# Find K-Th Smallest Pair Distance Problem

## Description

LeetCode Problem 719.

The distance of a pair of integers a and b is defined as the absolute difference between a and b. Given an integer array nums and an integer k, return the k^th smallest distance among all the pairs nums[i] and nums[j] where 0 <= i < j < nums.length.

Example 1:

``````1
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Input: nums = [1,3,1], k = 1
Output: 0
Explanation: Here are all the pairs:
(1,3) -> 2
(1,1) -> 0
(3,1) -> 2
Then the 1^st smallest distance pair is (1,1), and its distance is 0.
``````

Example 2:

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Input: nums = [1,1,1], k = 2
Output: 0
``````

Example 3:

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Input: nums = [1,6,1], k = 3
Output: 5
``````

Constraints:

• n == nums.length
• 2 <= n <= 10^4
• 0 <= nums[i] <= 10^6
• 1 <= k <= n * (n - 1) / 2

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class Solution {
public:
int smallestDistancePair(vector<int>& nums, int k) {
sort(nums.begin(), nums.end());
int n = nums.size(), low = 0, high = 1000000;
while (low < high) {
int mid = (low + high) / 2, cnt = 0;
for (int i = 0, j = 0; i < n; i++) {
while (j < n && nums[j]-nums[i] <= mid) j++;
cnt += j - i - 1;
}
if (cnt < k)
low = mid + 1;
else
high = mid;
}
return low;
}
};
``````