Sum of digits of N to the power P - c++

Question

My C++ code is supposed to take a number and an exponent as integer inputs, calculate the 'number' to the power of THAT 'exponent' and sum the digits of the result and output it. It works well for small exponent values like 10 or 20, but gives wrong answers for large values like ~ >500. I have limited my 'number' inputs to <5 for wease of computability. I cannot figure out what is wrong with my logic.
#include<iostream>
using namespace std;
#include <cmath>
int main(){
int number, exponent;
cin >> number >> exponent;
double product = 1;
int sum = 0;
// Write your code here
for (int i = 0; i < exponent; i++){
product = product * number;
}
cout << "THE MAIN PRODUCT IS: " << product << "\n\n";
while (product > 1){
sum = sum + fmod(product, 10.0); // kEEP ADDING THE DIGITS TO THE SUM
cout << "sum is " << sum << endl;
product = product / 10.000;
cout << "product is " << product << endl;
}
cout << endl;
cout << sum << endl;
}

Answer 1

The issue with a large exponent is the length of the final answer or the number of digits in the final answer.
In C++, the largest integer that can be represented is 18-19 digits.
If the number exceeds beyond a limit, it will cause an integer overflow.
So, the best way to tackle this problem is to make use of strings or integer arrays.
Have a look at the following implementation:
#include <iostream>
#include <math.h>
// Maximum number of digits in
// output
#define MAX 100000
int multiply(int x, int res[], int res_size) {
// Initialize carry
int carry = 0;
// One by one multiply n with
// individual digits of res[]
for (int i = 0; i < res_size; i++) {
int prod = res[i] * x + carry;
// Store last digit of
// 'prod' in res[]
res[i] = prod % 10;
// Put rest in carry
carry = prod / 10;
}
// Put carry in res and
// increase result size
while (carry) {
res[res_size] = carry % 10;
carry = carry / 10;
res_size++;
}
return res_size;
}
// This function finds
// power of a number x
long long power(int x, int n)
{
//printing value "1" for power = 0
if(n == 0 ){
return 1;
}
int res[MAX];
int res_size = 0;
int temp = x;
// Initialize result
// Representing base in reverse form
while (temp != 0) {
res[res_size++] = temp % 10;
temp = temp / 10;
}
// Multiply x n times
// (x^n = x*x*x....n times)
for (int i = 2; i <= n; i++)
res_size = multiply(x, res, res_size);
long long final_answer = 0;
//Finally taking sum of all the digits in the answer.
for(int i=0;i<res_size; i++){
final_answer += res[i];
}
return final_answer;
}
int main() {
int exponent = 8;
int base = 34;
std::cout<<power(base, exponent);
return 0;
}
Output:
76