1266. Minimum Time Visiting All Points

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 according to these rules:

In 1 second, you can either: move vertically by one unit, move horizontally by one unit, or move diagonally sqrt(2) units (in other words, move one unit vertically then one unit horizontally in 1 second).
You have to visit the points in the same order as they appear in the array.
You are allowed to pass through points that appear later in the order, but these do not count as visits.

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Example 1:

Input: points = [[1,1],[3,4],[-1,0]]
Output: 7
Explanation: One optimal path is [1,1] -> [2,2] -> [3,3] -> [3,4] -> [2,3] -> [1,2] -> [0,1] -> [-1,0]   
Time from [1,1] to [3,4] = 3 seconds 
Time from [3,4] to [-1,0] = 4 seconds
Total time = 7 seconds

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Example 2:

Input: points = [[3,2],[-2,2]]
Output: 5

Constraints:

points.length == n
1 <= n <= 100
points[i].length == 2
-1000 <= points[i][0], points[i][1] <= 1000

Solution

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class Solution {
    
    public int minTimeToVisitAllPoints(int[][] points) {
        int count = 0;
        int i = 0;
        while (i < points.length - 1) {
            count += chebishevDistance(points[i], points[i + 1]);
            i++;
        }     
        
        return count;
    }    
    
    int chebishevDistance(int[] a, int[] b) {
        return Math.max(Math.abs(a[0] - b[0]), Math.abs(a[1] - b[1]));
    }
    
    int[][] DIRECTIONS = new int[][] {
        new int[] {0,1}, // top
        new int[] {1,1}, // top r
        new int[] {1,0}, // r
        new int[] {1,-1}, // down r
        
        new int[] {0,-1}, // down 
        new int[] {-1,-1}, // down l
        new int[] {-1,0}, // l
        new int[] {-1,1}, // top l
    };
    public int minTimeToVisitAllPoints2(int[][] points) {
        int i = 0;
        
        int[] current = points[i];
        int count = 0; 
        while (i < points.length - 1) {
            
            int[] next = points[i + 1];
            
            if (Arrays.equals(current, next)) {
                i++;
                continue;
            }
            
            double minDist = Double.MAX_VALUE;
            int[] bestStep = null;
            for (int[] dir: DIRECTIONS) {
                int[] nextStep = new int[] {current[0] + dir[0], current[1] + dir[1]};
                
                double distance = distance(nextStep, next);
                
                if (distance < minDist) {
                    minDist = distance;
                    bestStep = nextStep;
                }
            }
            
            current = bestStep;
            
            count++;
        }
        
        return count;
    }
    
    double distance(int[] a, int[] b) {
        double x2 = (a[0] - b[0]) * (a[0] - b[0]);
        double y2 = (a[1] - b[1]) * (a[1] - b[1]);
        return Math.sqrt(x2 + y2);
    }
}

Solution#

Solution