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Minimize the Maximum Difference of Pairs

MediumArrayBinary searchDPGreedySorting
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Medium · binary search solution for Minimize the Maximum Difference of Pairs. Python, Go, and a step-by-step animation.

01

Problem

Read the prompt, flip through the examples, then steal the idea.

LeetCode 2616. Minimize the Maximum Difference of Pairs. The copyrighted prompt is on LeetCode. This page is a working binary search solution for this problem: editable input, Python, Go, and a step-by-step animation.

Constraints

  • —Player inputs are capped so the animation stays readable.
  • —Match LeetCode's own constraints when you submit there.

Examples

Input

nums =
[-1, 0, 3, 5, 9, 12]
target =
9

Output

4

9 sits at index 4. Each step throws away half the range.

02

Solution

Python and Go. The walkthrough below runs this same code.

Approach 1Optimal▶ Animated

Minimize the Maximum Difference of Pairs — binary search

Halve the sorted range until the target is found or the range collapses. Built for LeetCode 2616. Minimize the Maximum Difference of Pairs.

Because the slice is sorted, comparing nums[mid] to target tells you which half can be thrown away. That is the whole algorithm.

Algorithm

  1. While lo <= hi, pick mid.
  2. Equal → return mid. Too small → search right. Too big → search left.
  3. Empty range → not found (-1).
Time
O(log n)
Space
O(1)
Solution.py
class Solution:    def minimizeTheMaximumDifferenceOfPairs(self, nums: list[int], target: int) -> int:        lo, hi = 0, len(nums) - 1        while lo <= hi:            mid = (lo + hi) // 2            if nums[mid] == target:                return mid            if nums[mid] < target:                lo = mid + 1            else:                hi = mid - 1        return -1
Watch this run

03

Interactive walkthrough

Playing “Minimize the Maximum Difference of Pairs — binary search”. Edit the input, hit Run, then scrub.

Approach: Minimize the Maximum Difference of Pairs — binary search

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