poj 2954 Triangle

http://poj.org/problem?id=2954

匹克定理求多边形内部点的个数

//匹克定理S = A + E/2 - 1//S表示多边形面积//A表示多边形内部的点的个数//E表示在多边形上的点的个数//A = S - E/2 + 1#include<iostream>#include<math.h>using namespace std;int x1, yy, x2, y2, x3, y3;int area() {return abs((x1-x2) * (y2-y3) - (x2-x3) * (yy-y2));}int gcd(int a, int b) {if(!b) {return a;} else {return gcd(b, a%b);}}int onEdge() {int E = 0;E += gcd(abs(x1-x2), abs(yy-y2));E += gcd(abs(x2-x3), abs(y2-y3));E += gcd(abs(x3-x1), abs(y3-yy));return E;}int main() {//freopen("in.txt", "r", stdin);int S, E, A;while(scanf("%d%d%d%d%d%d", &x1, &yy, &x2, &y2, &x3, &y3) != EOF) {if(x1 == 0 && x1 == x2 && x1 == x3 && x1 == yy && x1 == y2 && x1 == y3) {break;}S = area() / 2;E = onEdge();A = S - E/2 + 1;printf("%d/n", A);}return 0;}