[POJ1873]The Fortified Forest（dfs+凸包）

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题目描述

传送门
题意：给出一些树（坐标，价值，长度），要求砍下一些树做成篱笆，将剩下的树围起来。求砍下的树最小价值的方案，如果有多种方案，输出砍的树的个数最少的。

题解

n只有15用dfs就可以了
dfs之后求凸包的周长，然后再判断价值什么的

代码

#include<algorithm>#include<iostream>#include<cstring>#include<cstdio>#include<cmath>using namespace std;#define inf 1000000000#define N 20const double eps=1e-9;int dcmp(double x){    if (x<=eps&&x>=-eps) return 0;    return (x>0)?1:-1;}struct Vector{    double x,y;    Vector(double X=0,double Y=0)    {        x=X,y=Y;    }    bool operator < (const Vector &a) const    {        return x<a.x||(x==a.x&&y<a.y);    }};typedef Vector Point;Vector operator - (Vector A,Vector B) {return Vector(A.x-B.x,A.y-B.y);}int T,n,Min,cnt,top;double ew;int v[N],wh[N],tr[N];double x[N],y[N],l[N];Point p[N],stack[N];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 Len(Vector A){    return sqrt(Dot(A,A));}void Graham(){    sort(p+1,p+cnt+1);    top=0;    for (int i=1;i<=cnt;++i)    {        while (top>1&&dcmp(Cross(stack[top]-stack[top-1],p[i]-stack[top-1]))<=0)            --top;        stack[++top]=p[i];    }    int k=top;    for (int i=cnt-1;i>=1;--i)    {        while (top>k&&dcmp(Cross(stack[top]-stack[top-1],p[i]-stack[top-1]))<=0)            --top;        stack[++top]=p[i];    }    if (cnt>1) --top;}void check(){    double len=0,ans=0;int val=0;    cnt=0;    for (int i=1;i<=n;++i)        if (wh[i]) p[++cnt]=Point(x[i],y[i]);        else len+=l[i],val+=v[i];    Graham();    for (int i=1;i<=top;++i)        ans+=Len(stack[i%top+1]-stack[(i+1)%top+1]);    if (dcmp(len-ans)>=0)    {        if (val<Min)        {            Min=val;ew=len-ans;tr[0]=0;            for (int i=1;i<=n;++i)                if (!wh[i]) tr[++tr[0]]=i;        }        else if (val==Min&&cnt<tr[0])        {            ew=len-ans;tr[0]=0;            for (int i=1;i<=n;++i)                if (!wh[i]) tr[++tr[0]]=i;        }    }}void dfs(int dep){    if (dep==n+1)    {        check();        return;    }    for (int i=1;i>=0;--i)    {        wh[dep]=i;        dfs(dep+1);    }}int main(){    while (~scanf("%d",&n))    {        if (!n) break;        for (int i=1;i<=n;++i) scanf("%lf%lf%d%lf",&x[i],&y[i],&v[i],&l[i]);        Min=inf;tr[0]=0;dfs(1);        printf("Forest %d\n",++T);        printf("Cut these trees:");        for (int i=1;i<=tr[0];++i) printf(" %d",tr[i]);puts("");        printf("Extra wood: %.2lf\n",ew);        puts("");    }}

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