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 ", 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 ", minCost); 114 } 115 return 0; 116 }