HDU 2108 Shape of HDU 【判断给定的多边形是凹还是凸多边形】水题

传送门
题意: 标题已经说明了一切

思路: 如果是凹的, 那么一定有两条相邻的边叉乘是负的.. 注意要把任意两条相邻的都判掉. 起点哪!!!

const int maxn = 1e5 + 5;
struct point {
    int x, y;
    friend int operator * (const point& a, const point& b){
        return a.x*b.y - a.y*b.x;
    }
    bool operator < (const point &_) const {
        if(_.x == x) return y < _.y;
        return x < _.x;
    }
}po[maxn];

point xl(const point& a, const point& b) {
    return point{b.x-a.x, b.y-a.y};
}

void solve() {
    int n;
    while(cin >> n && n) {
        for (int i = 1 ; i <= n ; i ++) {
            cin >> po[i].x >> po[i].y;
        }
        int f = 1; po[n+1] = po[1];
        for (int i = 2 ; i <= n + 1 ; i ++) {
            if (xl(po[i-1], po[i]) * xl(po[i], po[i%n+1]) < 0) {
                f = 0;
                break;
            }
        }
        printf("%s\n", f ? "convex":"concave");
    }
}