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Grokking the Coding Interview Patterns in C#

Solution: Minimum Time Visiting All Points

Understand how to determine the minimum time required to visit a sequence of points on a plane by calculating distances using coordinate differences and optimizing movement through diagonal paths. This lesson guides you through an O(n) time solution leveraging geometric insights for efficient pathfinding.

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Statement

You are given an array of nn points with integer coordinates on a 2D plane, points, where points[i] = [xi, yi]. Your task is to determine the minimum time in seconds required to visit all the points in the given order.

Movement rules:

  1. In one second, you can perform any one of the following:

    1. Move vertically by one unit.

    2. Move horizontally by one unit.

    3. Move diagonally (1 unit vertically and 1 unit horizontally in 1 second).

  2. You must visit the points in the exact sequence listed in the array.

  3. You may pass through points that appear later in the order, but they will not count as visits.

Constraints:

  • points.length =n= n

  • 1≤n ≤1021 \leq n \leq 10^2 ...