二分图最大权匹配 费用流&KM
费用流 建图时额外添加一个点A（左->A:(1,0) A->T:(inf,0)）来保证满流 边少点多较快 边多的情况下表现很差
1 #include<cstdio> 2 #include<cstring> 3 #include<cmath> 4 #include<ctime> 5 #include<iostream> 6 #include<algorithm> 7 #include<queue> 8 #include<set> 9 #define inf (1ll<<(61ll)) 10 #define l(a) ((a)<<1) 11 #define r(a) ((a)<<1|1) 12 #define b(a) (1<<(a)) 13 #define rep(i,a,b) for(int i=a;i<=(b);i++) 14 #define clr(a) memset(a,0,sizeof(a)) 15 typedef long long ll; 16 using namespace std; 17 int readint(){ 18 int t=0,f=1;char c=getchar(); 19 while(!isdigit(c)){ 20 if(c=='-') f=-1; 21 c=getchar(); 22 } 23 while(isdigit(c)){ 24 t=(t<<3)+(t<<1)+c-'0'; 25 c=getchar(); 26 } 27 return t*f; 28 } 29 const int maxn=1009,maxe=400009; 30 int n,m,en,S,A,T; 31 ll d[maxn]; 32 ll ans; 33 struct edge{ 34 ll v,w,c; 35 edge*next,*r; 36 }E[maxe],*pt=E,*fir[maxn],*cur[maxn],*rev[maxn]; 37 void add(int u,int v,int w,int c){ 38 pt->v=v;pt->w=w;pt->c=c; 39 pt->next=fir[u];fir[u]=pt++; 40 } 41 void addedge(int u,int v,int w,int c){ 42 add(u,v,w,c);add(v,u,0,-c); 43 fir[u]->r=fir[v];fir[v]->r=fir[u]; 44 } 45 bool p[maxn]; 46 ll spfa(){ 47 queue<int>Q;clr(p); 48 rep(i,S,T) d[i]=-inf; 49 Q.push(S);p[S]=1;d[S]=0; 50 while(!Q.empty()){ 51 int x=Q.front();Q.pop();p[x]=0; 52 for(edge*e=fir[x];e;e=e->next) if(e->w){ 53 if(d[e->v]<d[x]+e->c){ 54 d[e->v]=d[x]+e->c; 55 rev[e->v]=e; 56 if(!p[e->v]){ 57 Q.push(e->v);p[e->v]=1; 58 } 59 } 60 } 61 } 62 if(d[T]==-inf) return 0; 63 for(edge*e=rev[T];e;e=rev[e->r->v]){ 64 e->w-=1;e->r->w+=1; 65 } 66 return d[T]; 67 } 68 void Cal(){ 69 ll t; 70 while(t=spfa()) ans+=t; 71 } 72 int main(){ 73 //freopen("#input.txt","r",stdin); 74 //freopen("#output.txt","w",stdout); 75 n=readint();m=readint();en=readint();S=0;A=n+m+1;T=A+1; 76 rep(i,1,en){ 77 int U=readint(),V=readint(),C=readint(); 78 addedge(U,n+V,1,C); 79 } 80 rep(i,1,n) addedge(S,i,1,0); 81 rep(i,1,m) addedge(n+i,T,1,0); 82 rep(i,1,n) addedge(i,A,1,0);addedge(A,T,1000009,0); 83 Cal(); 84 cout<<ans<<endl; 85 rep(i,1,n){ 86 int f=0; 87 for(edge*e=fir[i];e;e=e->next){ 88 if(!e->w&&e->v!=A&&e->v!=S) f=e->v-n; 89 } 90 printf("%d",f);putchar(i==n?'\n':' '); 91 } 92 //fclose(stdin); 93 //fclose(stdout); 94 return 0; 95 }
km 调了一个下午 半个晚上你敢信？先写了一个貌似n^3的n^4 后来膜着tle的代码写出正确n^3 有空再重新复习敲一下
