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 nth super ugly number is guaranteed to fit in a 32-bit signed integer.

Rust Solution

struct Solution;
use std::cmp::Reverse;
use std::collections::BinaryHeap;
use std::collections::HashSet;

impl Solution {
    fn nth_super_ugly_number(mut n: i32, primes: Vec<i32>) -> i32 {
        let mut queue: BinaryHeap<Reverse<i32>> = BinaryHeap::new();
        let mut visited: HashSet<i32> = HashSet::new();
        queue.push(Reverse(1));
        while n > 1 {
            let min = queue.pop().unwrap().0;
            for &x in &primes {
                if let Some(y) = x.checked_mul(min) {
                    if visited.insert(y) {
                        queue.push(Reverse(y));
                    }
                }
            }
            n -= 1;
        }
        queue.pop().unwrap().0
    }
}

#[test]
fn test() {
    let n = 12;
    let primes = vec![2, 7, 13, 19];
    let res = 32;
    assert_eq!(Solution::nth_super_ugly_number(n, primes), res);
}

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