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网络流(置顶)
poj1637 判断混合图是否能形成欧拉回路:网络流做奇偶性判断(inspire)
1 //dinic算法: 2 #include <stdio.h> 3 #include <string.h> 4 #include <math.h> 5 #include <iostream> 6 #include <algorithm> 7 8 #define INF 0x3f3f3f3f 9 using namespace std; 10 const int maxn = 2010; 11 const int maxm = 19010; 12 13 int e,S,T; 14 int first[maxn],next[maxm],work[maxm]; 15 int u[maxm],v[maxm],w[maxm]; 16 17 void init(){ 18 e = 0; 19 memset(first,-1,sizeof(first)); 20 } 21 22 void addedge(int a,int b,int c){ 23 v[e] = b;next[e] = first[a];w[e] = c;first[a] = e++; 24 v[e] = a;next[e] = first[b];w[e] = 0;first[b] = e++; 25 } 26 int d[maxn],q[maxn]; 27 int bfs(){ 28 int rear = 0; 29 memset(d,-1,sizeof(d)); 30 d[S] = 0;q[rear++] = S; 31 for(int i = 0;i < rear;i++){ 32 for(int j = first[q[i]];j != -1;j = next[j]) 33 if(w[j] && d[v[j]] == -1){ 34 d[v[j]] = d[q[i]] + 1; 35 q[rear++] = v[j]; 36 if(v[j] == T) return 1; 37 } 38 } 39 return 0; 40 } 41 42 int dfs(int cur,int a){ 43 if(cur == T) return a; 44 for(int &i = work[cur];i != -1;i = next[i]){ 45 if(w[i] && d[v[i]] == d[cur] + 1) 46 if(int t = dfs(v[i],min(a,w[i]))){ 47 w[i] -= t;w[i^1] += t; 48 return t; 49 } 50 } 51 return 0; 52 } 53 54 int dinic(){ 55 int ans = 0; 56 while(bfs()){ 57 memcpy(work,first,sizeof(first)); 58 while(int t = dfs(S,INF)) ans += t; 59 } 60 return ans; 61 } 62 int M,N,CASE; 63 int ind[maxn],outd[maxn]; 64 int main(){ 65 scanf("%d",&CASE); 66 while(CASE--) 67 { 68 scanf("%d%d",&N,&M); 69 init(); 70 S=N+1;T=N+2; 71 memset(ind,0,sizeof(ind)); 72 memset(outd,0,sizeof(outd)); 73 for(int i=1;i<=M;i++){ 74 int x,y,c; 75 scanf("%d%d%d",&x,&y,&c); 76 if (c==1) outd[x]++,ind[y]++; 77 if (c!=1) { 78 outd[x]++,ind[y]++; 79 addedge(x,y,1); 80 } 81 } 82 bool isok=true; 83 for(int i=1;i<=N;i++) if ((outd[i]-ind[i])%2!=0) isok=false; 84 if (!isok) { 85 printf("impossible\n"); 86 continue; 87 } 88 int sum=0; 89 for(int i=1;i<=N;i++){ 90 int k=(outd[i]-ind[i])/2; 91 if (k<0) addedge(i,T,-k); 92 if (k>0) { 93 sum+=k; 94 addedge(S,i,k); 95 } 96 } 97 int flow=dinic(); 98 //// cout<<sum<<","<<flow<<endl; 99 if (flow==sum) printf("possible\n");else printf("impossible\n"); 100 } 101 return 0; 102 }
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