# Java Program to Reverse a Number using Recursion

Here is a Java program to reverse a number using recursion. To reverse a number we have to reverse the the sequence of digits in a number. After reversing, least significant digit(right most digit) will become most significant digit() of number and most significant digit becomes least significant digit and so on.

For Example:
Befor reverse : 745362
After reverse : 263547
Here, we will reverse the digits of of a number using reversion using below mentioned recursive equation.

```getReversedNumber(N) = lastDigitOf(N) x power(10, numberOfDigits(N/10))
+ getReversedNumber(N/10)
```
Gere is the detailed explanation of above algorithm.
Algorithm to reverse a number using recursion
• lastDigitOf(N) : This function returns the least significant digit of N. For Example :lastDigitOf(1234) = 4.

• power(A, B) : This function returns the value of AB. For Example: power(2,4) = 16.

• numberOfDigits(N) : This function returns the number of digits in N. log10(N) + 1, gives us the number of digits in N. For Example: numberOfDigits(1234) = log10(1234) + 1 = 4

• getReversedNumber(N) = This is a recursive function, which reverses the sequence of digits of N and returns it to the caller function.
##### For Example
• getReversedNumber(1234) = lastDigitOf(1234) x power(10, numberOfDigits(1234/10)) + getReversedNumber(1234/10)
• getReversedNumber(1234) = 4 x power(10, numberOfDigits(123)) + getReversedNumber(123)
• getReversedNumber(1234) = 4 x power(10, 3) + 321
• getReversedNumber(1234) = 4 x 1000 + 321
• getReversedNumber(1234) = 4321

• ## Java program Reverse digits of a number using recursion

```package com.tcc.java.programs;

import java.io.*;
import java.util.*;

public class ReverseNumberRecursion {
public static void main(String[] args) {
int number=0;
System.out.println("Input an Integer");
Scanner in = new Scanner(System.in);
number = in.nextInt();
System.out.print("Reversed Number : " + reverse(number));
}

public static int reverse(int number) {
int lastDigit, numberOfDigits, sign = 1;

if(number < 0){
number = number * -1;
sign = -1;
}
if(number < 10)
return number*sign;

lastDigit = number % 10;
number = number / 10;
/* log10(number) + 1 gives number of digits in number */
numberOfDigits = (int) (Math.log10((double)number) + 1);

return (int)(lastDigit*Math.pow((double)10,(doublumberOfDigits)
+ reverse(number)) * sign;
}
}
```
Output
```Input an Integer
435203
Reversed Number : 302534
```
```Input an Integer
4
Reversed Number : 4
```

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