POJ 1873 The Fortified Forest 凸包 二进制枚举

n最大15，二进制枚举不会超时。枚举不被砍掉的树，然后求凸包

#include<stdio.h>
#include<math.h>
#include<algorithm>
#include<iostream>
#include <cstring>
#define eps 1e-8
#define INF 1e9
using namespace std;

const int MAXN = 20;

struct Point
{
    int x,y;
    int v,l;
};

Point pot[MAXN];
int stck[MAXN],top;

int sgn(double x)
{
    if(fabs(x) < eps) return 0;
    return x < 0 ? -1:1;
}

int cross(Point p0,Point p1,Point p2) //计算叉积  p0p1 X p0p2
{
    return (p1.x-p0.x)*(p2.y-p0.y)-(p1.y-p0.y)*(p2.x-p0.x);
}

double dis(Point p1,Point p2)  //计算 p1p2的 距离
{
    return sqrt((double)(p2.x-p1.x)*(p2.x-p1.x)+(p2.y-p1.y)*(p2.y-p1.y));
}

bool cmp(Point p1,Point p2) //极角排序函数，角度相同则距离小的在前面
{
    int tmp=cross(pot[0],p1,p2);
    if(tmp>0) return true;
    else if(tmp==0&&dis(pot[0],p1)<dis(pot[0],p2)) return true;
    else return false;
}

void init(int n) //输入，并把最左下方的点放在 pot[0]。并且进行极角排序
{
    int i,k;
    Point p0;
    p0 = pot[0];
    k=0;
    for(i=1; i<n; i++)
    {
        if( (p0.y>pot[i].y) || ((p0.y==pot[i].y)&&(p0.x>pot[i].x)) )
        {
            p0 = pot[i];
            k=i;
        }
    }
    pot[k]=pot[0];
    pot[0]=p0;
    sort(pot+1,pot+n,cmp);
}

void graham(int n)
{
    int i;
    if(n==1)
    {
        top=0;
        stck[0]=0;
    }
    if(n==2)
    {
        top=1;
        stck[0]=0;
        stck[1]=1;
    }
    if(n>2)
    {
        for(i=0; i<=1; i++) stck[i]=i;
        top=1;

        for(i=2; i<n; i++)
        {
            while(top>0&&cross(pot[stck[top-1]],pot[stck[top]],pot[i])<=0) top--;
            top++;
            stck[top]=i;
        }
    }
}

Point p[MAXN];

int main()
{
//    freopen("in.txt","r",stdin);
    int n, val, len, minv, maxn, ans;
    double exc;
    int Case = 0;
    while(~scanf("%d", &n) && n)
    {
        val = len = 0;
        for(int i=0; i<n; i++)
        {
            scanf("%d%d%d%d", &p[i].x, &p[i].y, &p[i].v, &p[i].l);
            val += p[i].v;
            len += p[i].l;
        }
        minv = INF;
        maxn = 0;
        for(int i=1; i< (1<<n)-1; i++)
        {
            int cnt, tmp ,v ,l;
            cnt = 0;
            tmp = i;
            v = val;
            l = len;
            for(int j=0; j<n; j++)
            {
                if(tmp&1)
                {
                    pot[cnt++] = p[j];
                    v -= p[j].v;
                    l -= p[j].l;
                }
                tmp >>= 1;
            }
            init(cnt);
            graham(cnt);
            double d = 0;
            for(int j=0; j<=top; j++)
                d += dis(pot[stck[j]], pot[stck[(j+1)%(top+1)]]);
            if(sgn(l - d) >= 0)
            {
                if(v < minv || (v == minv && cnt > maxn))
                {
                    minv = v;
                    maxn = cnt;
                    ans = i;
                    exc = l - d;
                }
            }
        }
        printf("Forest %d\nCut these trees: ", ++Case);
        for(int i=0; i<n; i++)
        {
            if((ans&1) == 0) printf("%d ", i+1);
            ans >>= 1;
        }
        printf("\nExtra wood: %.2lf\n\n", exc);
    }
    return 0;
}