Leetcode #2616: Minimize the Maximum Difference of Pairs
In this guide, we solve Leetcode #2616 Minimize the Maximum Difference of Pairs 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
You are given a 0-indexed integer array nums and an integer p. Find p pairs of indices of nums such that the maximum difference amongst all the pairs is minimized.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Binary Search, Dynamic Programming, Sorting
Intuition
The problem structure suggests a monotonic decision, which makes binary search a natural fit.
By halving the search space each step, we reach the answer efficiently.
Approach
Search either directly on a sorted array or on the answer space using a check function.
Each check is fast, and the logarithmic search keeps the overall runtime low.
Steps:
- Define the search bounds.
- Check the mid point condition.
- Narrow the bounds until convergence.
Example
Input: nums = [10,1,2,7,1,3], p = 2
Output: 1
Explanation: The first pair is formed from the indices 1 and 4, and the second pair is formed from the indices 2 and 5.
The maximum difference is max(|nums[1] - nums[4]|, |nums[2] - nums[5]|) = max(0, 1) = 1. Therefore, we return 1.
Python Solution
class Solution:
def minimizeMax(self, nums: List[int], p: int) -> int:
def check(diff: int) -> bool:
cnt = i = 0
while i < len(nums) - 1:
if nums[i + 1] - nums[i] <= diff:
cnt += 1
i += 2
else:
i += 1
return cnt >= p
nums.sort()
return bisect_left(range(nums[-1] - nums[0] + 1), True, key=check)
Complexity
The time complexity is , where is the length of and is the difference between the maximum and minimum values in . The space complexity is .
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.