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Grokking the Coding Interview Patterns in Python

Solution: Minimize Manhattan Distances

Explore how to minimize the largest Manhattan distance between points by removing exactly one point. Understand the role of coordinate sums and differences, identify key candidate points, and apply an efficient O(n) solution to optimize the maximum distance on a 2D plane.

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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 ...