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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.
1using System;
2
3class MinimumTime {
4 public static int MinTimeToVisitAllPoints(int[][] points) {
5 int totalTime = 0;
6 for (int i = 0; i < points.Length - 1; i++) {
7 int xDiff = Math.Abs(points[i + 1][0] - points[i][0]);
8 int yDiff = Math.Abs(points[i + 1][1] - points[i][1]);
9 totalTime += Math.Max(xDiff, yDiff);
10 }
11 return totalTime;
12 }
13
14 static void Main() {
15 int[][] points = new int[][] {
16 new int[] {1, 1},
17 new int[] {3, 4},
18 new int[] {-1, 0}
19 };
20 Console.WriteLine(MinTimeToVisitAllPoints(points));
21 }
22}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.
The C solution involves computing the minimum time based on adjusting x and y coordinates according to maximum differences while iterating through each pair of points.