implementation.
public class Main
{
public static void main(String[] args)
{
int[] zap = {5, 2, 9, 1, 5, 6}; // Unsorted Array
iterative(zap); // Calling The Function
// Printing The Sorted Values
System.out.print("Merge Sort With Iterative Method: ");
for (int n : zap)
System.out.print(n + " ");
}
public static void iterative(int[] zap)
{
int p = zap.length;
int[] t = new int[p];
// Implementation Of The For Loops For Iteration
for (int s = 1; s < p; s = s*2)
{
for (int l = 0; l < p; l = l + 2 * s)
{
int m = Math.min(l + s - 1, p - 1); // Calculating The Middle
int r = Math.min(l + 2 * s - 1, p - 1); // Calculating The Right
merge(zap, t, l, m, r); // Calling The Merge Function
}
}
}
private static void merge(int[] zap, int[] t, int l, int m, int r)
{
int i = l, j = m + 1, k = l;
// Merging The Arrays With Each Other
while (i <= m && j <= r)
t[k++] = (zap[i] <= zap[j]) ? zap[i++] : zap[j++];
while (i <= m)
t[k++] = zap[i++];
while (j <= r)
t[k++] = zap[j++];
for (i = l; i <= r; i++)
zap[i] = t[i];
}
}
Steps Of The Code:
- At first, the Unsorted Array will be taken and will be shared with the Iterative() Function.
- In that function, we will access the array using two nested For Loops.
- We will calculate the Middle and the Right of the array from that calculation.
- Hence, it will create divisions in the unsorted array, which will be merged later.
- Now, the merge function will be called, where all the divisions will get merged using a While Loop.
- At last, we will print the new data where the array is now in sorted order.
Output:
Comparison Table Between Iterative Vs Recursive Java Merge Sort Algorithm:
As we have seen, the Merge Sort can be implemented both in a Recursive and an Iterative manner. So, it is time to deep dive into them. We are going to create a comparison table between them. Let us check out.
Criteria | Recursive Merge Sort | Iterative Merge Sort |
Implementation | Simple | Complex |
Readability | High | Medium |
Stack Usage | High | Low |
Memory | More | Less |
Practical Use | Common | Rare |
What Is The Time And Space Complexity Of The Java Merge Sort Algorithm?
After discussing the Implementation Process of Merge Sort in Java, we should have a look at the Time and Space Complexity as well. The Space and Time Complexity are important to understand the efficiency of the Merge Sort Algorithm.
Let us have a look at the Time Complexity from the following list:
- For the Best Case, the Time Complexity will be O(n log n).
- For the Worst Case, the Time Complexity will again be the O(n log n).
- And for Average Cases, the Time Complexity will still be the O(n log n).
The Space Complexity will be O(n) if the array is used. So, based on the Number of Elements, the Space Complexity will change for the array.
From Where The O(n log n) Time Complexity Is Coming?
When the Merge Sort is performing the division of arrays into two smaller parts, the Time Complexity becomes “log n”. And while combining the smaller parts, the Time Complexity becomes O(n). So, the Combination of these two Time Complexities makes the overall O(n log n).
What Are Some Advantages And Disadvantages Of Merge Sort?
Before further moving on to some advanced discussion on the Merge Sort Algorithm, let us discuss the Advantages and Disadvantages of Merge Sort to clarify the concept more. We will start with the advantages first.
Advantages Of Merge Sort:
- Merge Sort is a Stable Sorting that maintains the relative order of elements.
- Merge Sort can do a good job for External Sorting where data is stored on Disks.
- Merge Sort ensures that we get a good worst-case time complexity.
- With Merge Sort, we can do Parallel Processing which is easily adaptable for multi-threading.
Disadvantages Of Merge Sort:
- As Merge Sort uses High Memory Space, it should not be used in Memory-Constrained Environments.
- As Merge Sort uses the Recursion Method, it should not be used for Smaller Arrays.
