Java Tutorial Index

Java Tutorial Java Features C++ vs Java Java History Java Hello World Java Development Kit Java Runtime Environment Java Virtual Machine Difference between JDK, JRE, and JVM Memory Areas in Java Java Operators Java Keywords Primitive Data Types Variables

Java Loops

Java Do While Loop Java While Loop Java For Loop Java Enhanced For Loop

Java Programs

Java Basic Programs Factorial Program in Java Fibonacci Series Program in Java Prime Number Program in Java Palindrome Number Program in Java Armstrong Number Program in Java Anagram Program in Java Pattern Programs in Java Calculator Program in Java Leap Year Program in Java Addition Program in Java Number Pattern Programs in Java Star Pattern Programs in Java Package Program in Java Pyramid Program in Java Sorting Program in Java String Palindrome Program in Java Even Odd Program in Java For Loop Program in Java If Else Program in Java Switch Case Program in Java GCD Program in Java LCM Program in Java Hello Program in Java Matrix Program in Java Menu Driven Program in Java Series Program in Java Client Server Program in Java Swapping Program in Java Pig Latin Program in Java Tower of Hanoi Program in Java Recursion Program in Java Matrix Multiplication Program in Java Perfect Number Program in Java Classes and Objects in Java Example Programs String Programs in Java Array Programs in Java Constructor Program in Java Inheritance Program in Java Abstract class Program in Java Interface Program in Java Encapsulation Program in Java Polymorphism Program in Java Exception Handling Program in Java Multithreading Program in Java Thread Program in Java Collection Programs in Java ArrayList Program in Java Stack Program in Java Applet Program in Java Swing Program in Java JDBC Program in Java How to run Java program in command prompt How to run Java program in Eclipse Program to find and replace characters on string in java Program to find the duplicate characters in a string Program to check whether a given character is present in a string or not Java Program to Print Permutations of String Java program to find frequency of characters in a string Java Program to remove duplicate characters in a string

Java Sorting

Sorting Algorithms in Java Merge Sort in Java Quick Sort in Java Bubble Sort in Java Insertion Sort in Java Selection Sort in Java Heap Sort in Java Radix Sort in Java Topological Sort in Java Bucket Sort in Java Counting Sort in Java

Java OOPs Concepts

OOPs - Object Oriented Programming Objects and Classes in Java Methods in Java Java Naming Conventions Constructors in Java Java this keyword Java static keyword Inheritance in Java Aggregation in Java Java super keyword Constructor Chaining and Constructor Overloading Java Polymorphism Static and Dynamic Binding in Java Java Abstraction Abstract class in Java Interface in Java Difference between Abstract class and Interface Java final keyword Packages in Java Access Modifiers in Java Java Wrapper classes Java Numbers Java Characters Java Integer Java Boolean Java Arrays Java Command Line Arguments Java strictfp Keyword Java Math

Java Strings

Java Strings Java String Methods StringBuilder in Java StringBuffer in Java Java Regular Expressions StringBuffer vs StringBuilder String vs StringBuffer String vs StringBuilder String Manipulation in Java Java String Concatenation How to Reverse a String in Java String Array in Java How to Compare Two Strings in Java How to Concatenate Two Strings in Java Why String in Immutable in Java java.lang.NumberFormatException for Input String String Pool in Java Java Generate Random String How to take String Input in Java Java String Interview Questions

Java Exceptions

Exception Handling in Java Java try catch Java throw Java throws Difference between throw and throws Java finally Java Custom Exception Java Exception Propagation

Garbage Collection

Automatic Resource Management in Java Java Garbage Collection Java finalize() Java gc() Difference between final, finally and finalize


Multithreading in Java Process and Thread in Java Basic Terms in Multithreading Java Thread creation Thread Scheduler in Java Java Thread class DeadLock in Java

Java IO

Java IO Java Read File Java file Reader Java Buffer Reader Java file Writer Java BufferedWriter Java InputStreamReader Scanner in Java Java StringReader Java StringReader Class Java StringWriter Class Java PrintWriter Java File Java Read File Line By Line Java FileInputStream Java FileOutputStream Java Create File Java Delete File Java Open File Java Read File to String Java copy file Jar File in Java Java FileNotFoundException


Java Serialization Java transient


Java Network Programming Java Socket Programming Java URL Java URLConnection HttpURLConnection in Java Java InetAddress Java DatagramSocket and Java DatagramPacket


