• 网络最大流dinic


    P3376【模板】网络最大流
    在全机房的共同努力下搞出来的

    假的写法

    实测836ms比EK还慢
    (来自Blueqwq)

    #include<iostream>
    #include<cstdio>
    #include<cstdlib>
    #include<queue>
    #include<cstring>
    #define maxn 210
    #define maxm 10010
    #define int long long
    using namespace std;
    template<typename T>
    inline void read(T &x){
    	x=0; bool flag=0; char c=getchar();
    	for(;!isdigit(c);c=getchar()) if(c=='-') flag=1;
    	for(;isdigit(c);c=getchar()) x=x*10+(c^48);
    	if(flag) x=-x;
    }
    
    const int inf=1e18;
    int n,m,s,t,u,v,w;
    int ans=0,cnt,head[maxn],dep[maxn],now[maxn],depth,lim;
    bool vis[maxn];
    struct node{
        int nxt;
        int to;
        int v;
    }e[maxm];
    
    void add(int from,int to,int v){
        e[cnt].to=to;
        e[cnt].nxt=head[from];
        e[cnt].v=v;
        head[from]=cnt++;
    }
    
    bool bfs(){
        memset(dep,0,sizeof(dep));
        memset(vis,0,sizeof(vis));
        queue<int>q;
        q.push(s);
        dep[s]=1;
        vis[s]=true;
        while(!q.empty()){
            int x=q.front();
            q.pop();
            for(int i=head[x];i!=-1;i=e[i].nxt){
                int y=e[i].to,v=e[i].v;
                if(v&&!vis[y]){
                    vis[y]=1;
                    dep[y]=dep[x]+1;
                    q.push(y);
                }
            }
        }
        return vis[t];
    }
    
    int dfs(int x,int lim){
        if(x==t) return lim;
        int res=0;//res必为局部变量,因为如果是全局变量,中间就清零了,返回值就奇奇怪怪,可能会有负数 
        for(int i=head[x];i!=-1;i=e[i].nxt){
            int y=e[i].to,v=e[i].v;
            if(v&&dep[y]>dep[x]){
                int flow=dfs(y,min(v,lim));//因为这里还要dfs的 
                e[i].v-=flow;
                e[i^1].v+=flow;
                res+=flow;
                lim-=flow;
            }
        }
        if(res==0) dep[x]=0;
        return res;
    }
    
    int dinic(){
        while(bfs()) ans+=dfs(s,inf);
        return ans;
    }
    
    signed main(){
        read(n),read(m),read(s),read(t);
        memset(head,-1,sizeof(head));
        for(int i=1;i<=m;i++){
            read(u),read(v),read(w);
            add(u,v,w);
            add(v,u,0);
        }
        cout<<dinic()<<endl;
        return 0;
    }
    

    orz XiEn1847,orz Blueqwq

    真的写法1

    实测57ms
    (来自AWR2020)

    #include<cstdio>
    #include<algorithm>
    #include<iostream>
    #include<cstring>
    #include<queue>
    
    using namespace std;
    
    typedef long long ll;
    const int N = 5010;
    const long long inf = 0x0fffffffffffffff;
    
    int n, m, s, t;
    int ct = 1, hd[N], ver[N<<1], nxt[N<<1]; ll wt[N<<1];
    int dep[N]; bool inque[N];
    int cur[N];
    
    void add(int u, int v, ll w) {
    	ct ++;
    	ver[ct] = v;
    	wt[ct] = w;
    	nxt[ct] = hd[u];
    	hd[u] = ct;
    	ct ++;
    	ver[ct] = u;
    	wt[ct] = 0;
    	nxt[ct] = hd[v];
    	hd[v] = ct;
    }
    
    bool bfs() {
    	memset(dep, 0x3f, sizeof(dep));
    	memset(inque, 0, sizeof(inque));
    	queue<int> q;
    	q.push(s);
    	dep[s] = 0;
    	cur[s] = hd[s];
    	inque[s] = true;
    	while(q.size()) {
    		int x = q.front();
    		q.pop();
    		inque[x] = false;
    		for(int i = hd[x]; i; i = nxt[i]) {
    			int y = ver[i];
    			if(wt[i] && dep[y] > dep[x] + 1) {
    				dep[y] = dep[x] + 1;
    				cur[y] = hd[y];
    				if(!inque[y]) {
    					q.push(y);
    					inque[y] = true;
    				}
    			}
    		}
    	}
    	if(dep[t] != 0x3f3f3f3f)
    		return true;
    	return false;
    }
    