- Due to the High Space Complexity, the Merge Sort should not be used in Real-time Systems.
- Merge Sort is Less Cache-Friendly. So, it can consume the full memory of the CPU.
Comparison Table Between Merge Sort Algorithm And Other Sorting Algorithms:
In Data Structures and Algorithms, we will also find some other Sorting Algorithms. In the following comparison table, let us check the differences between the Merge Sort and Other Sorting Algorithms.
Here, we are comparing them based on Method, Approach, Dataset Type, etc.
Category | Merge Sort | Quick Sort | Bubble Sort | Selection Sort | Heap Sort |
Method | Divide | Partition | Swap | Select | Heapify |
Approach | Recursive | Recursive | Iterative | Iterative | Heap |
Dataset Type | Large | Large | Small | Small | Large |
In-Place | No | Yes | Yes | Yes | No |
Adaptive Nature | No | No | Yes | No | No |
Time Complexity (Average Case) | O(n log n) | O(n log n) | O(n ^2) | O(n ^2) | O(n log n) |
What Are Some Debugging Tips On Java Merge Sort?
After discussing the Comparison Table between different Sorting Algorithms, we can now move ahead with some Debugging Tips related to the Recursion in the Java Merge Sort Algorithm. This will help to implement recursion in Merge Sort in a better manner.
Let us have a look at the following list to know more about the Debugging Tips.
- We should trace the Recursive Calls in the Merge Sort using the Print Statement at the Entry and Exit points.
- To avoid infinite recursion loops, it would be better to create a Counter Variable to count the depth of the recursion.
- We can also print the Left and Right Sub arrays after each recursive call to check the division.
- We have to check the Sub-arrays before processing them in the Recursion to avoid premature exit.
What Are Some Optimization Strategies On Java Merge Sort?
We have learned that the Merge Sort Algorithm takes more Memory Spaces than any other sorting algorithm, which is counted as one of the disadvantages.
Now, we can use different Optimization Strategies to remove such issues with the Merge Sort Algorithm. Let’s check the following two Optimization Strategies.
Hybrid Sorting Algorithm Like Timsort:
One of the best optimization techniques will be the Hybrid Sorting Algorithm like Timsort. Here, the Merge Sort and the Insertion Sort are combined to get a better result than the Simple Merge Sort. The Timsort Name comes from the inventor’s name Tim Peters.
Let us check the following code snippet of the Timsort where the Merge and Insertion Sort both are involved.
// Implementing The Hybrid Sort (Timsort) Function
public static void hybridsort(int[] zap, int n)
{
// Implementation Insertion Sort For Smaller Arrays
for (int i = 0; i < n; i = i + r)
{
insertion(zap, i, Math.min((i + r - 1), (n - 1)));
}
// Implementation Merge Sort To Combine Smaller Arrays
for (int s = r; s < n; s = 2 * s) // Outer For Loop
{
for (int l = 0; l < n; l = l + 2 * s) // Inner For loop
{
int m = Math.min(l + s - 1, n - 1);
int r = Math.min((l + 2 * s - 1), (n - 1));
if (m < r)
{
merge(zap, l, m, r); // Calling The Merge Sort Function
}
}
}
}
- At first, a For Loop will be executed where the Insertion Sort Logic is developed.
- This Insertion Sort helps in sorting values into small divided arrays.
- Later, two nested For loops will be developed that will implement the Merge Sort.
- After sorting values in Small Arrays using the Insertion Sort, we merge them with the Merge Sort Logic.
Merge Sort On LinkedList:
Another Optimization Technique will be to use Merge Sort on the LinkedList. Instead of working on the Merge sort on a simple array concept, we can use the Merge Sort with LinkedList to get a better space complexity than the normal one.
Let us check the following code snippet of the Merge Sort implemented on the LinkedList.
