pick定理：面积=内部整数点数+边上整数点数/2-1

 1 //pick定理：面积=内部整数点数+边上整数点数/2-1
 2 // POJ 2954
 3 
 4 #include <iostream>
 5 #include <cstdio>
 6 #include <cstdlib>
 7 #include <algorithm>
 8 #include <vector>
 9 #include <math.h>
10 using namespace std;
11 #define LL long long
12 typedef pair<int,int> pii;
13 const double inf = 0x3f3f3f3f;
14 const LL MOD =100000000LL;
15 const int N =110;
16 #define clc(a,b) memset(a,b,sizeof(a))
17 const double eps = 1e-8;
18 void fre() {freopen("in.txt","r",stdin);}
19 void freout() {freopen("out.txt","w",stdout);}
20 inline int read() {int x=0,f=1;char ch=getchar();while(ch>'9'||ch<'0') {if(ch=='-') f=-1; ch=getchar();}while(ch>='0'&&ch<='9') {x=x*10+ch-'0';ch=getchar();}return x*f;}
21 
22 int sgn(double x){
23     if(fabs(x) < eps)return 0;
24     if(x < 0)return -1;
25     else return 1;
26 }
27 
28 struct Point{
29     int x,y;
30     Point(){}
31     Point(int _x,int _y){
32         x = _x;y = _y;
33     }
34     Point operator -(const Point &b)const{
35         return Point(x - b.x,y - b.y);
36     }
37     int operator ^(const Point &b)const{
38         return x*b.y - y*b.x;
39     }
40     int operator *(const Point &b)const{
41         return x*b.x + y*b.y;
42     }
43     friend bool operator<(const Point &a,const Point &b){
44         if(fabs(a.y-b.y)<eps) return a.x<b.x;
45         return a.y<b.y;
46     }
47 };
48 
49 int area(Point a,Point b,Point c){
50     return fabs((a-c)^(b-c));
51 }
52 //求多边形边上整点的数目，顶点必须为整数点
53 int fun(Point a,Point b){
54     int x,y;
55     x=abs(a.x-b.x);
56     y=abs(a.y-b.y);
57     return __gcd(x,y); 
58 }
59 int main(){
60     // fre();
61     int x1,y1,x2,y2,x3,y3;
62     while(~scanf("%d%d%d%d%d%d",&x1,&y1,&x2,&y2,&x3,&y3),x1||x2||x3||y1||y2||y3){
63         int ans=area(Point(x1,y1),Point(x2,y2),Point(x3,y3));
64         int cnt=0;
65         Point a,b,c;
66         a=Point(x1,y1);
67         b=Point(x2,y2);
68         c=Point(x3,y3);
69         cnt+=fun(a,b);
70         cnt+=fun(a,c);
71         cnt+=fun(b,c);
72         printf("%d
",(ans-cnt)/2+1);
73     }
74     return 0;
75 }