#include <iostream>
#include <vector>
// Example: 145 = 1! + 4! + 5! = 1 + 24 + 120 = 145
// Function to compute the factorial of a number
int factorial(int n) {
int fact = 1;
for (int i = 2; i <= n; i++) {
fact *= i;
}
return fact;
}
// Function to find all numbers equal to the sum of the factorials of their digits
void findDigitFactorialNumbers() {
// Precompute factorials of digits 0-9
std::vector<int> factorials(10);
for (int i = 0; i <= 9; i++) {
factorials[i] = factorial(i);
}
// Define an upper limit (7 * 9! is a safe limit for this problem)
const int upperLimit = 7 * factorials[9];
// Iterate through all numbers and check the condition
for (int num = 10; num <= upperLimit; num++) {
int sum = 0, temp = num;
// Calculate the sum of factorials of digits
while (temp > 0) {
int digit = temp % 10;
sum += factorials[digit];
temp /= 10;
}
// Check if the number equals the sum of the factorials of its digits
if (sum == num) {
std::cout << num << " is a digit factorial number." << std::endl;
}
}
}
int main() {
findDigitFactorialNumbers();
}
/*
run:
145 is a digit factorial number.
40585 is a digit factorial number.
*/
