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This approach centers on calculating the time taken to move from one point to another based solely on the maximum of the differences between x and y coordinates. This works because moving diagonally allows us to cover one unit in both x and y directions simultaneously. Therefore, the time taken to move from one point to another is always determined by the greater of the horizontal or vertical distances needed to cover.
Time Complexity: O(n), where n is the number of points. We process each pair of points once.
Space Complexity: O(1), as we use a constant amount of extra space.
1#include <vector>
2#include <cstdlib>
3#include <algorithm>
4#include <iostream>
5
6using namespace std;
7
8int minTimeToVisitAllPoints(vector<vector<int>>& points) {
9 int totalTime = 0;
10 for (size_t i = 0; i < points.size() - 1; ++i) {
11 int xDiff = abs(points[i+1][0] - points[i][0]);
12 int yDiff = abs(points[i+1][1] - points[i][1]);
13 totalTime += max(xDiff, yDiff);
14 }
15 return totalTime;
16}
17
18int main() {
19 vector<vector<int>> points = {{1, 1}, {3, 4}, {-1, 0}};
20 cout << minTimeToVisitAllPoints(points) << endl;
21 return 0;
22}In the C++ version, the abs function is used to calculate positive differences, and max is applied to determine the larger of the two direction distances. We accumulate the total time taken to traverse all points. The logic is encapsulated inside a loop over adjacent points.
This approach involves calculating the total distance for each x and y direction separately, but also accounting for the diagonal moves that can reduce total movement time. Here, the diagonal path is favored when both x and y movements can be made simultaneously, which is reflected in the use of the maximum function across the differences.
Time Complexity: O(n), where n is the number of points. We process each pair once.
Space Complexity: O(1), as we are using a constant amount of space.
This Python function calculates the minimum visit time based on maximum spatial parity inclusion.