1 #include<cstdio> 2 #include<cstring> 3 #include<cmath> 4 #include<ctime> 5 #include<iostream> 6 #include<algorithm> 7 #include<queue> 8 #include<set> 9 #define inf (0x7fffffffll) 10 #define l(a) ((a)<<1) 11 #define r(a) ((a)<<1|1) 12 #define b(a) (1<<(a)) 13 #define rep(i,a,b) for(int i=a;i<=(b);i++) 14 #define clr(a) memset(a,0,sizeof(a)) 15 typedef long long ll; 16 typedef unsigned long long ull; 17 using namespace std; 18 int readint(){ 19 int t=0,f=1;char c=getchar(); 20 while(!isdigit(c)){ 21 if(c=='-') f=-1; 22 c=getchar(); 23 } 24 while(isdigit(c)){ 25 t=(t<<3)+(t<<1)+c-'0'; 26 c=getchar(); 27 } 28 return t*f; 29 } 30 const int maxn=509; 31 int n,m,en,now,lp[maxn],rp[maxn],pre[maxn],ld[maxn],rd[maxn],a[maxn],w[maxn][maxn],lc[maxn],rc[maxn];; 32 ll ans; 33 queue<int>Q; 34 bool Bfs(){ 35 while(!Q.empty()){ 36 int u=Q.front();Q.pop(); 37 rep(v,1,m) if(rc[v]!=now){ 38 int t=ld[u]+rd[v]-w[u][v]; 39 if(!t){ 40 pre[v]=u; 41 if(!rp[v]){ 42 int V=v,tmp; 43 for(int U=u;V;U=pre[V]){ 44 tmp=lp[U];lp[U]=V;rp[V]=U;V=tmp; 45 } 46 return 1; 47 } 48 rc[v]=now; 49 if(lc[rp[v]]!=now){ 50 lc[rp[v]]=now;Q.push(rp[v]); 51 } 52 }else if(t<a[v]) a[v]=t,pre[v]=u; 53 } 54 } 55 return 0; 56 } 57 void KM(){ 58 rep(S,1,n){ 59 rep(i,1,m) a[i]=inf;clr(pre); 60 while(!Q.empty()) Q.pop();Q.push(S);lc[S]=++now; 61 for(;;){ 62 if(Bfs()) break; 63 int del=inf; 64 rep(i,1,m) if(rc[i]!=now) del=min(del,a[i]); 65 rep(i,1,n) if(lc[i]==now) ld[i]-=del; 66 rep(i,1,m) if(rc[i]==now) rd[i]+=del;else if(a[i]<inf) a[i]-=del; 67 bool flag=0; 68 rep(i,1,m) if(rc[i]!=now&&!a[i]){ 69 if(!rp[i]){ 70 int V=i,tmp; 71 for(int U=pre[i];V;U=pre[V]){ 72 tmp=lp[U];lp[U]=V;rp[V]=U;V=tmp; 73 } 74 flag=1;break; 75 } 76 rc[i]=now; 77 if(lc[rp[i]]!=now){ 78 lc[rp[i]]=now;Q.push(rp[i]);//将新增的点加入队列 避免重复的去匈牙利 79 } 80 } 81 if(flag) break; 82 } 83 } 84 rep(i,1,m) if(rp[i]) ans+=w[rp[i]][i]; 85 cout<<ans<<endl; 86 rep(i,1,n){ 87 printf("%d",w[i][lp[i]]?lp[i]:0); 88 putchar(i==n?'\n':' '); 89 } 90 } 91 int main(){ 92 //freopen("#input.txt","r",stdin); 93 //freopen("#output.txt","w",stdout); 94 n=readint();m=readint();en=readint(); 95 if(m<n) m=n; 96 while(en--){ 97 int u=readint(),v=readint(); 98 w[u][v]=readint();ld[u]=max(ld[u],w[u][v]); 99 } 100 KM(); 101 //fclose(stdin); 102 //fclose(stdout); 103 return 0; 104 }
