poj 1265 Area

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网格点围成一个多边形，顶点都在格点上，求多边形内部格点数，边上格点数和面积。

运用叉积求有向面积加起来得到面积，最大公约数得到边上格点数，再根据pick定理（S=a+b/2-1）计算内部格点数。注意输出最好用"%f"不要用"%lf"。

#include <iostream>#include <cstring>#include <cstdio>#include <queue>#include <algorithm>#include <stdlib.h>#include <math.h>#include <stack>using namespace std;const int mod=1e9+7;#define type double#define Vector Pointconst double PI = 3.14159265358979323;int Abs(int x){if(x<0)return -x;return x;}int gcd(int a,int b){if(b==0)return a;return gcd(b,a%b);}struct Point{type x,y;Point(){}Point(int x,int y):x(x),y(y){}Point operator-(Point other){return Point(x-other.x,y-other.y);}};//向量点积 type Dot(Vector a,Vector b){return a.x*b.x + a.y*b.y;}//向量叉积 type Cross(Vector a,Vector b){return a.x*b.y - a.y*b.x;}//向量长度 double Length(Vector a){return sqrt(a.x*a.x+a.y*a.y+0.0);}//两向量夹角 type Angle(Vector a,Vector b){return acos(Dot(a,b) / (Length(a)*Length(b))+0.0);}type Area(Point* pts,int sz){type re=0;for(int i=0;i<sz;i++){re+=Cross(pts[i+1],pts[i]);//cout<<"re="<<re<<endl;}re/=2.0;if(re<0)re=-re;return re;}Point pts[1010];bool cmp(const Point& a,const Point& b){if(a.x==b.x)return a.y<b.y;return a.x<b.x;}int main(){int t;cin>>t;int cas=0;while(t--){cas++;int n;cin>>n;pts[0].x=pts[0].y=0;int onEdge=0;for(int i=1;i<=n;i++){int dx,dy;cin>>dx>>dy;onEdge+=gcd(Abs(dx),Abs(dy));pts[i].x=pts[i-1].x+dx;pts[i].y=pts[i-1].y+dy;}pts[n+1].x=pts[n+1].y=0;double ans = Area(pts,n);int inside=ans+1-onEdge/2;printf("Scenario #%d:\n",cas);printf("%d %d %.1f\n\n",inside,onEdge,ans);}return 0;}

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