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How to Solve Maximize the Distance Between Points on a Square Problem
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Hard#3464
LeetCode ProblemMaximize the Distance Between Points on a Square
You are given an integer side, representing the edge length of a square with corners at (0, 0), (0, side), (side, 0), and (side, side) on a Cartesian plane. You are also given a positive integer k and a 2D integer array points, where points[i] = [xi, yi] represents the coordinate of a point lying on the boundary of the square. You need to select k elements among points such that the minimum Manhattan distance between any two points is maximized. Return the maximum possible minimum Manhattan distance between the selected k points. The Manhattan Distance between two cells (xi, yi) and (xj, yj) is |xi - xj| + |yi - yj|.
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Problem Breakdown
Understanding the Maximize the Distance Between Points on a Square Problem
Let's break down this LeetCode problem and understand what makes it challenging in interview settings.
Problem Statement
You are given an integer side, representing the edge length of a square with corners at (0, 0), (0, side), (side, 0), and (side, side) on a Cartesian plane. You are also given a positive integer k and a 2D integer array points, where points[i] = [xi, yi] represents the coordinate of a point lying on the boundary of the square. You need to select k elements among points such that the minimum Manhattan distance between any two points is maximized. Return the maximum possible minimum Manhattan distance between the selected k points. The Manhattan Distance between two cells (xi, yi) and (xj, yj) is |xi - xj| + |yi - yj|.
HardProblem #3464
LeetCodeMaximize the Distance Between Points on a Square
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Examples
# Example 1
Input
side = 2, points = [[0,2],[2,0],[2,2],[0,0]], k = 4
Output
2
# Example 2
Input
side = 2, points = [[0,0],[1,2],[2,0],[2,2],[2,1]], k = 4
Output
1
# Example 3
Input
side = 2, points = [[0,0],[0,1],[0,2],[1,2],[2,0],[2,2],[2,1]], k = 5
Output
1
Constraints
1 <= side <= 109
4 <= points.length <= min(4 * side, 15 * 103)
points[i] == [xi, yi]
The input is generated such that:
points[i] lies on the boundary of the square.
All points[i] are unique.
points[i] lies on the boundary of the square.
All points[i] are unique.
4 <= k <= min(25, points.length)
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Solve Maximize the Distance Between Points on a Square — You are given an integer side, representing the edge length of a square with cor...
Here's the optimal approach using Array:
def solve(input):
# Optimal O(n) solution
return result
Time: O(n) | Space: O(n)
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Frequently Asked Questions
Common questions about solving Maximize the Distance Between Points on a Square and using PhantomCodeAI during coding interviews.
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