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:

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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;
    }
};




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