?LeetCode刷題實(shí)戰(zhàn)469：凸多邊形
Given a list of points that form a polygon when joined sequentially, find if this polygon is convex (Convex polygon definition).
Note:
There are at least 3 and at most 10,000 points.
Coordinates are in the range -10,000 to 10,000.
You may assume the polygon formed by given points is always a simple polygon (Simple polygon definition). In other words, we ensure that exactly two edges intersect at each vertex, and that edges otherwise don't intersect each other.
示例? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
[[0,0],[0,1],[1,1],[1,0]]
輸出：True
[[0,0],[0,10],[10,10],[10,0],[5,5]]
輸出：False
解釋：
解題
class?Solution:
????def?isConvex(self, points: List[List[int]])?-> bool:
????????def?cal_cross_product(A, B, C):
????????????AB = [B[0] - A[0], B[1] - A[1]]
????????????AC = [C[0] - A[0], C[1] - A[1]]
????????????return?AB[0] * AC[1] - AB[1] * AC[0]
????????flag = 0
????????n = len(points)
????????for?i in?range(n):
????????????# cur > 0 表示points是按逆時(shí)針輸出的;cur < 0,順時(shí)針
????????????cur = cal_cross_product(points[i], points[(i + 1) % n], points[(i + 2) % n])
????????????if?cur != 0:
????????????????# 說(shuō)明異號(hào), 說(shuō)明有個(gè)角大于180度
????????????????if?cur * flag < 0:
????????????????????return?False
????????????????else:
????????????????????flag = cur
????????return?True
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