469. Convex Polygon

469. Convex Polygon

题目链接：https://leetcode.com/problems...

不会，参考这个博客的解释：
http://www.cnblogs.com/grandy...

计算三个点的法向量（叉乘），任意三个点必须同正或同负。这样判断三点组成的两边角度是否小于180。注意考虑90度的情况，这时候叉乘为0。

public class Solution {
    public boolean isConvex(List<List<Integer>> points) {
        int prev = 0;
        int n = points.size();
        for(int i = 0; i < n; i++) {
            // check the angle constructed by (p0, p1) and (p0, p2)
            List<Integer> p0 = points.get(i);
            List<Integer> p1 = points.get((i + 1) % n);
            List<Integer> p2 = points.get((i + 2) % n);
            int dx1 = p0.get(0) - p1.get(0), dx2 = p0.get(0) - p2.get(0);
            int dy1 = p0.get(1) - p1.get(1), dy2 = p0.get(1) - p2.get(1);
            
            int cur = getProduct(dx1, dx2, dy1, dy2);
            // product different
            if((prev < 0 && cur > 0) || (prev > 0 && cur < 0)) return false;
            prev = (cur == 0 ? prev : cur);
        }
        return true;
    }
    
    private int getProduct(int dx1, int dx2, int dy1, int dy2) {
        return dx1 * dy2 - dx2 * dy1;
    }
}