Find (a^b)%m where ‘a’ is very large in C++

In this tutorial, we are going to solve the equation (a^b)%m? where a is a very large number.

The equation (a^b)%m=(a%m)*(a%m)...b_times. We can solve the problem by finding the value of a%m and then multiplying it b? times.

Let's see the steps to solve the problem.

• Initialize the numbers a, b, and m.

• Write a function to find the a%m?.

  • Initialize the number with 0.

  • Iterate over the number in string format.

  • Add the last digits to the number.

  • Update the number with number modulo them.

• Get the value of a%m?.

• Write a loop that iterates b times.

  • Multiply the a%m? and modulo the result with m.

• Print the result.

Example

Let's see the code.

 Live Demo

#include<bits/stdc++.h>
using namespace std;
unsigned int aModm(string str, unsigned int mod) {
   unsigned int number = 0;
   for (unsigned int i = 0; i < str.length(); i++) {
      number = number * 10 + (str[i] - '0');
      number %= mod;
   }
   return number;
}
unsigned int aPowerBmodM(string &a, unsigned int b, unsigned int m) {
   unsigned int a_mod_m_result = aModm(a, m);
   unsigned int final_result = 1;
   for (unsigned int i = 0; i < b; i++) {
      final_result = (final_result * a_mod_m_result) % m;
   }
   return final_result;
}
int main() {
   string a = "123456789012345678901234567890123";
   unsigned int b = 3, m = 7;
   cout << aPowerBmodM(a, b, m) << endl;
   return 0;
}

Output

If you execute the above program, then you will get the following result.

1

Conclusion

If you have any queries in the tutorial, mention them in the comment section.