1726. Tuple with Same Product

Given an array nums of distinct positive integers, return the number of tuples (a, b, c, d) such that a * b = c * d where a, b, c, and d are elements of nums, and a != b != c != d.

 

Example 1:

Input: nums = [2,3,4,6]
Output: 8
Explanation: There are 8 valid tuples:
(2,6,3,4) , (2,6,4,3) , (6,2,3,4) , (6,2,4,3)
(3,4,2,6) , (4,3,2,6) , (3,4,6,2) , (4,3,6,2)

Example 2:

Input: nums = [1,2,4,5,10]
Output: 16
Explanation: There are 16 valids tuples:
(1,10,2,5) , (1,10,5,2) , (10,1,2,5) , (10,1,5,2)
(2,5,1,10) , (2,5,10,1) , (5,2,1,10) , (5,2,10,1)
(2,10,4,5) , (2,10,5,4) , (10,2,4,5) , (10,2,4,5)
(4,5,2,10) , (4,5,10,2) , (5,4,2,10) , (5,4,10,2)

Example 3:

Input: nums = [2,3,4,6,8,12]
Output: 40

Example 4:

Input: nums = [2,3,5,7]
Output: 0

 

Constraints:

  • 1 <= nums.length <= 1000
  • 1 <= nums[i] <= 104
  • All elements in nums are distinct.

Rust Solution

struct Solution;

use std::collections::HashMap;

impl Solution {
    fn tuple_same_product(nums: Vec<i32>) -> i32 {
        let mut count: HashMap<i32, usize> = HashMap::new();
        let n = nums.len();
        let mut res = 0;
        for i in 0..n {
            for j in i + 1..n {
                let product = nums[i] * nums[j];
                let x = count.entry(product).or_default();
                res += *x;
                *x += 1;
            }
        }
        res as i32 * 8
    }
}

#[test]
fn test() {
    let nums = vec![2, 3, 4, 6];
    let res = 8;
    assert_eq!(Solution::tuple_same_product(nums), res);
    let nums = vec![1, 2, 4, 5, 10];
    let res = 16;
    assert_eq!(Solution::tuple_same_product(nums), res);
    let nums = vec![2, 3, 4, 6, 8, 12];
    let res = 40;
    assert_eq!(Solution::tuple_same_product(nums), res);
    let nums = vec![2, 3, 5, 7];
    let res = 0;
    assert_eq!(Solution::tuple_same_product(nums), res);
}

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