题解 | #判断一个点是否在三角形内部#

方法一 利用向量积（叉乘）

#include <iostream>
using namespace std;
struct Point {
    double x, y;
    double operator^ (Point b) {
        return x * b.y - y * b.x;
    }
    Point operator- (Point b) {
        Point ans;
        ans.x = x - b.x;
        ans.y = y - b.y;
        return ans;
    }
};

int main() {
    Point p[4];
    for (int i = 0; i < 4; i++) {
        cin >> p[i].x >> p[i].y;
    }
    int res = 0;
    for (int i = 0; i < 3; i++) {
        if (i != 2) {
            double ans = (p[i] - p[i + 1]) ^ (p[i] - p[3]);
            if (ans > 0) {
                res += 1;
            } else if (ans < 0) {
                res += -1;
            }
        } else {
            double ans = (p[2] - p[0]) ^ (p[2] - p[3]);
            if (ans > 0) {
                res += 1;
            } else if (ans < 0) {
                res += -1;
            }
        }
    }
    if (res == 3 || res == -3) {
        cout << "Yes";
    } else {
        cout << "No";
    }
}

方法二 利用面积 TODO