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Grokking the Coding Interview Patterns

Solution: Minimize Manhattan Distances

Explore how to determine the smallest possible maximum Manhattan distance between points in a 2D plane after removing exactly one point. Understand the role of coordinate sums and differences in identifying key points and learn an efficient O(n) approach to solve the problem without brute force.

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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 ...