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Grokking the Coding Interview Patterns in C#

Solution: Minimize Manhattan Distances

Understand how to minimize the maximum Manhattan distance between points in a 2D plane by removing one strategic point. Explore how sums and differences of coordinates help identify which point to remove, and learn an efficient approach to solve this problem with linear time complexity.

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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 ...