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K-th digit in ‘a’ raised to power ‘b’
  • Difficulty Level : Easy
  • Last Updated : 11 May, 2018

Given three numbers a, b and k, find k-th digit in ab from right side

Examples:

Input : a = 3, b = 3, 
        k = 1
Output : 7
Explanation
3^3 = 27 for k = 1. First digit is 7 in 27

Input : a = 5, b = 2, 
        k = 2
Output : 2
Explanation
5^2 = 25 for k = 2. First digit is 2 in 25

Method
1) Compute a^b
2) Iteratively remove the last digit until k-th digit is not meet

C++




// CPP program for finding k-th digit in a^b
#include <bits/stdc++.h>
using namespace std;
  
// To compute k-th digit in a^b
int kthdigit(int a, int b, int k)
{
    // computing a^b
    int p = pow(a, b);
  
    int count = 0;
    while (p > 0 && count < k) {
  
        // getting last digit
        int rem = p % 10;
  
        // increasing count by 1
        count++;
  
        // if current number is required digit
        if (count == k)
            return rem;
  
        // remove last digit
        p = p / 10;
    }
  
    return 0;
}
  
// Driver code
int main()
{
    int a = 5, b = 2;
    int k = 1;
    cout << kthdigit(a, b, k);
    return 0;
}


Java




// Java program for finding k-th digit in a^b
import java.util.*;
import java.lang.*;
  
public class GfG {
    // To compute k-th digit in a^b
    public static int kthdigit(int a, int b, int k)
    {
        // Computing a^b
        int p = (int)Math.pow(a, b);
  
        int count = 0;
        while (p > 0 && count < k) {
  
            // Getting last digit
            int rem = p % 10;
  
            // Increasing count by 1
            count++;
  
            // If current number is required digit
            if (count == k)
                return rem;
  
            // Remove last digit
            p = p / 10;
        }
  
        return 0;
    }
      
    // Driver Code 
    public static void main(String argc[]) {
        int a = 5, b = 2;
        int k = 1;
        System.out.println(kthdigit(a, b, k));
    }
      
}
  
// This code is contributed by Sagar Shukla.


Python3




# Python3 code to compute k-th 
# digit in a^b
def kthdigit(a, b, k):
      
    # computin a^b in python
    p = a ** b
    count = 0
      
    while (p > 0 and count < k):
          
        # getting last digit
        rem = p % 10
  
        # increasing count by 1
        count = count + 1
  
        # if current number is 
        # required digit
        if (count == k):
            return rem
  
        # remove last digit
        p = p / 10;
      
# driver code    
a = 5
b = 2
k = 1
ans = kthdigit(a, b, k)
print (ans)
  
# This code is contributed by Saloni Gupta


C#




// C# program for finding k-th digit in a^b
using System;
  
public class GfG {
      
    // To compute k-th digit in a^b
    public static int kthdigit(int a, int b, int k)
    {
        // Computing a^b
        int p = (int)Math.Pow(a, b);
  
        int count = 0;
        while (p > 0 && count < k) {
  
            // Getting last digit
            int rem = p % 10;
  
            // Increasing count by 1
            count++;
  
            // If current number is required digit
            if (count == k)
                return rem;
  
            // Remove last digit
            p = p / 10;
        }
  
        return 0;
    }
      
    // Driver Code 
    public static void Main() {
        int a = 5, b = 2;
        int k = 1;
        Console.WriteLine(kthdigit(a, b, k));
    }
      
}
  
// This code is contributed by vt_m.


PHP




<?php
// PHP program for finding 
// k-th digit in a^b
  
// To compute k-th 
// digit in a^b
function kthdigit($a, $b, $k)
{
      
    // computing a^b
    $p = pow($a, $b);
  
    $count = 0;
    while ($p > 0 and $count < $k)
    {
  
        // getting last digit
        $rem = $p % 10;
  
        // increasing count by 1
        $count++;
  
        // if current number is
        // required digit
        if ($count == $k)
            return $rem;
  
        // remove last digit
        $p = $p / 10;
    }
  
    return 0;
}
  
    // Driver Code
    $a = 5;
    $b = 2;
    $k = 1;
    echo kthdigit($a, $b, $k);
  
// This code is contributed by anuj_67.
?>



Output:

5

How to avoid overflow?
We can find power under modulo 10sup>k to avoid overflow. After finding the power under modulo, we need to return first digit of the power.

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