// Implementing The Merge Sort Function For Linked List
public class LinkedListMerge
{
// Function To Sort Linked List Using Merge Sort
public static ListNode mergesort(ListNode head)
{
if (h == null || h.next == null) // Implementing The Base Case
{
return h;
}
// We Will Split The Linked list Into Two Smaller Parts
ListNode m = getMiddle(h);
ListNode n = m.next;
m.next = null;
// We Will Recursively Sort Both The Parts
ListNode l = mergesort(h);
ListNode r = mergesort(n);
return merge(l, r); // We Will Merge Sorted Parts
}
- At first, the Base Case will be implemented to check the Void LinkedList.
- Then, the LinkedList will be divided into two smaller parts for sorting the values.
- Now, we will recursively call both parts to sort the values. One will sort from Head to Middle, and the other will sort from Middle to End.
- At last, we will call the Merge Function to add those two sorted Linked Lists.
What Are Some Real-world Applications Of Java Merge Sort Algorithm?
Now, if you are thinking that there is practically no use of the Merge Sort Algorithm in Java other than for the Educational Purposes, then you are thinking wrong.
There are many Real-World Applications of Java Merge Sort. Here, we will discuss some important real-world applications of Merge Sort.
1. Sorting Large Datasets in Database:
If we want to sort any large data in any Database or File System, then the use of the Merge Sort is necessary. As merge sort uses Divide and Conquer, sorting large arrays will be an easy task.
When To Use In Real-World Applications:
- In Relational Databases, Merge Sort is used to fit large datasets into memory.
- In File Management Systems, Merge Sort helps to organize large logs and structured data.
2. Disk-based Sorting:
If the data can’t be loaded entirely into the memory, then we can perform sorting into the External Disk as well. And that is done with the help of the Merge Sort Algorithm.
When To Use In Real-World Applications:
- In Cloud Storage, Merge Sort is used to sort large distributed datasets across different nodes.
- To Sort Virtual Memory Data in the Operating System, the Merge Sort is highly used.
3. Image Processing and Pixel Sorting:
If we want to do Image Processing where Pixel Intensities are sorted to do several operations like Noise Reduction and Histogram Equalization, then the use of the Merge Sort is inevitable.
When To Use In Real-World Applications:
- Merge Sort is used to do Pixel Sorting in Medical Imaging to analyze the X-ray data.
- To increase Image Clarity and Contrast, the Merge Sort is also used in Satellite Image Processing.
What Are Some Common Mistakes With Merge Sort Algorithm In Java?
We hope that whatever we have discussed till now will be enough to make you eager to work on the Merge Sort algorithm as much as possible. But while working on Merge Sort, you should keep in mind some Common Errors that most of the students commit.
Let us check the following list where some Common Mistakes of the Merge Sort Algorithm are discussed.
- While calculating the Mid Part of the Array, we oftentimes make some Logical Mistakes.
- Oftentimes we put incorrect Base Case in Recursion, which ends in an Infinite Recursion Loop.
- Occasionally, we forget to use the Temporary Array and modify the Original Array.
- Sometimes, we use improper Merging Logic which might Cause an Unsorted Array or Exceptions.
Conclusion:
As we saw, “Merge sort in Java” programming language is a very important topic to know.
The implementation process of the merge sort algorithm depends upon the use of an array in the program. So, the Data Structure concept along with the Algorithm part needs to be cleared before moving to the implementation process.
Still facing issues, you can always hire a Java expert if you are stuck implementing Merge sort from CodingZap to clear all your doubts.
It is also advisable to clear some basic concepts in the Java programming language. You should first have a nice grip on the preliminary idea of the Java programming language. Then the implementation will become a cakewalk for you.
Takeaways:
- We should not use the Iteration Method like Loops to create the Merge Sort Algorithm.
- The Time Complexity of the Merge Sort Algorithm is O(n log n).
- The Space Complexity of the Merge Sort is O(n) which is not a Constraint one.
- In Data Compression and Image Processing, the use of Merge Sort is high.
