動機

人生第一次凸包

Problem

You are given an array trees where trees[i] = [xi, yi] represents the location of a tree in the garden.

You are asked to fence the entire garden using the minimum length of rope as it is expensive. The garden is well fenced only if all the trees are enclosed.

Return the coordinates of trees that are exactly located on the fence perimeter.

 

Example 1:

Input: points = [[1,1],[2,2],[2,0],[2,4],[3,3],[4,2]]Output: [[1,1],[2,0],[3,3],[2,4],[4,2]]

Example 2:

Input: points = [[1,2],[2,2],[4,2]]Output: [[4,2],[2,2],[1,2]]

 

Constraints:

    t
  • 1 <= points.length <= 3000
    • t
  • points[i].length == 2
    • t
  • 0 <= xi, yi <= 100
    • t
  • All the given points are unique.

Sol

用向量外積看，前一個點與現在要加的點是不是方向是對的!! 不對就把前一個點pop

class Solution:
    def outerTrees(self, trees: List[List[int]]) -> List[List[int]]:
        def cross(o, a, b):
            return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0])
        
        ps = sorted(trees, key=lambda p: (p[0],p[1]))
        ps = [(x,y) for (x,y) in ps]
        
        up,down = [], []
        for p in ps:
            while len(up) >= 2 and cross(up[-2],up[-1],p) < 0:
                up.pop()
            up.append(p)
        for p in reversed(ps):
            while len(down) >= 2 and cross(down[-2],down[-1],p) < 0:
                down.pop()
            down.append(p)
        return list(set(up+down))