1 #include<cstdio> 2 #include<cstring> 3 #include<cmath> 4 #include<ctime> 5 #include<iostream> 6 #include<algorithm> 7 #include<queue> 8 #include<set> 9 #define inf (0x7fffffff) 10 #define l(a) ((a)<<1) 11 #define r(a) ((a)<<1|1) 12 #define b(a) (1<<(a)) 13 #define rep(i,a,b) for(int i=a;i<=(b);i++) 14 #define clr(a) memset(a,0,sizeof(a)) 15 typedef long long ll; 16 typedef unsigned long long ull; 17 using namespace std; 18 int readint(){ 19 int t=0,f=1;char c=getchar(); 20 while(!isdigit(c)){ 21 if(c=='-') f=-1; 22 c=getchar(); 23 } 24 while(isdigit(c)){ 25 t=(t<<3)+(t<<1)+c-'0'; 26 c=getchar(); 27 } 28 return t*f; 29 } 30 const int maxn=509; 31 int n,m,en,now,pre[maxn],ld[maxn],rd[maxn],lc[maxn],rc[maxn],lp[maxn],rp[maxn],a[maxn],w[maxn][maxn]; 32 queue<int>Q; 33 bool Bfs(){ 34 while(!Q.empty()){ 35 int u=Q.front();Q.pop(); 36 rep(v,1,m) if(rc[v]!=now){ 37 int t=ld[u]+rd[v]-w[u][v];//u,v不能写错 38 if(!t){ 39 pre[v]=u; 40 if(!rp[v]){ 41 rp[v]=u; 42 int V=v,tmp; 43 for(int U=u;V;U=pre[V]){ 44 tmp=lp[U];lp[U]=V;rp[V]=U;V=tmp; 45 } 46 return 1; 47 } 48 rc[v]=now;//注意 49 if(lc[rp[v]]!=now){ 50 lc[rp[v]]=now;Q.push(rp[v]); 51 } 52 }else if(a[v]>t){ 53 a[v]=t;pre[v]=u; 54 } 55 } 56 } 57 return 0; 58 } 59 void KM(){ 60 rep(S,1,n){ 61 while(!Q.empty()) Q.pop(); 62 rep(i,1,m) a[i]=inf;clr(pre); 63 Q.push(S);lc[S]=++now; 64 for(;;){ 65 bool flag=0; 66 if(Bfs()) break; 67 int del=inf; 68 rep(i,1,m) if(rc[i]!=now) del=min(del,a[i]); 69 rep(i,1,n) if(lc[i]==now) ld[i]-=del; 70 rep(i,1,m) if(rc[i]==now) rd[i]+=del;else if(a[i]<inf) a[i]-=del;//理解 71 rep(i,1,m) if(rc[i]!=now&&!a[i]){ 72 if(!rp[i]){ 73 int V=i,tmp; 74 for(int U=pre[i];V;U=pre[V]){ 75 tmp=lp[U];lp[U]=V;rp[V]=U;V=tmp; 76 } 77 flag=1;break; 78 } 79 rc[i]=now;//注意 80 if(lc[rp[i]]!=now){ 81 lc[rp[i]]=now;Q.push(rp[i]);//将后面的BFS合起来 避免无意义的BFS 82 } 83 } 84 if(flag) break; 85 } 86 } 87 ll ans=0; 88 rep(i,1,n) if(lp[i]) ans+=w[i][lp[i]]; 89 cout<<ans<<endl; 90 rep(i,1,n){ 91 printf("%d",w[i][lp[i]]?lp[i]:0); 92 putchar(i==n?'\n':' '); 93 } 94 } 95 int main(){ 96 //freopen("#input.txt","r",stdin); 97 //freopen("#output.txt","w",stdout); 98 n=readint();m=readint();en=readint(); 99 if(m<n) m=n; 100 while(en--){ 101 int u=readint(),v=readint(); 102 w[u][v]=readint();ld[u]=max(ld[u],w[u][v]); 103 } 104 KM(); 105 //fclose(stdin); 106 //fclose(stdout); 107 return 0; 108 }
有几个要注意的点！
