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Find K-th Smallest Pair Distance

Given an integer array, return the k-th smallest distance among all the pairs. The distance of a pair (A, B) is defined as the absolute difference between A and B.



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 1st smallest distance pair is (1,1), and its distance is 0.


Note:

  1. 2 <= len(nums) <= 10000.

  2. 0 <= nums[i] < 1000000.

  3. 1 <= k <= len(nums) * (len(nums) - 1) / 2.

Solution:

class Solution {
    public int smallestDistancePair(int[] nums, int k) {
        Arrays.sort(nums);
        int left=0;
        int right = nums[nums.length-1]-nums[0];
        while(left<right)
        {
            int mid=(left+right)/2;
            if(issmallpairs(nums,k,mid))
                right=mid;
            else
                left=mid+1;
        }
        return left;
    }
    
    private boolean issmallpairs(int[] nums,int k,int mid)
    {
        int count=0, left=0;
        for(int right=1;right<nums.length;right++)
        {
            while(nums[right]-nums[left]>mid) left++;
            count+=right-left;
        }
        return (count>=k);
    }
}

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