POJ3565

Posted 2021-03-20 knife-rose

题目大意：

给定(n)个蚂蚁和(n)颗苹果树的坐标，要求每个蚂蚁爬到一颗苹果树旁，使得每个蚂蚁路线不相交且路线总长度最小，求每个蚂蚁爬到哪个苹果树旁？

首先假设有两只蚂蚁路径相交，那么这两个蚂蚁交换目标一定使得总路线缩短且不相交，所以总长度最短时所有蚂蚁路线一定不相交

怎么让总路线最短呢？二分图最小权匹配

其实只要把边权全部取反然后跑最大权匹配就好了

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
using namespace std;
namespace red{
#define int long long
#define eps (1e-6)
    inline int read()
    {
        int x=0;char ch,f=1;
        for(ch=getchar();(ch<'0'||ch>'9')&&ch!='-';ch=getchar());
        if(ch=='-') f=0,ch=getchar();
        while(ch>='0'&&ch<='9'){x=(x<<1)+(x<<3)+ch-'0';ch=getchar();}
        return f?x:-x;
    }
    const int N=210;
    int n;
    struct node
    {
        int x,y;
    }ant[N],tr[N];
    double jx[N][N];
    inline int sqr(int x){return x*x;}
    inline double dis(int i,int j)
    {
        return sqrt(sqr(ant[i].x-tr[j].x)+sqr(ant[i].y-tr[j].y));
    }
    double exl[N],exr[N],slack[N];
    bool visl[N],visr[N];
    int f[N],g[N];
    inline bool find(int x)
    {
        visl[x]=1;
        for(int y=1;y<=n;++y)
        {
            if(visr[y]) continue;
            double tmp=exl[x]+exr[y]-jx[x][y];
            if(fabs(tmp)<eps)
            {
                visr[y]=1;
                if(!f[y]||find(f[y]))
                {
                    f[y]=x;
                    g[x]=y;
                    return 1;
                }
            }
            else slack[y]=min(tmp,slack[y]);
        }
        return 0;
    }
    inline void km()
    {
        for(int i=1;i<=n;++i)
        {
            exl[i]=jx[i][1];
            for(int j=2;j<=n;++j)
            {
                exl[i]=max(exl[i],jx[i][j]);
            }
        }
        for(int i=1;i<=n;++i)
        {
            for(int j=1;j<=n;++j)
            {
                visl[j]=visr[j]=0;
                slack[j]=1e9+7;
            }
            if(find(i)) continue;
            while("haku")
            {
                double tmp=1e9+7;
                int t;
                for(int j=1;j<=n;++j)
                    if(!visr[j]) tmp=min(tmp,slack[j]);
                for(int j=1;j<=n;++j)
                {
                    if(visl[j]) exl[j]-=tmp;
                    if(visr[j]) exr[j]+=tmp;
                    else
                    {
                        slack[j]-=tmp;
                        if(fabs(slack[j])<eps) t=j;
                    }
                }
                if(!f[t]) break;
                visr[t]=1,visl[f[t]]=1;
                t=f[t];
                for(int j=1;j<=n;++j)
                    slack[j]=min(slack[j],exl[t]+exr[j]-jx[t][j]);
            }
            memset(visl,0,sizeof(visl));
            memset(visr,0,sizeof(visr));
            find(i);
        }
        for(int i=1;i<=n;++i) printf("%lld
",g[i]);
    }
    inline void main()
    {
        while(~scanf("%lld",&n))
        {
            memset(f,0,sizeof(f));
            memset(g,0,sizeof(g));
            memset(exl,0,sizeof(exl));
            memset(exr,0,sizeof(exr));
            for(int i=1;i<=n;++i)
            {
                ant[i].x=read(),ant[i].y=read();
            }
            for(int i=1;i<=n;++i)
            {
                tr[i].x=read(),tr[i].y=read();
            }
            for(int i=1;i<=n;++i)
            {
                for(int j=1;j<=n;++j)
                {
                    jx[i][j]=-dis(i,j);
                }
            }
            km();
        }
        
    }
}
signed main()
{
    red::main();
return 0;
}