Leetcode #719: Find K-th Smallest Pair Distance
In this guide, we solve Leetcode #719 Find K-th Smallest Pair Distance in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
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.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Two Pointers, Binary Search, Sorting
Intuition
The constraints hint that we can reason about two ends of the data at once, which is perfect for a two-pointer scan.
Moving one pointer at a time keeps the invariant intact and avoids nested loops.
Approach
Place pointers at the left and right ends and move them based on the comparison or target condition.
This yields a clean linear pass after any required sorting.
Steps:
- Set left and right pointers.
- Move a pointer based on the condition.
- Update the best answer while scanning.
Example
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.
Python Solution
class Solution:
def smallestDistancePair(self, nums: List[int], k: int) -> int:
def count(dist):
cnt = 0
for i, b in enumerate(nums):
a = b - dist
j = bisect_left(nums, a, 0, i)
cnt += i - j
return cnt
nums.sort()
return bisect_left(range(nums[-1] - nums[0]), k, key=count)
Complexity
The time complexity is O(n) (after optional sort O(n log n)). The space complexity is O(1).
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.