Java AWT


Swing in Java

Java Collections

Collections in Java Java List Interface ArrayList in Java LinkedList in Java Vector in Java Stack in Java ArrayList vs LinkedList in Java ArrayList vs Vector in Java Java Set Interface HashSet in Java LinkedHashSet in Java TreeSet in Java Java Queue Interface PriorityQueue in Java Deque in Java ArrayDeque in Java Java Map Interface HashMap in Java LinkedHashMap in Java TreeMap in Java Dictionary in Java Hashtable in Java Properties in Java Collections class in Java Java Comparable Java Comparator Comparable vs Comparator in Java

Java Generics

Generics in Java

Java Annotations

Annotations in Java


Java JDBC Tutorial JDBC Architecture Types of JDBC Drivers JDBC vs ODBC Java Database Connectivity with MySQL Java Database Connectivity with Oracle Statements in java Prepared statement in Java Resultset in java Java ResultSetMetaData DatabaseMetaData in Java Callable Statement in Java Transaction Management in Java Design of JDBC

Java Differences

Java vs DotNET Java vs JavaScript Python vs Java Kotlin vs Java Java vs C++ C# vs Java Java float vs double Java vs Scala Java vs Go Java vs Golang Java Extends vs Implements Java vs Node.js Static vs Non-static in Java C vs Java int vs Integer in Java Java protected vs private Java vs Dot Net Stack vs Heap in Java Java Array vs ArrayList Java SE vs EE Class vs Object in Java Java vs Bedrock Difference between = = and equals ( ) in java Difference between C, C++, java HashMap Vs HashTable Checked vs Unchecked Exceptions in Java Difference between print() and println() in Java Differences between Lock and Monitor in Java Concurrency Differences between Set and List in Java How to calculate time difference in Java Char and String differences in Java Difference between String, StringBuffer and StringBuilder in java Difference between String and Char Array in Java Differences between Byte Code and Machine Code Difference between String Tokenizer and split Method in Java Difference between JIT and JVM in Java Difference Between Data Hiding and Abstraction in Java Difference between String Tokenizer and Split Method in Java Difference Between BufferedReader and FileReader Difference Between Thread.start() and

How to

How to convert String to String array in Java How to find length of integer in Java How to get Day Name from Date in Java How to open the Java control panel How to resolve Illegal state exceptions in Java How to reverse a linked list in java How to encrypt password in Java How to calculate time complexity of any program in Java How to check version of java in Linux How to enable java in chrome How to run Java program How to set path in Java How to check the Java version in cmd How to install Java in Windows 10 How to run Java program in cmd How to add double quotes in a string in Java How to convert list to String in Java How to call a method in Java How to Set Environment Variables for Java How to sort an array in Java How to Create Immutable Classes in Java How to iterate HashMap in Java How to write Java program How to create an array in Java How to create a package in Java How to generate random numbers in Java How to input String in Java How to Create Singleton Class in Java How to create thread in Java How to find length of String in Java How to sort a string in Java How to use scanner in Java How to achieve multiple inheritance in Java How to find the length of an Array in Java How to Read Java JSON file How to run Java program in Eclipse How to call a function in Java How to create array of objects in Java How to create custom exception in Java How to import packages in Java How to run applet Program in Java How to take Array Input in Java How to achieve abstraction in Java How to call static method in Java How to compare characters in Java How to compare dates in Java How to create a linked list in Java How to download Eclipse for Java How to get ASCII value of char in Java How to get the current date and time in Java How to handle NullPointerException in Java How to initialize string array in Java How to Install Java on MAC How to run java program in ubuntu How to find characters with the maximum number of times in a string java How to Set Java_home in Linux How to Split the String in Java with Delimiter How to take Multiple String Input in Java using Scanner class How to uninstall the Java in Ubuntu How to Update Java How to add Elements in Array in Java How to avoid deadlock in java How to Split String by Comma in Java How to remove special characters from String in Java How to remove last character from String in Java How to Read XML Files in Java How to download and install Eclipse in Windows How to Create an API in Java How to Round Double Float up to Two Decimal Places in Java How to create a mirror image of a 2D array in Java How to set timer in Java

Java 8 Features

Java 8 Features Lambda Expressions in Java Functional Interface in Java Streams in Java Java Base64 Encoding and Decoding Type Annotations in Java Java Stringjoiner Class Parallel Arrays Sort in Java Bifunction in java 8 Java 8 filters list Java 8 Consumer Interface in Java

