problem 34

/*145 is a curious number, as 1! + 4! + 5! = 1 + 24 + 120 = 145.

Find the sum of all numbers which are equal to the sum of the factorial of their digits.

Note: as 1! = 1 and 2! = 2 are not sums they are not included.
*/

#include <iostream>
#include<string>

using namespace std;

int factorial(int num){
  int  factorial[] = {1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880};
  return factorial[num];
}

int factorial_digits(int num){
  int total_fact = 0; 
  while(num){
    int first = num % 10;
    total_fact += factorial(first);
    num = num / 10;
  }
  return total_fact;
}

int main(){
 int sum_of_all_curious = 0;
 const int LIMIT = 100000;
 for(int num = 10; num < LIMIT; num++){
   int result = factorial_digits(num);
   if(result == num){
    sum_of_all_curious += result;
   }
  }
  cout << sum_of_all_curious <<endl;
  return 0;
}