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Grokking the Coding Interview Patterns in C#

Solution: Minimize Manhattan Distances

Explore how to minimize the maximum Manhattan distance between points on a plane by strategically removing one point. Understand the role of coordinate sums and differences in simplifying the problem, and learn an efficient method that checks only key candidate points, improving over brute-force solutions.

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Statement

You are given an array, points, where each element in points[i] =[xj,yi]= [x_j, y_i] represents the integer coordinates of a point in a 2D plane. The distance between any two points is defined as the Manhattan distanceThe Manhattan distance between two cells (x1, y1) and (x2, y2) is |x_1 - x_2| + |y_1 - y_2|..

Your task is to determine and return the smallest possible value for the maximum distance between any two points after removing exactly one point from the array.

Constraints:

  • 3≤3 \leq points.length ≤103\leq 10^3 ...