Java 9 Features

Java 9 Tutorial Java 9 Try With Resources Java 9 Interface Private Method

Java 12

What’s new in Java 12

Java 13

Java 13 New Features

Java 14

New Features of Java 14

Java 15

What’s New in Java 15

Java 16

Java 16

Java 17

What is new in Java 17

Java Servlet Tutorial

Java Servlets Tutorial

Java JSP Tutorial

Java JSP Tutorial

Hiberate Tutorial

Hibernate Tutorial

Spring Tutorial

Spring Tutorial

Spring MVC Tutorial

Spring MVC Tutorial

Jenkins Tutorial

Jenkins Tutorial Jenkins java net socket connection time out

Java Math Methods

Math.abs() Math.acos() Math.addExact() Math.asin() Math.atan () Math.atan2() Math.cbrt() Math.ceil() Math.copysign() Math.cos() Math.cosh() Math.decrementExact() Math.exp() Math.expm1() Math.floor() Math.floorDiv() Math.floorMod() Math.fma() Math.getExponent() Math.hypot() Math.IEEEremainder() Math.incrementExact() Math.log() Math.log10() Math.log1p() Math.max() Math.min() Math.multiplyExact() Math.multiplyFull() Math.negateExact() Math.nextAfter() Math.nextDown() Math.nextUp() Math.pow() Math.random() Math.rint() Math.round() Math.scalb() Math.signum() Math.sin() Math.sinh() Math.sqrt() Math.subtractExact() Math.tan() Math.tanh() Math.toDegrees() Math.toIntExact() Math.toRadians() Math.ulp()

Java String Methods

toCharArray() copyValueOf() endsWith() equals() equalsIgnoreCase() format() getBytes() getChars() hashCode() indexOf() intern() isEmpty() join() lastIndexOf() length() replace() replaceAll() replaceFirst() split() startsWith() subSequence() substring() toLowerCase() toUpperCase() trim() valueOf()

Java Conversion

Java Convert String to int Java Convert int to String Java Convert String to long Java Convert long to String Java Convert String to float Java Convert float to String Java Convert String to double Java Convert double to String Java Convert String to Date Java Convert Date to String Java Convert String to Object Java Convert Object to String Java Convert String to char Java Convert char to String Java Convert int to long Java Convert long to int


List all files in a Directory in Java Nonagonal number in Java Null Pointer Exception in Java Package naming convention in Java Packages Program in java Pangram Program in Java PriorityBlockingQueue Class in Java Race Condition in Java Repdigit Numbers in Java Reserved Keywords in Java Rotate matrix by 90 degrees in Java Segment Tree in Java Sierpinski Number in Java Sort Dates in Java Thread Safety and How to Achieve it in Java Normal and Trace of a Matrix in Java Transient variable in Java Tribonacci series in Java Web Crawler in Java Zigzag Traversal of Binary Tree in Java Java Full Stack Java IO filenotfoundexception Java Output Formatting Java Plot Java Pop Java program to print matrix in Z form Java Set to List Java Switch string Java Thread Lifecycle: States and Stages Java Viva Questions and Answers Lazy Propagation in Segment Tree in Java Level order Traversal of a Binary Tree in Java Method chaining in Java Narcissistic Number in Java Java Case Keyword Java Try-Catch Block Java Class KeywordJava concurrency interview questions Java Continue Keyword Java CountDownLatch Java Default Keyword Java Double Keyword Java Editors Java Else Keyword Java Enum Keyword Java Extends keywordJava Finally Keyword Java Font Example of Static import in Java How Many Ways to Create Objects in Java Implementing Queue Using Array in Java Instanceof operator in Java Interchange Diagonal elements in Java Java Arrays Fill Java Char Keyword Convert list to array Java Convert milliseconds to date in Java Copy data/content from one file to another in java CRC Program in Java Creating a Jar file in Java Crown Pattern in Java Difference Between Access Specifiers and Modifiers in Java Difference Between Java and PHP Difference Between replace() and replaceall() in Java Duodecimal in Java Finding middle node of a linked list in Java Group by in Java 8 Hollow Diamond Pattern in Java How annotations work in Java Java Boyer Moore Catalan number in Java Cosmic Superclass in Java Difference between this and super in Java Fall through in Java Figurate Number in Java Java Anon Proxy Java RMI Lazy loading in Java Magnanimous Number in java Shallow copy in Java String to JSON in Java Tetranacci Number in Java Vigesimal in Java Why main method is static in Java Add Time in Java Bellman Ford Algorithm in Java Best Java Libraries Blockchain in Java Blocking Queue in Java Example Bully Algorithm code in Java Contextual keywords in Java Convert JSON File to String in Java Determine the Upper Bound of a Two-Dimensional Array in Java Web Service Response Time Calculation in Java Functional Interfaces in Java Singleton class in Java Awesome explanation of Strings in Java Object class in Java Static class in Java All the important string methods in Java String Handling Method in Java What are Array strings in Java Advantages and Disadvantages of Strings in Java Big Decimal class in Java Class definition in Java Replace character in string Java String Coding Interview Questions in Java What is String in Java? 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Recursion Program in Java

