README.md

313. Super Ugly Number

Write a program to find the nth super ugly number.

Super ugly numbers are positive numbers whose all prime factors are in the given prime list primes of size k.

Example:

Input: n = 12, primes = [2,7,13,19]
Output: 32
Explanation: [1,2,4,7,8,13,14,16,19,26,28,32] is the sequence of the first 12 
             super ugly numbers given primes = [2,7,13,19] of size 4.

Note:

• 1 is a super ugly number for any given primes.
• The given numbers in primes are in ascending order.
• 0 < k ≤ 100, 0 < n ≤ 10⁶, 0 < primes[i] < 1000.
• The n^th super ugly number is guaranteed to fit in a 32-bit signed integer.

Solutions (Rust)

1. Dynamic Programming

impl Solution {
    pub fn nth_super_ugly_number(n: i32, primes: Vec<i32>) -> i32 {
        let mut uglys = vec![1];
        let mut points = vec![0; primes.len()];

        for _ in 1..n {
            let mut min_ugly = primes[0] * uglys[points[0]];
            for i in 1..points.len() {
                min_ugly = min_ugly.min(primes[i] * uglys[points[i]]);
            }

            uglys.push(min_ugly);

            for i in 0..points.len() {
                if primes[i] * uglys[points[i]] == min_ugly {
                    points[i] += 1;
                }
            }
        }

        uglys[n as usize - 1]
    }
}