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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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poj3281最大流，巧妙构图
1 //poj2391 2 #include <stdio.h> 3 #include <string.h> 4 #include <math.h> 5 #include <iostream> 6 #include <algorithm> 7 #define LL long long 8 #define INF 1<<30 9 #define maxn 510 10 #define maxm 51000 11 using namespace std; 12 13 14 int v[maxm],next[maxm],w[maxm]; 15 int first[maxn],d[maxn],work[maxn],q[maxn]; 16 int e,S,T,n,m; 17 18 void init(){ 19 e = 0; 20 memset(first,-1,sizeof(first)); 21 } 22 23 void addedge(int a,int b,int c){ 24 v[e] = b;next[e] = first[a];w[e] = c;first[a] = e++; 25 v[e] = a;next[e] = first[b];w[e] = 0;first[b] = e++; 26 } 27 28 int bfs(){ 29 int rear = 0; 30 memset(d,-1,sizeof(d)); 31 d[S] = 0;q[rear++] = S; 32 for(int i = 0;i < rear;i++){ 33 for(int j = first[q[i]];j != -1;j = next[j]) 34 if(w[j] && d[v[j]] == -1){ 35 d[v[j]] = d[q[i]] + 1; 36 q[rear++] = v[j]; 37 if(v[j] == T) return 1; 38 } 39 } 40 return 0; 41 } 42 43 int dfs(int cur,int a){ 44 if(cur == T) return a; 45 for(int &i = work[cur];i != -1;i = next[i]){ 46 if(w[i] && d[v[i]] == d[cur] + 1) 47 if(int t = dfs(v[i],min(a,w[i]))){ 48 w[i] -= t;w[i^1] += t; 49 return t; 50 } 51 } 52 return 0; 53 } 54 55 int dinic(){ 56 int ans = 0; 57 while(bfs()){ 58 memcpy(work,first,sizeof(first)); 59 while(int t = dfs(S,INF)) ans += t; 60 } 61 return ans; 62 } 63 64 int F,D,N; 65 int main(){ 66 while(~scanf("%d%d%d",&N,&F,&D)){ 67 init(); 68 S=0;T=2*N+F+D+1; 69 for(int i=1;i<=F;i++) addedge(S,i,1); 70 for(int i=1;i<=D;i++) addedge(F+2*N+i,T,1); 71 for(int i=1;i<=N;i++) addedge(F+i,F+N+i,1); 72 for(int i=1;i<=N;i++){ 73 int k1,k2; 74 scanf("%d%d",&k1,&k2); 75 for(int j=1;j<=k1;j++){ 76 int k;scanf("%d",&k); 77 addedge(k,F+i,1); 78 } 79 80 81 for(int j=1;j<=k2;j++){ 82 int k;scanf("%d",&k); 83 addedge(F+N+i,F+2*N+k,1); 84 } 85 } 86 int flow=dinic(); 87 printf("%d\n",flow); 88 } 89 return 0; 90 }
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//注意规范建点建边，注意建图本身
woj1124 差分约束系统+最大流
1 //woj1124 2 #include <stdio.h> 3 #include <string.h> 4 #include <math.h> 5 #include <vector> 6 #include <iostream> 7 #include <algorithm> 8 #define LL long long 9 #define INF 1<<30 10 #define maxn 1310 11 #define maxm 51000 12 using namespace std; 13 14 15 int v[maxm],next[maxm],w[maxm]; 16 int first[maxn],d[maxn],work[maxn],q[maxn]; 17 int e,S,T,n,m; 18 19 void init(){ 20 e = 0; 21 memset(first,-1,sizeof(first)); 22 } 23 24 void addedge(int a,int b,int c){ 25 v[e] = b;next[e] = first[a];w[e] = c;first[a] = e++; 26 v[e] = a;next[e] = first[b];w[e] = 0;first[b] = e++; 27 } 28 29 int bfs(){ 30 int rear = 0; 31 memset(d,-1,sizeof(d)); 32 d[S] = 0;q[rear++] = S; 33 for(int i = 0;i < rear;i++){ 34 for(int j = first[q[i]];j != -1;j = next[j]) 35 if(w[j] && d[v[j]] == -1){ 36 d[v[j]] = d[q[i]] + 1; 37 q[rear++] = v[j]; 38 if(v[j] == T) return 1; 39 } 40 } 41 return 0; 42 } 43 44 int dfs(int cur,int a){ 45 if(cur == T) return a; 46 for(int &i = work[cur];i != -1;i = next[i]){ 47 if(w[i] && d[v[i]] == d[cur] + 1) 48 if(int t = dfs(v[i],min(a,w[i]))){ 49 w[i] -= t;w[i^1] += t; 50 return t; 51 } 52 } 53 return 0; 54 } 55 56 int dinic(){ 57 int ans = 0; 58 while(bfs()){ 59 memcpy(work,first,sizeof(first)); 60 while(int t = dfs(S,INF)) ans += t; 61 } 62 return ans; 63 } 64 int N,M; 65 int score[110]; 66 struct Node{ 67 int u,v; 68 }; 69 vector<Node>Com; 70 int main(){ 71 while(~scanf("%d%d",&N,&M)){ 72 Com.clear(); 73 for(int i=1;i<=N;i++) scanf("%d",&score[i]); 74 for(int i=1;i<=M;i++){ 75 int u,v; 76 scanf("%d%d",&u,&v); 77 if (u==N || v==N) score[N]+=2;else Com.push_back((Node){u,v}); 78 } 79 bool flag=true; 80 for(int i=1;i<N;i++) { 81 if (score[i]>=score[N]) flag=false; 82 } 83 if (!flag){ 84 printf("NO\n"); 85 continue; 86 } 87 S=0;T=1300; 88 init(); 89 /*队伍：1--N；比赛：N+1--N+COM.SIZE()；S;T*/ 90 for(int i=1;i<N;i++) addedge(i,T,score[N]-score[i]-1);//差分约束系统 91 for(int i=1;i<=Com.size();i++) addedge(S,N+i,2); 92 for(int i=0;i<Com.size();i++){ 93 int u,v,k; 94 u=Com[i].u,v=Com[i].v,k=i+1; 95 addedge(N+k,u,2); 96 addedge(N+k,v,2); 97 } 98 int flow=dinic(); 99 // cout<<flow<<endl; 100 if (flow==2*Com.size()) printf("YES\n");else printf("NO\n"); 101 } 102 return 0; 103 }
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//注意T的设置
sgu326 差分约束系统+最大流
1 //sgu326 2 #include <stdio.h> 3 #include <string.h> 4 #include <math.h> 5 #include <vector> 6 #include <iostream> 7 #include <algorithm> 8 #define LL long long 9 #define INF 1<<30 10 #define maxn 510 11 #define maxm 91000 12 using namespace std; 13 14 15 int v[maxm],next[maxm],w[maxm]; 16 int first[maxn],d[maxn],work[maxn],q[maxn]; 17 int e,S,T,n,m; 18 19 void init(){ 20 e = 0; 21 memset(first,-1,sizeof(first)); 22 } 23 24 void addedge(int a,int b,int c){ 25 v[e] = b;next[e] = first[a];w[e] = c;first[a] = e++; 26 v[e] = a;next[e] = first[b];w[e] = 0;first[b] = e++; 27 } 28 29 int bfs(){ 30 int rear = 0; 31 memset(d,-1,sizeof(d)); 32 d[S] = 0;q[rear++] = S; 33 for(int i = 0;i < rear;i++){ 34 for(int j = first[q[i]];j != -1;j = next[j]) 35 if(w[j] && d[v[j]] == -1){ 36 d[v[j]] = d[q[i]] + 1; 37 q[rear++] = v[j]; 38 if(v[j] == T) return 1; 39 } 40 } 41 return 0; 42 } 43 44 int dfs(int cur,int a){ 45 if(cur == T) return a; 46 for(int &i = work[cur];i != -1;i = next[i]){ 47 if(w[i] && d[v[i]] == d[cur] + 1) 48 if(int t = dfs(v[i],min(a,w[i]))){ 49 w[i] -= t;w[i^1] += t; 50 return t; 51 } 52 } 53 return 0; 54 } 55 56 int dinic(){ 57 int ans = 0; 58 while(bfs()){ 59 memcpy(work,first,sizeof(first)); 60 while(int t = dfs(S,INF)) ans += t; 61 } 62 return ans; 63 } 64 int cnt,u2[410],v2[410],r2[410]; 65 int w2[25]; 66 int N; 67 int main(){ 68 while(~scanf("%d",&N)){ 69 for(int i=1;i<=N;i++) scanf("%d",&w2[i]); 70 for(int i=1;i<=N;i++) { 71 int k;scanf("%d",&k); 72 if (i==1) w2[1]+=k; 73 } 74 cnt=0; 75 for(int i=1;i<=N;i++){ 76 for(int j=1;j<=N;j++){ 77 int k;scanf("%d",&k); 78 if (i==1 || j==1 || k==0 || i>=j) continue; 79 u2[cnt]=i;v2[cnt]=j;r2[cnt++]=k; 80 } 81 } 82 bool isok=true; 83 for(int i=2;i<=N;i++) if (w2[i]>w2[1]) { 84 isok=false;break; 85 } 86 if (!isok){ 87 printf("NO\n"); 88 continue; 89 } 90 int sum=0; 91 S=0;T=501; 92 init(); 93 //比赛：N+1--N+cnt，队伍1--N 94 for(int i=0;i<cnt;i++){ 95 addedge(S,N+i+1,r2[i]); 96 sum+=r2[i]; 97 } 98 for(int i=2;i<=N;i++){ 99 addedge(i,T,w2[1]-w2[i]); 100 } 101 for(int i=0;i<cnt;i++){ 102 addedge(N+i+1,u2[i],r2[i]); 103 addedge(N+i+1,v2[i],r2[i]); 104 } 105 int flow=dinic(); 106 if (flow==sum) printf("YES\n");else printf("NO\n"); 107 } 108 return 0; 109 }
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