POJ 1113-Wall（凸包-Graham演算法）

Description

Once upon a time there was a greedy King who ordered his chief Architect to build a wall around the King's castle. The King was so greedy, that he would not listen to his Architect's proposals to build a beautiful brick wall with a perfect shape and nice tall towers. Instead, he ordered to build the wall around the whole castle using the least amount of stone and labor, but demanded that the wall should not come closer to the castle than a certain distance. If the King finds that the Architect has used more resources to build the wall than it was absolutely necessary to satisfy those requirements, then the Architect will loose his head. Moreover, he demanded Architect to introduce at once a plan of the wall listing the exact amount of resources that are needed to build the wall. 

Your task is to help poor Architect to save his head, by writing a program that will find the minimum possible length of the wall that he could build around the castle to satisfy King's requirements. 

The task is somewhat simplified by the fact, that the King's castle has a polygonal shape and is situated on a flat ground. The Architect has already established a Cartesian coordinate system and has precisely measured the coordinates of all castle's vertices in feet.

Input

Output

Sample Input

9 100
200 400
300 400
300 300
400 300
400 400
500 400
500 200
350 200
200 200

Sample Output

1628

Hint

Source

#include<cstdio>
#include<iostream>
#include<vector>
#include<cmath>
#include<cstring>
#include<queue>
#include<algorithm>
#include<set>
#include<queue>
#define INF 0xfffffff
const int MAXN = 1010;
using namespace std;
const double eps = 1e-8;
const double PI = acos(-1.0);
int sgn(double x)
{
    if(fabs(x) < eps)return 0;
    if(x < 0)return -1;
    else return 1;
}

struct Point
{
    double x,y;
    Point() {}  Point(double _x,double _y)
    {
        x = _x;
        y = _y;
    }
    Point operator -(const Point &b)const
    {
        return Point(x - b.x,y - b.y);
    }  //叉積
    double operator ^(const Point &b)const
    {
        return x*b.y - y*b.x;     //點積
    }
    double operator *(const Point &b)const
    {
        return x*b.x + y*b.y;     //繞原點旋轉角度B（弧度值），後x,y的變化
    }
    void transXY(double B)
    {
        double tx = x,ty = y;
        x = tx*cos(B) - ty*sin(B);
        y = tx*sin(B) + ty*cos(B);
    }
};
/*
* 求凸包，Graham演算法
* 點的編號0~n-1
* 返回凸包結果Stack[0~top-1]為凸包的編號
*/
Point list[MAXN];
int Stack[MAXN],top;
double dist(Point a,Point b)
{
    return sqrt((a-b)*(a-b));
}
//相對於list[0]的極角排序
bool _cmp(Point p1,Point p2)
{
    double tmp = (p1-list[0])^(p2-list[0]);
    if(sgn(tmp) > 0) return true;
    else if(sgn(tmp) == 0 && sgn(dist(p1,list[0]) - dist(p2,list[0])) <= 0)   return true;
    else return false;
}
void Graham(int n)
{
    Point p0;
    int k = 0;
    p0 = list[0];  //找最下邊的一個點
    for(int i = 1; i < n; i++)
    {
        if( (p0.y > list[i].y) || (p0.y == list[i].y && p0.x > list[i].x) )
        {
            p0 = list[i];
            k = i;
        }
    }
    swap(list[k],list[0]);
    sort(list+1,list+n,_cmp);//排序
    if(n == 1)
    {
        top = 1;
        Stack[0] = 0;
        return;
    }
    if(n == 2)
    {
        top = 2;
        Stack[0] = 0;
        Stack[1] = 1;
        return ;
    }
    Stack[0] = 0;
    Stack[1] = 1;
    top = 2;
    for(int i = 2; i < n; i++)
    {
        while(top > 1 && sgn((list[Stack[top-1]]-list[Stack[top-2]])^(list[i]-list[Stack[top-2]])) <= 0)
            top--;
        Stack[top++] = i;
    }
}
int main()
{
    int n,l;
    while(scanf("%d%d",&n,&l)!=EOF)
    {
        for(int i=0; i<n; ++i)
            scanf("%lf%lf",&list[i].x,&list[i].y);
        Graham(n);
        double ans=0;
        for(int i=0; i<top-1; ++i)
            ans+=fabs(dist(list[Stack[i]],list[Stack[i+1]]));
        ans+=fabs(dist(list[Stack[0]],list[Stack[top-1]]));
        ans+=PI*2*l;
        //cout<<ans<<endl;
        //ans=int(ans+0.5);//四捨五入
        printf("%d\n",int(ans+0.5));//不做四捨五入而直接寫成printf("%.0f\n",ans);也能AC

    }
    return 0;
}
/*
9 100
200 400
300 400
300 300
400 300
400 400
500 400
500 200
350 200
200 200
*/