二分图匹配
https://www.luogu.org/problemnew/show/P3386
最快的方法 dinic：
O(n*sqrt(m))
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <ctime> 5 #include <cstring> 6 #include <string> 7 #include <map> 8 #include <set> 9 #include <list> 10 #include <queue> 11 #include <stack> 12 #include <vector> 13 #include <bitset> 14 #include <algorithm> 15 #include <iostream> 16 using namespace std; 17 #define ll long long 18 const int maxn=2e3+10;///两边的点，加上新增的起点和终点，注意！！！ 19 const int inf=1e9; 20 21 struct node 22 { 23 int d,len; 24 node *next,*opp; 25 }*e[maxn],*pre[maxn]; 26 27 int s,t,dep[maxn],q[maxn]; 28 bool vis[maxn]; 29 30 void add_edge(int x,int y,int len) 31 { 32 node *p1=(node*) malloc (sizeof(node)); 33 node *p2=(node*) malloc (sizeof(node)); 34 35 p1->d=y; 36 p1->len=len; 37 p1->next=e[x]; 38 p1->opp=p2; 39 e[x]=p1; 40 41 p2->d=x;///注意 42 p2->len=0;///注意 43 p2->next=e[y]; 44 p2->opp=p1;; 45 e[y]=p2; 46 } 47 48 bool bfs() 49 { 50 int head=0,tail=1,d,dd; 51 node *p; 52 memset(vis,0,sizeof(vis)); 53 q[1]=s; 54 dep[s]=0; 55 vis[s]=1; 56 while (head<tail) 57 { 58 head++; 59 d=q[head]; 60 p=e[d]; 61 while (p) 62 { 63 dd=p->d; 64 if (p->len>0 && !vis[dd]) 65 { 66 vis[dd]=1; 67 tail++; 68 q[tail]=dd; 69 dep[dd]=dep[d]+1; 70 } 71 p=p->next; 72 } 73 } 74 if (vis[t]) 75 return 1; 76 return 0; 77 } 78 79 int dfs(int d,int add) 80 { 81 if (!add || d==t) 82 return add; 83 int totf=0,f,dd; 84 node *p=e[d]; 85 while (p) 86 { 87 dd=p->d; 88 if (dep[dd]==dep[d]+1 && (f=dfs(dd,min(add,p->len)))>0)///注意 89 { 90 totf+=f; 91 add-=f;///注意 92 p->len-=f; 93 p->opp->len+=f; 94 if (!f) 95 break; 96 } 97 p=p->next; 98 } 99 return totf; 100 } 101 102 int main() 103 { 104 int n,m,e,x,y,i,sum=0; 105 scanf("%d%d%d",&n,&m,&e); 106 s=0,t=n+m+1; 107 for (i=1;i<=n;i++) 108 add_edge(s,i,1); 109 for (i=n+1;i<=n+m;i++) 110 add_edge(i,t,1); 111 for (i=1;i<=e;i++) 112 { 113 scanf("%d%d",&x,&y); 114 if (x>n || y>m) 115 continue; 116 add_edge(x,y+n,1); 117 } 118 while (bfs()) 119 sum+=dfs(s,inf); 120 printf("%d",sum); 121 return 0; 122 }
vis:是否在配对中使用过
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <cstring> 5 #include <time.h> 6 #include <string> 7 #include <set> 8 #include <map> 9 #include <list> 10 #include <stack> 11 #include <queue> 12 #include <vector> 13 #include <bitset> 14 #include <ext/rope> 15 #include <algorithm> 16 #include <iostream> 17 using namespace std; 18 #define ll long long 19 #define minv 1e-6 20 #define inf 1e9 21 #define pi 3.1415926536 22 #define duishu 2.7182818284 23 const ll mod=1e9+7;//998244353 24 const int maxn=1e3+10; 25 26 struct node 27 { 28 int d; 