The recursion program in Java demonstrates the usage of recursion. The process by which a function/ method calls itself, again and again, is called recursion. Each recursive call is pushed to the stack. The function/ method upon which recursion calls are made is called the recursive method. Recursion is similar to iteration. However, recursion and iteration are not the same. The similarity is both recursion and iteration execute the same piece of code again and again. In a loop, there is a condition part that is responsible for the loop termination if evaluated as false. Whereas in recursion, there is a base case responsible for the termination of recursion. Before moving ahead in recursion, we must know the following two things:

1) The base case that will terminate the recursion.

2) Must know how to divide a bigger problem into smaller problems and then, dividing the smaller problems into even smaller subproblems and continue to do so until we reach the base case.

What is the base case?

A base case is a solution to a basic problem (elementary). That is, it cannot be further divided into a smaller problem. Let’s understand recursion by the factorial of a number.

Suppose we want to find the factorial of the number 5. Now, we split this problem into further smaller problems.

5! = 5 × 4!

Now, the problem is to find the factorial of 4, and this problem can also be reduced.

4! = 4 × 3!

Similarly, 3! is reduced to

3! = 3 × 2!

For 2! we have

2! = 2 × 1!

For 1! we have

1! = 1 × 0!

In Mathematics, 0! is defined as 1. Thus,

0! = 1

Now, we cannot reduce 0! to further smaller problems as the factorial of a negative number is not possible. Thus 0! = 1 is the base case of the factorial problem. The base case helps to break the recursion. In the absence of the base case, the recursion will keep on running infinitely and eventually result in the stack overflow. The stack overflow occurs because each recursive call consumes some memory (Remember! Each recursive call is pushed to the stack), and memory is limited, resulting in the stack overflow. Let’s see some applications of recursion.

Applications of Recursion

Some common applications of recursion are:

1) To find minimum value in an Array


 // importing the class Arrays
 import java.util.Arrays;
 public class MinimumValueExample 
 // Method for finding minimum element in the array   
 static int findMin(int inputArr[], int index, int size)
     // base case
     if(size == 1)
         return inputArr[index];
     // recursively solving the problem by diving it in the smaller problems
     return Math.min( inputArr[index], findMin(inputArr, index + 1, size - 1));
 public static void main(String argvs[]) 
     int numArr[] = { 27, 56, 90, 12, 120, 263 }; // input array
     // displaying the input array
     System.out.println("The input Array is : " + Arrays.toString(numArr));
     int length = numArr.length; // finding size of the input array
     int minVal = findMin(numArr, 0, length); // calling the method and storing its result
     // displaying the final outcome
     System.out.print("Minimum element of the input array is: " + minVal + " \n ");


 The input Array is : [27, 56, 90, 12, 120, 263]
 Minimum element of the input array is: 12 

Explanation: In the code, the method findMin() is recursively finding the minimum value element of the input array. In each recursive call, the method findMin() splits the larger array into the smaller array and keeps reducing the size of the array until the size of the input array is 1, i.e., there is only one element present in the array. If an array contains only one element, then that element is the minimum element. It forms the base case of the problem. Let’s learn how recursion work here.

