// Example: 145 = 1! + 4! + 5! = 1 + 24 + 120 = 145
// Function to compute the factorial of a number
fn factorial(n: u32) -> u32 {
let mut fact = 1;
for i in 2..=n {
fact *= i;
}
fact
}
// Function to find all numbers equal to the sum of the factorials of their digits
fn find_digit_factorial_numbers() {
// Precompute factorials of digits 0-9
let factorials: Vec<u32> = (0..=9).map(factorial).collect();
// Define an upper limit (7 * 9! is a safe limit for this problem)
let upper_limit = 7 * factorials[9];
// Iterate through all numbers and check the condition
for num in 10..=upper_limit {
let mut sum = 0;
let mut temp = num;
// Calculate the sum of factorials of digits
while temp > 0 {
let digit = temp % 10;
sum += factorials[digit as usize];
temp /= 10;
}
// Check if the number equals the sum of the factorials of its digits
if sum == num {
println!("{} is a digit factorial number.", num);
}
}
}
fn main() {
find_digit_factorial_numbers();
}
/*
run:
145 is a digit factorial number.
40585 is a digit factorial number.
*/
