poj 2195 Going Home

  1 /*
  2    做网络流的题建图真的是太重要了！
  3    本题是将人所在的位置和房子所在的位置建立边的联系，其中man到house这一条边的流量为 1， 费用为两者的距离
  4    而方向边的流量为 0， 费用为正向边的相反数（也就是沿着反向边进行增广时，费用要减少，更改先前错误的选择） 
  5    最后增加一个源点和一个汇点完毕（源点映射到man， house映射到汇点， 费用为0， 流量为1） 
　　　　  6 */
  7 #include<iostream> 
  8 #include<cmath>
  9 #include<cstdio>
 10 #include<cstring>
 11 #include<queue>
 12 #define Max 0x3f3f3f3f
 13 #define N 205
 14 using namespace std;
 15 
 16 class node
 17 {
 18 public:  
 19    int x, y;
 20 };
 21 
 22 node xyM[N];
 23 node xyH[N];
 24 int cost[N][N], cap[N][N];
 25 int cntM, cntH;
 26 int pre[N*2], dist[N*2], vis[N*2], n, m;
 27 
 28 void addE(int i, int j, int ct, int cp)
 29 {
 30     cost[i][j]=ct;
 31     cap[i][j]=cp;
 32     cost[j][i]=-ct;
 33     //cap[j][i]=0;
 34 }
 35 
 36 int s, t, minCost;
 37 
 38 void buildMap()
 39 {
 40    int i, j;
 41    memset(cap, 0, sizeof(cap));
 42    s=0; t=cntM+cntH+1;
 43    for(i=0; i<cntM; ++i)
 44      addE(0, i+1, 0, 1);  
 45    for(i=0; i<cntH; ++i)
 46      addE(cntM+i+1, t, 0, 1);
 47    for(i=0; i<cntM; ++i)
 48      for(j=0; j<cntH; ++j)
 49        addE(i+1, cntM+j+1, abs(xyM[i].x-xyH[j].x)+abs(xyM[i].y-xyH[j].y), 1);
 50 }
 51 
 52 queue<int>q;
 53 
 54 int spfa()
 55 {
 56     int u, v;
 57     memset(dist, 0x3f, sizeof(dist));
 58     dist[0]=0;
 59     q.push(0);
 60     vis[0]=1;
 61     while(!q.empty())
 62     {
 63         u=q.front();
 64         q.pop();
 65         vis[u]=0;
 66         for(v=0; v<=t; ++v)
 67           if(cap[u][v]>0 && dist[v]>dist[u]+cost[u][v])
 68           {
 69               dist[v]=dist[u]+cost[u][v];
 70               pre[v]=u;
 71               if(!vis[v])
 72               {
 73                     vis[v]=1;
 74                     q.push(v);
 75           }
 76       }
 77     }
 78     if(dist[t]==Max)
 79       return 0;
 80     return 1;
 81 }
 82 
 83 void updateEdge()
 84 { 
 85    int u, minFlow=Max;
 86    for(u=t; u!=s; u=pre[u])//通过最短路径寻找这条路径上的最小流量 
 87       if(cap[pre[u]][u]<minFlow)
 88         minFlow=cap[pre[u]][u];
 89     for(u=t; u!=s; u=pre[u])
 90     {
 91         cap[pre[u]][u]-=minFlow;
 92         cap[u][pre[u]]+=minFlow;
 93         minCost+=cost[pre[u]][u];
 94     }
 95 }
 96 
 97 int main()
 98 {
 99    int i, j;
100    char c;
101    while(scanf("%d%d", &n, &m) && (n||m))
102    {
103        cntM=cntH=0;
104        minCost=0;
105        for(i=1; i<=n; ++i)
106          {
107            getchar();
108        for(j=1; j<=m; ++j)
109              {
110             scanf("%c", &c);
111             if(c=='m')
112             {
113                xyM[cntM].x=i;
114                xyM[cntM++].y=j;
115         }
116         else if(c=='H')
117         {
118            xyH[cntH].x=i;
119                xyH[cntH++].y=j;
120         }
121          }
122         }
123         buildMap();
124         while(spfa())
125           updateEdge();
126         printf("%d\n", minCost);
127    }
128    return 0;
129 }

