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Leetcode 1266. Minimum Time Visiting All Points

Problem Statement

You are given an array points representing the coordinates of different points on a 2D plane, where points[i] = [xi, yi]. The task is to find the minimum time required to visit all points in the order given by points.

You can move from a point (x1, y1) to another point (x2, y2) in the following ways:

• A diagonal move that covers one unit in both x and y directions, i.e., from (x1, y1) to (x1+1, y1+1) or (x1-1, y1-1).
• A horizontal move that covers one unit in the x direction, i.e., from (x1, y1) to (x1+1, y1) or (x1-1, y1).
• A vertical move that covers one unit in the y direction, i.e., from (x1, y1) to (x1, y1+1) or (x1, y1-1).

The time to move from (x1, y1) to (x2, y2) is the maximum of the absolute differences in their coordinates: max(abs(x2 - x1), abs(y2 - y1)).

Write a function minTimeToVisitAllPoints that returns the minimum time required to visit all the given points in order.

Clarifying Questions

1. Are the points guaranteed to be in integer coordinates?
2. Is there a minimum number of points that the input can contain?
3. Are all the points distinct?
4. Is the sequence of points guaranteed to be meaningful (i.e., does not jump large distances unnecessarily)?

Example

Given points:

[[1,1],[3,4],[-1,0]]
Output: 7

Strategy

1. Iterate through each pair of subsequent points.
2. For each pair, calculate the time required using the formula max(abs(x2 - x1), abs(y2 - y1)), where (x1, y1) is the current point and (x2, y2) is the next point.
3. Sum these times to get the total minimum time to visit all points.

Time Complexity

The time complexity for this solution is O(N) where N is the number of points. This is because we are simply iterating through the list of points once.

Code

Here is the implementation in C++:

#include <vector>
#include <cmath>

class Solution {
public:
    int minTimeToVisitAllPoints(std::vector<std::vector<int>>& points) {
        int total_time = 0;
        
        for (size_t i = 1; i < points.size(); ++i) {
            int x1 = points[i-1][0], y1 = points[i-1][1];
            int x2 = points[i][0], y2 = points[i][1];
            
            total_time += std::max(std::abs(x2 - x1), std::abs(y2 - y1));
        }
        
        return total_time;
    }
};

This code will correctly compute the minimum time required to visit all points in the given order by adhering to the movements defined in the problem statement.

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