POJ 2954 Triangle （Pick定理）

给定三角形，求出给定三角形内部整点的个数。

 1 /*
 2 Memory: 116 KB        Time: 0 MS
 3 Language: C++        Result: Accepted
 4 By coolwind
 5 */
 6 #include <stdio.h>
 7 #include <string.h>
 8 
 9 #define MAXN 105
10 struct Point {
11     int x,y;
12     Point(int a = 0, int b = 0)
13             :x(a),y(b){}
14 };
15 
16 Point pt[3];
17 
18 int gcd(int a, int b)
19 {
20     if(b == 0) return a;
21     return gcd(b,a%b);
22 }
23 
24 int abs(int x)
25 {
26     if( x < 0) return -x;
27     return x;
28 }
29 
30 int Xmul(Point a ,Point b, Point o)
31 {
32     return (a.x - o.x) * (b.y - o.y) -
33             (a.y - o.y) * (b.x - o.x);
34 }
35 
36 int main()
37 {
38     while(true)
39     {
40         scanf("%d%d%d%d%d%d",&pt[0].x,&pt[0].y,
41                 &pt[1].x,&pt[1].y,&pt[2].x,&pt[2].y);
42         if(pt[0].x == 0&&pt[0].y == 0&&pt[1].x == 0
43                 &&pt[1].y == 0&&pt[2].x == 0&&pt[2].y == 0)
44             break;
45         int area = Xmul(pt[1],pt[2],pt[0]);
46         int on = 0;
47         for(int i = 0 ;i < 3; i ++)
48             on += gcd(abs(pt[(i + 1) % 3].x - pt[i].x)
49                     ,abs(pt[(i + 1) % 3].y - pt[i].y));
50         int in = (abs(area) - on + 2) / 2;
51         printf("%d\n",in);
52     }
53     return 0;
54 }