README.md

719. Find K-th Smallest Pair Distance

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 1st 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

Solutions (Python)

1. Solution

class Solution:
    def smallestDistancePair(self, nums: List[int], k: int) -> int:
        nums.sort()

        lo = 0
        hi = nums[-1] - nums[0]

        while lo < hi:
            mid = (lo + hi) // 2
            count = 0

            for i in range(len(nums)):
                j = bisect.bisect(nums, nums[i] + mid, lo=i + 1)
                count += j - i - 1

            if count < k:
                lo = mid + 1
            else:
                hi = mid

        return hi