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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.
class MinimumTime {
public static int MinTimeToVisitAllPoints(int[][] points) {
int totalTime = 0;
for (int i = 0; i < points.Length - 1; i++) {
int xDiff = Math.Abs(points[i + 1][0] - points[i][0]);
int yDiff = Math.Abs(points[i + 1][1] - points[i][1]);
totalTime += Math.Max(xDiff, yDiff);
}
return totalTime;
}
static void Main() {
int[][] points = new int[][] {
new int[] {1, 1},
new int[] {3, 4},
new int[] {-1, 0}
};
Console.WriteLine(MinTimeToVisitAllPoints(points));
}
}C# computes the same logic through a loop mechanism, relying on Math.Abs and Math.Max to achieve the optimal travel time between 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.
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 = {{3, 2}, {-2, 2}};
20 cout << minTimeToVisitAllPoints(points) << endl;
21 return 0;
22}The logic in C++ is encapsulated within a loop over adjacent points where maximum directional differences contribute to total path time.