//邻接表

  1 #include<iostream>
  2 #include<queue>
  3 #include<cstring>
  4 #include<cstdio>
  5 #include<algorithm>
  6 #define INF 0x3f3f3f3f
  7 #define N 1000005
  8 using namespace std;
  9 
 10 int cntH, cntM;
 11 
 12 struct node{
 13     int x, y;
 14 };
 15 
 16 struct EDGE{
 17     int u, v, cap, cost, nt;
 18 };
 19 EDGE edge[N];
 20 
 21 queue<int>q;
 22 node man[105], house[105];
 23 int first[205];
 24 int dist[205];
 25 int pre[205], flow[205], vis[205];
 26 int cnt, t;
 27 int minCost;
 28 int n, m;
 29 
 30 void addEdge(int u, int v, int cap, int cost){
 31     edge[cnt].u=u;
 32     edge[cnt].v=v;
 33     edge[cnt].cap=cap;
 34     edge[cnt].nt=first[u];
 35     edge[cnt].cost=cost;
 36     first[u]=cnt++;
 37     
 38     edge[cnt].u=v;
 39     edge[cnt].v=u;
 40     edge[cnt].cap=0;
 41     edge[cnt].nt=first[v];
 42     edge[cnt].cost=-cost;
 43     first[v]=cnt++;
 44 }
 45 
 46 void buildMap(){
 47     memset(first, -1, sizeof(first));
 48     t=cntH+cntM+1;
 49     for(int i=1; i<=cntM; ++i)
 50         for(int j=1; j<=cntH; ++j)
 51             addEdge(i, cntM+j, 1, abs(man[i].x-house[j].x) + abs(man[i].y-house[j].y));
 52     for(int i=1; i<=cntM; ++i)
 53         addEdge(0, i, 1, 0);
 54     for(int i=1; i<=cntH; ++i)
 55         addEdge(cntM+i, t, 1, 0); 
 56 }
 57 
 58 bool MCMF(){
 59     memset(dist, 0x3f, sizeof(dist));
 60     memset(vis, 0, sizeof(vis));
 61     q.push(0);
 62     flow[0]=INF;
 63     dist[0]=0;
 64     vis[0]=1;
 65     while(!q.empty()){
 66         int u=q.front(); q.pop();
 67         vis[u]=0;
 68         for(int e=first[u]; ~e; e=edge[e].nt){
 69             int v=edge[e].v, cap=edge[e].cap, cost=edge[e].cost;
 70             if(cap>0 && dist[v]>dist[u]+cost){
 71                 dist[v]=dist[u]+cost;
 72                 flow[v]=min(flow[u], cap);
 73                 pre[v]=e;
 74                 if(!vis[v]){
 75                     vis[v]=1;
 76                     q.push(v);
 77                 }
 78             }
 79         }
 80     }
 81     if(dist[t]==INF) return false;
 82     minCost+=dist[t];
 83     int x=t;
 84     while(x!=0){
 85         edge[pre[x]].cap-=flow[t];
 86         edge[pre[x]^1].cap+=flow[t];
 87         x=edge[pre[x]].u;
 88     }
 89     return true;
 90 }
 91  
 92 int main(){
 93     while(scanf("%d%d", &n, &m) && (n||m)){
 94         cnt=cntH=cntM=0;
 95         for(int i=1; i<=n; ++i){
 96             getchar();
 97             for(int j=1; j<=m; ++j){
 98                 char ch;
 99                 scanf("%c", &ch);
100                 if(ch=='m'){
101                     man[++cntM].x=i;
102                     man[cntM].y=j;
103                 }
104                 else if(ch=='H'){
105                     house[++cntH].x=i;
106                     house[cntH].y=j;
107                 }
108             }
109         }
110         buildMap();
111         minCost=0;
112         while(MCMF());
113         printf("%d\n", minCost);
114     }
115     return 0;
116 }