LeetCode-in-Java

719. Find K-th Smallest Pair Distance

Hard

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 kth smallest distance among all the pairs nums[i] and nums[j] where 0 <= i < j < nums.length.

Example 1:

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:

Input: nums = [1,1,1], k = 2

Output: 0

Example 3:

Input: nums = [1,6,1], k = 3

Output: 5

Constraints:

• n == nums.length
• 2 <= n <= 104
• 0 <= nums[i] <= 106
• 1 <= k <= n * (n - 1) / 2

Solution

import java.util.Arrays;

public class Solution {
    public int smallestDistancePair(int[] nums, int k) {
        Arrays.sort(nums);
        int length = nums.length;
        int maxDiff = nums[length - 1] - nums[0];
        int start = 0;
        int end = maxDiff;
        while (start < end) {
            int mid = start + (end - start) / 2;
            if (isPair(nums, mid, k)) {
                end = mid;
            } else {
                start = mid + 1;
            }
        }
        return start;
    }

    private boolean isPair(int[] nums, int mid, int k) {
        int count = 0;
        int i = 0;
        for (int j = 1; j < nums.length; j++) {
            while (nums[j] - nums[i] > mid) {
                i++;
            }
            count += j - i;
        }
        return (count >= k);
    }
}

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