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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.
1def minTimeToVisitAllPoints(points):
2 total_time = 0
3 for i in range(len(points) - 1):
4 x_diff = abs(points[i+1][0] - points[i][0])
5 y_diff = abs(points[i+1][1] - points[i][1])
6 total_time += max(x_diff, y_diff)
7 return total_time
8
9points = [[1, 1], [3, 4], [-1, 0]]
10print(minTimeToVisitAllPoints(points))This Python solution traverses the points, computing absolute differences in x and y coordinates for consecutive points. The maximum of these is summed into a total that gives the minimum time required for traversal.
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.
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[] {3, 2},
new int[] {-2, 2}
};
Console.WriteLine(MinTimeToVisitAllPoints(points));
}
}C# computes this straightforward maximum arithmetic across point pairs efficiently.