pick公式：多边形的面积=多边形边上的格点数目/2+多边形内部的格点数目-1。
多边形边上的格点数目可以枚举每条边求出。如果是水平或者垂直，显然可以得到，否则则是坐标差的最大公约数减1.(注这里是不计算端点的，端点必然在格点上，最后统计)
#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cstdlib>
#include <cmath>
#include <map>
#include <sstream>
#include <queue>
#include <vector>
#define MAXN 111111
#define MAXM 211111
#define PI acos(-1.0)
#define eps 1e-8
#define INF 1000000001
using namespace std;
int dblcmp(double d)
{
if (fabs(d) < eps) return 0;
return d > eps ? 1 : -1;
}
struct point
{
double x, y;
point(){}
point(double _x, double _y):
x(_x), y(_y){};
void input()
{
scanf("%lf%lf",&x, &y);
}
double dot(point p)
{
return x * p.x + y * p.y;
}
double distance(point p)
{
return hypot(x - p.x, y - p.y);
}
point sub(point p)
{
return point(x - p.x, y - p.y);
}
double det(point p)
{
return x * p.y - y * p.x;
}
bool operator < (point a)const
{
return dblcmp(a.x - x) == 0 ? dblcmp(y - a.y) < 0 : x < a.x;
} }p[MAXN]; int n;
double getarea()
{
double res = 0;
for(int i = 1; i < n; i++) res += p[i].sub(p[0]).det(p[i + 1].sub(p[0]));
res = fabs(res) / 2;
return res;
}
int getinedge()
{
int ans = 0;
for(int i = 1; i <= n; i++)
{
int x = (int)fabs(p[i].x - p[i - 1].x);
int y = (int)fabs(p[i].y - p[i - 1].y);
if(x == 0 && y == 0) continue;
if(x == 0) ans += y - 1;
else if(y == 0) ans += x - 1;
else ans += __gcd(x, y) - 1;
}
return ans + n;
}
int main()
{
int T;
double x, y;
int cas = 0;
scanf("%d", &T);
while(T--)
{
scanf("%d", &n);
p[0].x = 0, p[0].y = 0;
for(int i = 1; i <= n; i++)
{
scanf("%lf%lf", &x, &y);
p[i].x = p[i - 1].x + x;
p[i].y = p[i - 1].y + y;
}
double area = getarea();
int inedge = getinedge();
int inside = (int)area + 1 - inedge / 2;
printf("Scenario #%d:\n%d %d %.1f\n\n",++cas, inside, inedge, area);
}
return 0;
}