786. K-th Smallest Prime Fraction

You are given a sorted integer array `arr` containing `1` and prime numbers, where all the integers of `arr` are unique. You are also given an integer `k`.

For every `i` and `j` where `0 <= i < j < arr.length`, we consider the fraction `arr[i] / arr[j]`.

Return the `kth` smallest fraction considered. Return your answer as an array of integers of size `2`, where `answer == arr[i]` and `answer == arr[j]`.

Example 1:

```Input: arr = [1,2,3,5], k = 3
Output: [2,5]
Explanation: The fractions to be considered in sorted order are:
1/5, 1/3, 2/5, 1/2, 3/5, and 2/3.
The third fraction is 2/5.
```

Example 2:

```Input: arr = [1,7], k = 1
Output: [1,7]
```

Constraints:

• `2 <= arr.length <= 1000`
• `1 <= arr[i] <= 3 * 104`
• `arr == 1`
• `arr[i]` is a prime number for `i > 0`.
• All the numbers of `arr` are unique and sorted in strictly increasing order.
• `1 <= k <= arr.length * (arr.length - 1) / 2`

786. K-th Smallest Prime Fraction
``````struct Solution;
use std::cmp::Ord;
use std::cmp::Ordering;

use std::collections::BinaryHeap;

struct Fraction(i32, i32, usize, usize);

impl PartialEq for Fraction {
fn eq(&self, other: &Self) -> bool {
self.0 * other.1 == self.1 * other.0
}
}

impl Eq for Fraction {}

impl PartialOrd for Fraction {
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}

impl Ord for Fraction {
fn cmp(&self, other: &Self) -> Ordering {
(self.1 * other.0).cmp(&(self.0 * other.1))
}
}

impl Solution {
fn kth_smallest_prime_fraction(a: Vec<i32>, k: i32) -> Vec<i32> {
let mut queue: BinaryHeap<Fraction> = BinaryHeap::new();
let n = a.len();
let k = k as usize;
for i in 0..n {
queue.push(Fraction(a[i], a[n - 1], i, n - 1));
}
for _ in 0..k - 1 {
let f = queue.pop().unwrap();
if f.3 - 1 > f.2 {
queue.push(Fraction(a[f.2], a[f.3 - 1], f.2, f.3 - 1));
}
}
let f = queue.pop().unwrap();
vec![f.0, f.1]
}
}

#[test]
fn test() {
let a = vec![1, 2, 3, 5];
let k = 3;
let res = vec![2, 5];
assert_eq!(Solution::kth_smallest_prime_fraction(a, k), res);
let a = vec![1, 7];
let k = 1;
let res = vec![1, 7];
assert_eq!(Solution::kth_smallest_prime_fraction(a, k), res);
}
``````