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POJ-1548 A Round Peg in a Ground Hole 凸多边形

2013-01-20 02:18 375 查看
  题目链接:http://poj.org/problem?id=1584

  首先判断是否为凸多边形,叉积判断即可,然后判断点是否在多边形内,先用叉积然后点到直线距离。

//STATUS:C++_AC_0MS_192KB
#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<queue>
#include<stack>
using namespace std;
#define LL __int64
#define pii pair<int,int>
#define Max(a,b) ((a)>(b)?(a):(b))
#define Min(a,b) ((a)<(b)?(a):(b))
#define mem(a,b) memset(a,b,sizeof(a))
#define lson l,mid,rt<<1
#define rson mid+1,r,rt<<1|1
const int N=210,M=1000000,INF=0x3f3f3f3f,MOD=1999997;
const LL LLNF=0x3f3f3f3f3f3f3f3fLL;
const double DNF=100000000;

struct Node{
double x,y;
}nod
,peg;
int n;
double pr;

double disln(Node &l1,Node &l2,Node &o){
double A,B,C;
A=-(l1.y-l2.y);
B=l1.x-l2.x;
C=-A*l1.x-B*l1.y;
return fabs(A*o.x+B*o.y+C)/sqrt(A*A+B*B);
}

inline void getr(Node &r,Node *a)
{
r.x=a[1].x-a[0].x;
r.y=a[1].y-a[0].y;
}

int ispro(Node *a)
{
int i,ok;
double ini;
Node r1,r2;
getr(r1,a);getr(r2,a+1);
ini=r1.x*r2.y-r2.x*r1.y;
for(i=2;i<=n;i++){
r1=r2;
getr(r2,a+i);
if((r1.x*r2.y-r2.x*r1.y)*ini<0)return 0;
}

return 1;
}

int isconcir(Node *a)
{
int i,j;
Node r1,r2;
double ini;
for(i=0;i<n;i++)
if(disln(a[i],a[i+1],peg)<pr)return 0;
getr(r1,a);
r2.x=peg.x-a[0].x;r2.y=peg.y-a[0].y;
ini=r1.x*r2.y-r2.x*r1.y;
for(i=1;i<n;i++){
getr(r1,a+i);
r2.x=peg.x-a[i].x;r2.y=peg.y-a[i].y;
if((r1.x*r2.y-r2.x*r1.y)*ini<0)return 0;
}
return 1;
}

int main()
{
//   freopen("in.txt","r",stdin);
int i,j;
while(~scanf("%d",&n) && n>2)
{
scanf("%lf%lf%lf",&pr,&peg.x,&peg.y);
for(i=0;i<n;i++){
scanf("%lf%lf",&nod[i].x,&nod[i].y);
}
nod
.x=nod[0].x;nod
.y=nod[0].y;
nod[n+1].x=nod[1].x;nod[n+1].y=nod[1].y;

if(!ispro(nod))printf("HOLE IS ILL-FORMED\n");
else if(isconcir(nod))printf("PEG WILL FIT\n");
else printf("PEG WILL NOT FIT\n");
}
return 0;
}
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