学步园

求点阵上取3点组成的三角形内部的点数，利用PICK定理

PICK定理：平面上以格子点为顶点的简单多边形的面积=边上的点数/2+内部的点数-1

这样只要利用叉积求出三角形面积，在利用gcd求出边上点数，就可以计算了

代码：

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

struct Point {
    int x, y;
    Point() {}
    Point(int x, int y) {
        this->x = x;
        this->y = y;
    }
    void read() {
        scanf("%d%d", &x, &y);
    }
} p[5];

typedef Point Vector;

Vector operator + (Vector A, Vector B) {
    return Vector(A.x + B.x, A.y + B.y);
}

Vector operator - (Vector A, Vector B) {
    return Vector(A.x - B.x, A.y - B.y);
}

int Cross(Vector A, Vector B) {return A.x * B.y - A.y * B.x;} //叉积

int gcd(int a, int b) {
    if (!b) return a;
    return gcd(b, a % b);
}

int x1, y1, x2, y2, x3, y3;

int cal(Point a, Point b) {
    int dx = a.x - b.x;
    if (dx < 0) dx = -dx;
    int dy = a.y - b.y;
    if (dy < 0) dy = -dy;
    return gcd(dx, dy);
}

int main() {
    while (~scanf("%d%d%d%d%d%d", &x1, &y1, &x2, &y2, &x3, &y3)) {
        if (!x1 && !y1 && !x2 &&!y2 && !x3 && !y3) break;
        p[0] = Point(x1, y1);
        p[1] = Point(x2, y2);
        p[2] = Point(x3, y3);
        int d = 0;
        d = cal(p[0], p[1]) + cal(p[1], p[2]) + cal(p[2], p[0]);
        int ans = Cross(p[1] - p[0], p[2] - p[0]);
        if (ans < 0) ans = -ans;
        printf("%d\n", (ans - d + 2) / 2);
    }
    return 0;
}