In order to find the minimum value of the input array containing 6 elements, we can find the minimum value in the last 5 elements of the array and compare it with the first element. Suppose x is the minimum value of the last 5 elements, then compare x with the first element, i.e., 27. The minimum of x and 27 is our answer. The same thing is happening in the first recursive call. Mathematically,

Min of (27, 56, 90, 12, 120, 263) = Min of (27, Min of (56, 90 12, 120 263))

Similarly, for the second recursive call

Min of (27, Min of (56, 90 12, 120 263)) = Min of (27, Min of (56, Min of (90, 12, 120, 263)))

For the third recursive call

Min of (27, Min of (56, Min of (90, 12, 120, 263))) = Min of (27, Min of (56, Min of (90, Min of (12, 120, 263))))

For the fourth recursive call

Min of (27, Min of (56, Min of (90, Min of (12, 120, 263)))) = Min of (27, Min of (56, Min of (90, Min of (12, Min of (120, 263)))))

For the fifth recursive call

Min of (27, Min of (56, Min of (90, Min of (12, Min of (120, 263))))) = Min of (27, Min of (56, Min of (90, Min of (12, Min of (120, Min of (263))))))

Now we reach the base case, i.e., Min of (263), which is 263.

As each recursive call is pushed to the stack, therefore first, the last recursive call comes into the picture. It is because a stack works on the LIFO (Last In First Out) principle.

Thus, the fifth recursive call is reduced to

Min of(27, Min of(56, Min of(90, Min of(12, Min of(120, 263))))) = Min of(27, Min of(56, Min of(90, Min of(12, Min of(120, 263)))))

We know the min of 120 and 263 is 120. Thus, for the fourth recursive call, we have

Min of(27, Min of(56, Min of(90, Min of(12, 120, 263)))) = Min of(27, Min of(56, Min of(90, Min of(12, 120))))

Minimum of 12 and 120 is 12. Hence, for the third recursive call

Min of(27, Min of(56, Min of(90, 12, 120, 263))) = Min of(27, Min of(56, Min of(90, 12)))

Similarly, for the second recursive call, we have

Min of (27, Min of ( 56, 90 12, 120 263)) = Min of(27, 12)

Minimum of 27 and 12 is 12, eventually, for the first recursive call

Min of (27, 56, 90, 12, 120, 263) = 12.

Hence, 12 is the minimum value of the input array.

Note that the recursion used in the above program is called tail recursion. Because the recursive calls are the last statements in the findMin() method.

2) To print a string in reverse order


 public class ReverseStringExample
     // Method for printing the input string in the reverse order
     public static void reverseString(String str, int size, int index)
         // Handling the base case
         if(index == size)
         // recursively printing the string in the reverse order
         reverseString(str, size, index + 1);
         // Printing the string in reverse order
     public static void main(String argvs[])
         String s = "apple"; // input string
         int length = s.length(); // calculating length of the input string
         // calling the method reverseString
         reverseString(s, length, 0);



Explanation: In the above program, we have used the in-built stack that stores each recursive call to reverse the input string. The print statement coming after the recursive call is pushed to the stack. In the first recursive call, the value of the variable index is 0. Thus, the statement System.out.print(str.charAt(0)); gets pushed to the stack. The following diagram shows the same.

Recursion Program in Java

For the second recursive call, the value of the index is 1. Hence, the statement System.out.print(str.charAt(1)); gets pushed to stack. The current state of the stack after the second recursive call is:

Recursion Program in Java

For the third recursive call, index = 2. Thus, the updated state after the third recursive call is:

Recursion Program in Java

Similarly, for the fourth recursive call index = 3, and the stack stores four statements. As we have shown in the following diagram.

Recursion Program in Java

After the fifth and final recursive call, the stack contains five statements. Observe the following diagram.

Recursion Program in Java

After the fifth recursive call, the value of the index is 5. Thus, we meet the base case, and the recursion is terminated. Now, whatever statement is present in the stack gets executed one by one. Since a stack works on the LIFO principle, the statement System.out.print(str.charAt(4)); gets executed first. In the string apple, the character present at the 4th index is e. Thus, the letter e is printed first. Then, the statement System.out.print(str.charAt(3)); is executed and the letter l is printed. After that, the statement System.out.print(str.charAt(2)); is executed and the letter p is printed. Then, System.out.print(str.charAt(1)); prints the letter p, and eventually the letter a is printed. Thus, it prints elppa.

The recursion used in the above program is called head recursion. In the head recursion, the recursive statement is not the last statement of the method upon which recursion is called. In the code, after the recursion, there is a print statement.

Difference between Iteration and Recursion

Iteration is applicable to loops.

Recursion is applicable to methods.
Executes the code again and again until the condition part of the loop is evaluated as false.

