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Grokking the Coding Interview Patterns in Python

Solution: Minimize Manhattan Distances

Understand how to minimize the maximum Manhattan distance between any two points on a 2D plane by strategically removing one point. Explore the properties of Manhattan distances, sums and differences of coordinates, and learn to identify candidate points for removal to achieve an optimal solution efficiently.

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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 ...