pku 2954(pick定理的应用)

/*  
*  pick定理的应用
*  pick定律： area = inside + onedge / 2 - 1; 
*/

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <iostream>

using namespace std;

struct point {
    int x;
    int y;
}A, B, C;

int crossProd(point A, point B, point C) {
    return (B.x-A.x)*(C.y-A.y) - (B.y-A.y)*(C.x-A.x);
} 

int gcd(int a, int b) {
    return b ? gcd(b, a%b) : a;
}

int edgeNum(point A, point B) {
    int x = A.x - B.x;
    if (x < 0) x = 0 - x;
    int y = A.y - B.y;
    if (y < 0) y = 0 - y;
    return gcd(x, y);
}

int main() {
    while (scanf("%d%d%d%d%d%d", &A.x, &A.y, &B.x, &B.y, &C.x, &C.y)) {
        if (A.x==0 && A.y==0 && B.x==0 && B.y==0 && C.x==0 && C.y==0) break;
        int area = crossProd(A, B, C) / 2; //求面积 
        if (area < 0) area = 0 - area;
        int onEdge = 0;
        onEdge = edgeNum(A, B) + edgeNum(B, C) + edgeNum(C, A);//求边上的整点数 
        int inside = area - onEdge / 2 + 1; //pick定律 
        printf ("%d\n", inside);
    }
    return 0;
}