29 node *next; 30 }*e[maxn]; 31 32 bool vis[maxn]={0}; 33 int conx[maxn],cony[maxn]={0}; 34 35 inline void read(int &x) 36 { 37 x=0; 38 char ch=getchar(); 39 // bool f; 40 // while (ch<'0' || ch>'9') 41 // f|=ch=='-',ch=getchar(); 42 while (ch<'0' || ch>'9') //no negative number 43 ch=getchar(); 44 while (ch>='0' && ch<='9') 45 x=x*10+ch-'0',ch=getchar(); 46 } 47 48 bool dfs(int x) 49 { 50 node *p=e[x]; 51 int y; 52 while (p) 53 { 54 y=p->d; 55 if (!vis[y]) 56 { 57 vis[y]=1; 58 if (cony[y]==0 || dfs(cony[y])) 59 { 60 conx[x]=y; 61 cony[y]=x; 62 return 1; 63 } 64 } 65 p=p->next; 66 } 67 return 0; 68 } 69 70 int main() 71 { 72 node *p; 73 int n,m,E,x,y,i,sum=0; 74 scanf("%d%d%d",&n,&m,&E); 75 for (i=1;i<=n;i++) 76 e[i]=NULL; 77 while (E--) 78 { 79 read(x),read(y); 80 if (x<=n && y<=m) 81 { 82 p=(node*) malloc (sizeof(node)); 83 p->d=y; 84 p->next=e[x]; 85 e[x]=p; 86 } 87 } 88 for (i=1;i<=n;i++) 89 { 90 memset(vis,0,sizeof(vis)); 91 sum+=dfs(i); 92 } 93 cout<<sum; 94 return 0; 95 }
题目：
https://www.luogu.org/problemnew/show/P2319
[HNOI2006]超级英雄
1 #include <cstdio> 2 #include <cstdlib> 3 #include <cmath> 4 #include <cstring> 5 #include <time.h> 6 #include <string> 7 #include <set> 8 #include <map> 9 #include <list> 10 #include <stack> 11 #include <queue> 12 #include <vector> 13 #include <bitset> 14 #include <ext/rope> 15 #include <algorithm> 16 #include <iostream> 17 using namespace std; 18 #define ll long long 19 #define minv 1e-6 20 #define inf 1e9 21 #define pi 3.1415926536 22 #define duishu 2.7182818284 23 const ll mod=1e9+7;//998244353 24 const int maxn=1e3+10; 25 26 struct node 27 { 28 int d; 29 node *next; 30 }*e[maxn]; 31 32 int conx[maxn],cony[maxn]; 33 bool vis[maxn]; 34 35 bool dfs(int x) 36 { 37 node *p=e[x]; 38 int y; 39 while (p) 40 { 41 y=p->d; 42 if (!vis[y]) 43 { 44 vis[y]=1; 45 if (cony[y]==-1 || dfs(cony[y])) 46 { 47 conx[x]=y; 48 cony[y]=x; 49 return 1; 50 } 51 } 52 p=p->next; 53 } 54 return 0; 55 } 56 57 int main() 58 { 59 node *p; 60 int n,m,x,y,i,l,r,M,sum; 61 scanf("%d%d",&n,&m); 62 for (i=1;i<=m;i++) 63 { 64 scanf("%d%d",&x,&y); 65 p=(node*) malloc (sizeof(node)); 66 p->d=x; 67 p->next=e[i]; 68 e[i]=p; 69 70 if (x==y) 71 continue; 72 p=(node*) malloc (sizeof(node)); 73 p->d=y; 74 p->next=e[i]; 75 e[i]=p; 76 } 77 78 l=1,r=n; 79 while (l<=r) 80 { 81 M=(l+r)>>1; 82 for (i=0;i<n;i++) 83 cony[i]=-1; 84 sum=0; 85 for (i=1;i<=M;i++) 86 { 87 memset(vis,0,sizeof(vis)); 88 sum+=dfs(i); 89 } 90 if (sum==M) 91 l=M+1; 92 else 93 r=M-1; 94 } 95 96 printf("%d\n",r); 97 for (i=1;i<=r;i++) 98 printf("%d\n",conx[i]); 99 return 0; 100 }