Executes the code again and again until the base condition is met.
Memory consumption is less.Memory consumption is more as each recursive call is pushed to the stack.  
Time consumption is less.Time consumption is more because each recursive call takes some time.
Iteration can continue forever if the condition part of the loop is always true.If the base condition is not mentioned or not reached, the recursion stops due to stack overflow error.
Iteration is verbose. Hence, easy to understand.Recursion is not verbose. Hence, difficult to understand.

Which one to choose: Iteration or Recursion or both?

From the above table, one can conclude that iteration should take precedence over recursion, which is true to some extent but not always. There are many scenarios where writing code using the iterative approach becomes extremely difficult. For example, the Tower of Hanoi puzzle cannot be solved with the help of a loop.

Traversal of a tree is another example where recursion takes precedence over iteration. Thus, we observe that even though iteration is fast, knowing recursion is a must.

Recursion and iteration, when used together, are a deadly combination. There are many scenarios where it is not possible to solve the problem either using iteration or recursion. However, if recursion and iteration are both used simultaneously, we can solve the problem. One such example is to print the permutation of a string.

Permutation of a String

Suppose, we have a string abc. Then, the permutation of string abc is:

abc      acb      bac      bca      cab      cba

The approach is to fix the position of one of the letters of the given string at the first position and then do the permutation of the rest of the letters of the string. The steps involved to permute the letters of the string abc is given below.

Step 1: First, we fix the letter a at the first position. Then, the permutation of the remaining letters are: bc and cb. Hence, we get abc and acb. In order to achieve the permutations of b and c. First, we fix b at the second position and c at the third position to get bc. Then, c at the second position and b at the third position to get cb.

Step 2: Now, we fix letter b at the first position. Hence, the remaining letters are a and c, and their permutation is ac and ca. This time, we get bac and bca. The permutations of the letters a and c are done in the same way we did in step 1.

Step 3: Similarly, we fix c at the first position and do the permutation of the rest of the letters to get cab and cba.

The following diagram demonstrates the same.

Recursion Program in Java

In the diagram, if we look at the first three arrows, we see Swap(a, a), Swap(a, b), Swap(a, c) written on it. Swap(a, a) means; first, we have fixed the letter a at the first position. Swap(a, b) means b is fixed at the first position, and Swap(a, c) means c is fixed at the first position. In a similar way, whatever is written on the other arrows can also be explained.

Now, observe the following Java program.


 public class StringPermutation
     // for swapping characters of the input string
     public static String swap(String s, int i,  int j)
         // convreting the string into character array
         char[] ch = s.toCharArray();
         // swapping characters of the index i and j
         char t = ch[i];
         ch[i] = ch[j];
         ch[j] = t;
         // converting the character array into a new String
         String newString = new String(ch);
         //returning the new string
         return newString;
     // Method to find the permutation of the input string.
     // The method takes three arguments: first is the input string
     // second is the starting index, and third is the ending index
     public static void permuteString(String s, int st, int end)
         // Handling the base case
         if(st == end)
             System.out.println(s); // printing the string
         // iterating over every character of the input string
         for(int i = st; i <= end; i++)
             // In the first swap, we are
             // fixing the letters of the input string at the index st.
             String swappedString = swap(s, st, i);
             // recursive call for the next character
             permuteString(swappedString, st + 1, end);
             // second swap for doing backtracking to re-store
             // the state of string that was present before the recursive call
             swap(swappedString, st, i);
     public static void main(String argvs[])
         String str = "abc"; // input string
         int size = str.length(); // calculating length of the input string
         // calling the method permuteString()
         permuteString(str, 0, size - 1);



Explanation: In the above program, we see that the recursive call is placed between the two swap statements. The first swap is to fix the position of the letter at a particular index, and the second swap is to restore the state of the string before recursion. The above diagram also says the same. If we look at the first three arrows, we see that it is emerging from the same state of the string, i.e., abc. Each of these three arrows gives birth to two different states of the string abc. But the problem is if we have printed abc and acb, how can we print bac or bca. This is where the second swap comes to the rescue. The second swap reinstates the change, and eventually, we get the original string, i.e., abc from bca. Thus, first we moved from abc to bca and again from bca to abc, i.e., moving the reverse direction of the arrow mentioned in the diagram. This is called backtracking. After we got abc from acb, the first swap again acts on the abc and then we get bac and bca. A similar explanation for the strings cba and cab.