102 lines
2.0 KiB
C++
102 lines
2.0 KiB
C++
#include<iostream>
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#include<cstdio>
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#include<cstdlib>
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#include<cstring>
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#include<algorithm>
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#include<cmath>
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using namespace std;
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const int MAXN=100010;
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const double ZERO=1e-8;
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struct node
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{
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double x,y;
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}q[MAXN],p[MAXN];
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int N,M;
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void Init()
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{
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scanf("%d",&N);
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for (int i=0;i<N;i++)
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scanf("%lf%lf",&p[i].x,&p[i].y);
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}
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double det(node a,node b,node c)
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{
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return (b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y);
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}
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double dot(node a,node b,node c)
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{
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return (b.x-a.x)*(c.x-a.x)+(b.y-a.y)*(c.y-a.y);
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}
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double det3(node a,node b,node c)
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{
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double s=det(a,b,c);
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if (fabs(s)<=ZERO) return 0;
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if (s<0) return -1; else return 1;
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}
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void Graham_scan(node *c,int &M0,int base,node q)
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{
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while (M0>base && det3(c[M0-2],c[M0-1],q)<=0) --M0;
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c[M0]=q;
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++M0;
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}
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bool cmp(node a,node b)
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{
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if ((a.y<b.y) || (a.y==b.y && a.x<b.x)) return 1; else return 0;
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}
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node c[MAXN];
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void Graham(node *p,int N0,node *q,int &M0)
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{
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for (int i=0;i<=N0;++i) q[i]=p[i];
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sort(q,q+N0,cmp);
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M0=0;
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for (int i=0;i<N0;++i)
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Graham_scan(c,M0,1,q[i]);
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int M1=M0;
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for (int i=N0-1;i>=0;--i)
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Graham_scan(c,M0,M1,q[i]);
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for (int i=0;i<M0;++i)
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q[i]=c[i];
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}
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int Find(node a,node b,node c)
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{
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double s=dot(b,a,c);
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if (s>ZERO) return 0; else return 1;
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}
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bool Cleck(node a,node b,node c)
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{
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return ((!Find(a,b,c))&&(!Find(a,c,b)));
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}
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void Solve()
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{
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node o,o1;
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double s=0,s1;
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o.x=o.y=0;
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for (int i=1;i<N-1;++i)
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{
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o1.x=(p[0].x+p[i].x+p[i+1].x)/3;
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o1.y=(p[0].y+p[i].y+p[i+1].y)/3;
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s1=det(p[0],p[i],p[i+1]);
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s+=s1;
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o.x+=o1.x*s1;
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o.y+=o1.y*s1;
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}
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o.x/=s;
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o.y/=s;
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Graham(p,N,q,M);
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q[M]=q[0];
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int ans=0;
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for (int i=0;i<M;++i)
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if (Cleck(o,q[i],q[i+1])) ++ans;
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printf("%d\n",ans);
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}
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int main()
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{
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int test;
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scanf("%d",&test);
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while (test--)
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{
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Init();
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Solve();
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}
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return 0;
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}
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