POJ 2007 Scrambled Polygon [凸包 极角排序]
Time Limit: 1000MS | Memory Limit: 30000K | |
Total Submissions: 8636 | Accepted: 4105 |
Description
A closed polygon is called convex if the line segment joining any two points of the polygon lies in the polygon. Figure 1 shows a closed polygon which is convex and one which is not convex. (Informally, a closed polygon is convex if its border doesn't have any "dents".)
The subject of this problem is a closed convex polygon in the coordinate plane, one of whose vertices is the origin (x = 0, y = 0). Figure 2 shows an example. Such a polygon will have two properties significant for this problem.
The first property is that the vertices of the polygon will be confined to three or fewer of the four quadrants of the coordinate plane. In the example shown in Figure 2, none of the vertices are in the second quadrant (where x < 0, y > 0).
To describe the second property, suppose you "take a trip" around the polygon: start at (0, 0), visit all other vertices exactly once, and arrive at (0, 0). As you visit each vertex (other than (0, 0)), draw the diagonal that connects the current vertex with (0, 0), and calculate the slope of this diagonal. Then, within each quadrant, the slopes of these diagonals will form a decreasing or increasing sequence of numbers, i.e., they will be sorted. Figure 3 illustrates this point.
Input
Output
Sample Input
0 0
70 -50
60 30
-30 -50
80 20
50 -60
90 -20
-30 -40
-10 -60
90 10
Sample Output
(0,0)
(-30,-40)
(-30,-50)
(-10,-60)
(50,-60)
(70,-50)
(90,-20)
(90,10)
(80,20)
(60,30)
Source
显然极角排序 用叉积 但WA好多次最后发现必须要保证第一个点在开始,排序直接跳过就行了
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=;
const double eps=1e-; inline int read(){
char c=getchar();int x=,f=;
while(c<''||c>''){if(c=='-')f=-; c=getchar();}
while(c>=''&&c<=''){x=x*+c-''; c=getchar();}
return x*f;
} inline int sgn(double x){
if(abs(x)<eps) return ;
else return x<?-:;
} struct Vector{
double x,y;
Vector(double a=,double b=):x(a),y(b){}
};
typedef Vector Point;
double Dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}
double Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;} int n,x,y;
Point p[N],S;
bool cmpPolar(Point a,Point b){
return sgn(Cross(a,b))>;
}
int main(int argc, const char * argv[]) {
while(scanf("%d",&x)!=EOF){
y=read();
p[++n]=Point(x,y);
}
sort(p+,p++n,cmpPolar);
for(int i=;i<=n;i++) printf("(%.0f,%.0f)\n",p[i].x,p[i].y);
return ;
}
#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <vector>
using namespace std;
typedef long long ll;
const int N=;
const double eps=1e-;
const double pi=acos(-); inline int read(){
char c=getchar();int x=,f=;
while(c<''||c>''){if(c=='-')f=-; c=getchar();}
while(c>=''&&c<=''){x=x*+c-''; c=getchar();}
return x*f;
} inline int sgn(double x){
if(abs(x)<eps) return ;
else return x<?-:;
} struct Vector{
double x,y;
Vector(double a=,double b=):x(a),y(b){}
bool operator <(const Vector &a)const{
//return x<a.x||(x==a.x&&y<a.y);
return sgn(x-a.x)<||(sgn(x-a.x)==&&sgn(y-a.y)<);
}
};
typedef Vector Point;
Vector operator +(Vector a,Vector b){return Vector(a.x+b.x,a.y+b.y);}
Vector operator -(Vector a,Vector b){return Vector(a.x-b.x,a.y-b.y);}
Vector operator *(Vector a,double b){return Vector(a.x*b,a.y*b);}
Vector operator /(Vector a,double b){return Vector(a.x/b,a.y/b);}
bool operator ==(Vector a,Vector b){return sgn(a.x-b.x)==&&sgn(a.y-b.y)==;} double Dot(Vector a,Vector b){return a.x*b.x+a.y*b.y;}
double Cross(Vector a,Vector b){return a.x*b.y-a.y*b.x;}
double DisPP(Point a,Point b){
Point t=b-a;
return sqrt(t.x*t.x+t.y*t.y);
}
int ConvexHull(Point p[],int n,Point ch[]){//cannot handle repeat point
sort(p+,p++n);
int m=;
for(int i=;i<=n;i++){
while(m>&&sgn(Cross(ch[m]-ch[m-],p[i]-ch[m-]))<=) m--;
ch[++m]=p[i];
}
int k=m;
for(int i=n-;i>=;i--){
while(m>k&&sgn(Cross(ch[m]-ch[m-],p[i]-ch[m-]))<=) m--;
ch[++m]=p[i];
}
if(n>) m--;//the first point
return m;
}
int n,x,y;
double ans;
Point p[N],ch[N];
int main(int argc, const char * argv[]) {
while(scanf("%d",&x)!=EOF){
y=read();
p[++n]=Point(x,y);
}
ConvexHull(p,n,ch);
Point S(,);int p;
for(p=;p<=n;p++) if(ch[p]==S) break; for(int i=p;i<=n;i++) printf("(%.0f,%.0f)\n",ch[i].x,ch[i].y);
for(int i=;i<p;i++) printf("(%.0f,%.0f)\n",ch[i].x,ch[i].y);
return ;
}
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