Going Home +最小费用流+spay
题目链接:Going Home
题意:有N个人回家,每移动一步花费1,求让所有的人回家的最小花费
题解:建立一个源点s与所有的人连接flow为1,cost为0,一个汇点t与所有的房子连接flow为1,cost为0,然后吧每个人与每个房子连接,权值flow=1,花费为曼哈顿距离.然后求s到t的最小费用流
//#include<bits/stdc++.h>
#include<iostream>
#include<cstring>
#include<cstdio>
#include <cstdlib>
#include<queue>
#define min(a,b) a<b?a:b
#define pb push_back
#define ll long long
#define PI 3.14159265
#define ls l,m,rt<<1
#define rs m+1,r,rt<<1|1
#define eps 1e-7
const int inf=0x4f4f4f4f4f4f;
const int maxn=1e4+10;
using namespace std;
struct edge
{
int to,flow,cost;
}ed[maxn<<2];
int pre[maxn],pad[maxn],dis[maxn],edge_num,n,m,s,t;
bool vis[maxn];
vector<int>g[maxn];
char mp[120][120];
void add_edge(int from,int to,int flow,int cost)
{
g[from].pb(edge_num);
ed[edge_num].to=to;ed[edge_num].flow=flow;ed[edge_num++].cost=cost;
g[to].pb(edge_num);
ed[edge_num].to=from;ed[edge_num].flow=0;ed[edge_num++].cost=-cost;
}
int spaf()
{
// memset(pre,-1,sizeof(pre));
memset(dis,inf,sizeof(dis));
memset(vis,false,sizeof(vis));
// cout<<inf<<" "<<dis[0]<<endl;
queue<int>q;
q.push(s);
dis[s]=0;
vis[s]=true;
while(!q.empty())
{
int v=q.front();q.pop();
vis[v]=false;
for(int i=0;i<g[v].size();i++)
{
int u=ed[g[v][i]].to;
// cout<<v<<"..."<<u<<endl;
if(ed[g[v][i]].flow>0&&dis[u]>dis[v]+ed[g[v][i]].cost)
{
pre[u]=v;
pad[u]=g[v][i];
dis[u]=dis[v]+ed[g[v][i]].cost;
if(!vis[u])
{
q.push(u);vis[u]=true;
}
}
}
}
return dis[t];
}
int min_cost()
{
int ans=0,max_flow=0;
while(1)
{
int tmp=spaf();
// cout<<"tmp="<<tmp<<endl;
if(tmp==inf)break;
int aug=inf;
for(int i=t;;i=pre[i])
{
//int id=g[i][pad[i]];
if(i==s)break;
aug=min(aug,ed[pad[i]].flow);
}
// cout<<"aug="<<aug<<endl;
for(int i=t;;i=pre[i])
{
if(i==s)break;
ed[pad[i]].flow-=aug;
ed[pad[i]^1].flow+=aug;
}
ans+=tmp;
max_flow+=aug;
}
return ans;
}
int main()
{
while(scanf("%d %d",&n,&m)&&n&&m)
{
for(int i=1;i<=n;i++)
{
scanf("%s",mp[i]+1);
}
edge_num=0;
s=n*m+1,t=s+1;
int h[110],c[110],cnt1=0;
int h1[110],c1[110],cnt2=0;
for(int i=1;i<=n;i++)
{
for(int j=1;j<=m;j++)
{
if(mp[i][j]=='H')
{
add_edge((i-1)*m+j,t,1,0);
h[cnt1]=i;c[cnt1++]=j;
}
else if(mp[i][j]=='m')
{
add_edge(s,(i-1)*m+j,1,0);
h1[cnt2]=i;c1[cnt2++]=j;
}
}
}
for(int i=0;i<cnt2;i++)
{
for(int j=0;j<cnt1;j++)
{
add_edge((h1[i]-1)*m+c1[i],(h[j]-1)*m+c[j],1,abs(h1[i]-h[j])+abs(c1[i]-c[j]));
}
}
printf("%d\n",min_cost());
for(int i=0;i<=t;i++)
{
g[i].clear();
}
}
}