Wall POJ - 1113 [凸包]

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

裸凸包

#include<stdio.h>
#include<string.h>
#include<iostream>
#include <math.h>
#include<algorithm>
#define PI acos(-1.0)
using namespace std;
typedef long long ll;

const int MAX_N=1005;
const int MOD=1e9+7;
const int INF=0x3f3f3f3f;


struct node{
    int x,y;
};
node stackk[MAX_N];
node vex[MAX_N];
int sx,sy;
bool cmp1(node a,node b){
    if(a.y==b.y)
        return a.x<b.x;
    else
        return a.y<b.y;
}

bool cmp2(node a,node b){
    if(atan2(a.y-sy,a.x-sx)!=atan2(b.y-sy,b.x-sx))
        return atan2(a.y-sy,a.x-sx)<atan2(b.y-sy,b.x-sx);
    return a.x<b.x;
}

int cross(node a,node b,node c){
    return (b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y);
}

double dis(node a,node b){
    return sqrt(1.0*(a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}

int main(void){
    int n,l;
    while(cin >> n >>l){
        memset(stackk,0,sizeof stackk);
        memset(vex,0,sizeof vex);
        for(int i=0;i<n;i++)    scanf("%d%d",&vex[i].x,&vex[i].y);
        sort(vex,vex+n,cmp1);
        memset(stackk,0,sizeof(stackk));
        stackk[0]=vex[0];
        sx=stackk[0].x;
        sy=stackk[0].y;
        sort(vex+1,vex+n,cmp2);
        stackk[1]=vex[1];
        int top=1;
        for(int i=2;i<n;i++){
            while(i>=1 && cross(stackk[top-1],stackk[top],vex[i])<0)
                top--;
            stackk[++top]=vex[i];
    //        printf("~%d %d\n",vex[i].x,vex[i].y);
        }
        double ans=0;
        for(int i=1;i<=top;i++) /*cout<<stackk[i].x<<" "<<stackk[i].y*/ans+=dis(stackk[i],stackk[i-1]);
        ans+=dis(stackk[0],stackk[top]);
    //    printf("%.8f\n",ans);
            ans+=1.0*2*PI*l;
        cout << (int)(ans+0.5)<<endl;
    }
    return 0;
}