Find Last Digit of a^b for Large Numbers in C++

In this problem, we are given two numbers a and b. Our task is to find Last Digit of a^b for Large Numbers. 

Let’s take an example to understand the problem, 

Input: a = 4 b = 124

Output: 6

Explanation: 

The value of a^b is 4.523128486 * 10⁷⁴

Solution Approach

The solution to the problem is based on the fact that all the exponents of a number will be repeated after 4 exponent values.

So, we will find the value of b%4. Also, for any base value, the last digit of its power is decided by the last digit of the base value.

So, the resultant value will be calculated as

Last value of a  ^ (b%4)

Program to illustrate the working of our solution,

Example

Live Demo

#include <bits/stdc++.h>
using namespace std;

int calcModulus(char b[], int a)
{
   int mod = 0;

   for (int i = 0; i < strlen(b); i++)
      mod = (mod * 10 + b[i] - '0') % a;

   return mod;
}

int calcLastDigitInExpo(char a[], char b[]) {

   int len_a = strlen(a), len_b = strlen(b);

   if (len_a == 1 && len_b == 1 && b[0] == '0' && a[0] == '0')
      return 1;
   if (len_b == 1 && b[0] == '0')
      return 1;
   if (len_a == 1 && a[0] == '0')
      return 0;

   int exponent = (calcModulus(b, 4) == 0) ? 4 : calcModulus(b, 4);
   int base = a[len_a - 1] - '0';
   int result = pow(base, exponent);
   return result % 10;
}

int main()
{
   char a[] = "559", b[] = "4532";
   cout<<"The last digit in of the value is "<<calcLastDigitInExpo(a, b);
   return 0;
}

Output

The last digit in of the value is 1

Sudhir sharma

Published on 25-Jan-2021 04:58:24

• Related Questions & Answers
• Find the last digit when factorial of A divides factorial of B in C++
• Find the sum of first and last digit for a number using C language
• C++ Program to Find Factorial of Large Numbers
• Print all 3 digit repeating numbers in a very large number in C++
• Find (a^b)%m where ‘a’ is very large in C++
• Count of Numbers in Range where first digit is equal to last digit of the number in C++
• Sum of two large numbers in C++
• Divisible by 37 for large numbers in C++ Program
• Large Fibonacci Numbers in C#
• Handling large numbers in C++?
• Program to find last digit of n’th Fibonnaci Number in C++
• Find N % (Remainder with 4) for a large value of N in C++
• Find last five digits of a given five digit number raised to power five in C++
• Find numbers a and b that satisfy the given condition in C++
• Find records with a specific last digit in column with MySQL