网络流 KM dinic
study from：
https://blog.csdn.net/A_Comme_Amour/article/details/79356220
1.
Edmonds-Karp 无优化
最坏时间复杂度O(n*m*m) n为点数，m为边数
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=1e4+10; 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 sum=0,s,t,add[maxn]; 28 queue<int> st; 29 bool vis[maxn]; 30 31 void add_edge(int x,int y,int len) 32 { 33 node *p1=(node*) malloc (sizeof(node)); 34 node *p2=(node*) malloc (sizeof(node)); 35 36 p1->d=y; 37 p1->len=len; 38 p1->next=e[x]; 39 p1->opp=p2; 40 e[x]=p1; 41 42 p2->d=x;///注意 43 p2->len=0;///注意 44 p2->next=e[y]; 45 p2->opp=p1; 46 e[y]=p2; 47 } 48 49 void bfs() 50 { 51 int d,dd,v; 52 node *p; 53 while (1) 54 { 55 memset(add,0,sizeof(add)); 56 ///vis不用初始化 57 add[s]=inf; 58 vis[s]=1; 59 st.push(s); 60 while (!st.empty()) 61 { 62 d=st.front(); 63 st.pop(); 64 p=e[d]; 65 while (p) 66 { 67 dd=p->d; 68 v=min(add[d],p->len); 69 if (add[dd]<v) 70 { 71 add[dd]=v; 72 pre[dd]=p->opp; 73 if (!vis[dd]) 74 { 75 vis[dd]=1; 76 st.push(dd); 77 } 78 } 79 p=p->next; 80 } 81 vis[d]=0; 82 } 83 84 if (add[t]==0) 85 break; 86 87 sum+=add[t]; 88 d=t; 89 while (d!=s) 90 { 91 pre[d]->len+=add[t]; 92 pre[d]->opp->len-=add[t]; 93 d=pre[d]->d; 94 } 95 } 96 } 97 98 int main() 99 { 100 int n,m,x,y,z; 101 scanf("%d%d%d%d",&n,&m,&s,&t); 102 while (m--) 103 { 104 scanf("%d%d%d",&x,&y,&z); 105 add_edge(x,y,z); 106 } 107 bfs(); 108 printf("%d",sum); 109 return 0; 110 }
2.
study from https://www.luogu.org/problemnew/solution/P3376 第一个题解的dinic
dinic
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=1e4+10; 19 const int inf=1e9; 20 21 struct node 22 { 23 int d,len; 24 node *next,*opp; 25 }*e[maxn]; 26 27 int sum=0,s,t; 28 int q[maxn],dep[maxn]; 29 bool vis[maxn]; 30 31 void add_edge(int x,int y,int len) 32 { 33 node *p1=(node*) malloc (sizeof(node)); 34 node *p2=(node*) malloc (sizeof(node)); 35 36 p1->d=y; 37 p1->len=len; 38 p1->next=e[x]; 39 p1->opp=p2; 40 e[x]=p1; 41 42 p2->d=x; 43 p2->len=0;///注意 44 p2->next=e[y]; 45 p2->opp=p1; 46 e[y]=p2; 47 } 48 49 ///前面的网络流算法，每进行一次增广，都要做 一遍BFS，十分浪费。能否少做几次BFS? 50 51 bool bfs() 52 { 53 int head=0,tail=1,d,dd; 54 node *p; 55 memset(vis,0,sizeof(vis)); 56 vis[s]=1; 57 dep[s]=1; 58 q[1]=s; 59 60 while (head<tail) 61 { 62 head++; 63 d=q[head]; 64 p=e[d]; 65 while (p) 66 { 67 dd=p->d; 68 if (p->len>0 && !vis[dd]) 69 { 70 tail++; 71 q[tail]=dd; 72 vis[dd]=1; 73 dep[dd]=dep[d]+1; 74 } 75 p=p->next; 76 } 77 } 78 if (vis[t]) 79 return 1; 80 return 0; 81 } 82 83 ///DFS找到一条增广路径后，并不立即结束，而是回溯后继续DFS寻找下一个增广路径 84 85 int dfs(int d,int add) 86 { 87 if (!add || d==t) 88 return add; 89 int totf=0,f,dd; 90 node *p=e[d]; 91 while (p) 92 { 93 dd=p->d; 94 if (dep[dd]==dep[d]+1 && (f=dfs(dd,min(add,p->len)))>0)///注意 95 { 96 totf+=f; 97 add-=f;///注意 98 p->len-=f; 99 p->opp->len+=f; 100 } 101 p=p->next; 102 } 103 return totf; 104 } 105 106 int main() 107 { 108 int n,m,x,y,z; 109 scanf("%d%d%d%d",&n,&m,&s,&t); 110 while (m--) 111 { 112 scanf("%d%d%d",&x,&y,&z); 113 add_edge(x,y,z); 114 } 115 while (bfs()) 116 sum+=dfs(s,inf); 117 printf("%d",sum); 118 return 0; 119 }
