3649 - Number of Perfect Pairs.

Medium

You are given an integer array nums.

A pair of indices (i, j) is called perfect if the following conditions are satisfied:

• i < j

• Let a = nums[i], b = nums[j]. Then:

Return the number of distinct perfect pairs.

Note: The absolute value |x| refers to the non-negative value of x.

Example 1:

Input: nums = 0,1,2,3

Output: 2

Explanation:

There are 2 perfect pairs:

| (i, j) | (a, b) | min(|a − b|, |a + b|) | min(|a|, |b|) | max(|a − b|, |a + b|) | max(|a|, |b|) | |----------|-----------|-------------------------------------|-----------------|-------------------------------------|-----------------| | (1, 2) | (1, 2) | min(|1 − 2|, |1 + 2|) = 1 | 1 | max(|1 − 2|, |1 + 2|) = 3 | 2 | | (2, 3) | (2, 3) | min(|2 − 3|, |2 + 3|) = 1 | 2 | max(|2 − 3|, |2 + 3|) = 5 | 3 |

Example 2:

Input: nums = -3,2,-1,4

Output: 4

Explanation:

There are 4 perfect pairs:

| (i, j) | (a, b) | min(|a − b|, |a + b|) | min(|a|, |b|) | max(|a − b|, |a + b|) | max(|a|, |b|) | |----------|-----------|-----------------------------------------------|-----------------|-----------------------------------------------|-----------------| | (0, 1) | (-3, 2) | min(|-3 - 2|, |-3 + 2|) = 1 | 2 | max(|-3 - 2|, |-3 + 2|) = 5 | 3 | | (0, 3) | (-3, 4) | min(|-3 - 4|, |-3 + 4|) = 1 | 3 | max(|-3 - 4|, |-3 + 4|) = 7 | 4 | | (1, 2) | (2, -1) | min(|2 - (-1)|, |2 + (-1)|) = 1 | 1 | max(|2 - (-1)|, |2 + (-1)|) = 3 | 2 | | (1, 3) | (2, 4) | min(|2 - 4|, |2 + 4|) = 2 | 2 | max(|2 - 4|, |2 + 4|) = 6 | 4 |

Example 3:

Input: nums = 1,10,100,1000

Output: 0

Explanation:

There are no perfect pairs. Thus, the answer is 0.

Constraints:

• <code>2 <= nums.length <= 10⁵</code>

• <code>-10⁹<= numsi<= 10⁹</code>