Problem Description
On a 2D plane, there are n points with integer coordinates points[i] = [xi, yi]. Return the minimum time in seconds to visit all the points in the order given by points. You can move vertically, horizontally, or diagonally, and you have to visit the points in the same order as they appear in the array.
Key Insights
- The movement can be horizontal, vertical, or diagonal, where diagonal movement covers both x and y directions simultaneously.
- The time taken to move from one point to another can be calculated using the maximum of the absolute differences in x and y coordinates.
- The total time is the sum of the time taken to move between each pair of consecutive points.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve the problem, we iterate through the list of points and for each pair of consecutive points, we calculate the time taken to move between them. The time taken to move from point A (x1, y1) to point B (x2, y2) is determined by max(abs(x2 - x1), abs(y2 - y1)). This accounts for both diagonal and straight movements. We sum these times for all pairs of points to get the total minimum time required to visit all the points.