    ll dfs(int x, ll flow) {
    	ll ret = 0;
    	if(x == t)
    		return flow;
    	for(int i = cur[x]; i; i = nxt[i]) {
    		cur[x] = i;
    		int y = ver[i];
    		if(wt[i] && dep[y] == dep[x] + 1) {
    			if(ret = dfs(y, min(flow, wt[i]))) {
    				wt[i] -= ret;
    				wt[i^1] += ret;
    				return ret;
    			}
    		}
    	}
    	return 0;
    }
    
    ll dinic() {
    	ll maxflow = 0, flow;
    	while(bfs())
    		while(flow = dfs(s, inf))
    			maxflow += flow;
    	return maxflow;
    }
    
    int main() {
    	cin >> n >> m >> s >> t;
    	for(int i = 1; i <= m; i ++) {
    		int u, v; ll w;
    		scanf("%d%d%lld", &u, &v, &w);
    		add(u, v, w);
    	}
    	cout << dinic() << endl;
    	return 0;
    }
    

    orz AWR2020

    真的写法2

    实测54ms
    (来自lhm_)

    #include<iostream>
    #include<cstdio>
    #include<cstdlib>
    #include<queue>
    #include<cstring>
    #define maxn 10010
    #define maxm 200010
    #define int long long
    using namespace std;
    template<typename T>
    inline void read(T &x){
    	x=0; bool flag=0; char c=getchar();
    	for(;!isdigit(c);c=getchar()) if(c=='-') flag=1;
    	for(;isdigit(c);c=getchar()) x=x*10+(c^48);
    	if(flag) x=-x;
    }
    
    const int inf=1e18;
    int n,m,s,t,u,v,w;
    int ans,cnt=1,head[maxn],dep[maxn],cur[maxn],depth,lim,res;//pay attention! ans=1!!!
    struct node{
    	int nxt;
    	int to;
    	int v;
    }e[maxm];
    
    void add(int from,int to,int v){
    	e[++cnt].to=to;
    	e[cnt].nxt=head[from];
    	head[from]=cnt;
    	e[cnt].v=v;
    }
    
    bool bfs(){
    	memcpy(cur,head,sizeof(head));//********
    	memset(dep,0,sizeof(dep));
    	queue<int>q;
    	q.push(s);
    	dep[s]=1;
    	while(!q.empty()){
    		int x=q.front();
    		q.pop();
    		for(int i=head[x];i;i=e[i].nxt){
    			int y=e[i].to,v=e[i].v;
    			if(!v||dep[y]) continue;
    			dep[y]=dep[x]+1;
    			q.push(y);
    		}
    	}
    	return dep[t];
    }
    
    int dfs(int x,int lim){
    	if(x==t) return lim;
    	int res=lim,flow;
    	for(int &i=cur[x];i;i=e[i].nxt){//当前弧优化,cur会和i一起改 
    		int y=e[i].to,v=e[i].v;
    		if(!v||dep[y]!=dep[x]+1) continue;
    		flow=dfs(y,min(v,res));
    		res-=flow;
    		e[i].v-=flow;
    		e[i^1].v+=flow;
    		if(res<=0) break;
    	}
    	return lim-res;
    }
    
    /*
    int dfs(int x,int lim){
    	if(x==t) return lim;
    	int res=lim,flow;
    	for(int i=cur[x];i;i=e[i].nxt){//和上面的写法等效 
    		cur[x]=i;
    		int y=e[i].to,v=e[i].v;
    		if(!v||dep[y]!=dep[x]+1) continue;
    		flow=dfs(y,min(v,res));
    		res-=flow;
    		e[i].v-=flow;
    		e[i^1].v+=flow;
    		if(res<=0) break;
    	}
    	return lim-res;
    }
    */
    
    int dinic(){
    	while(bfs()) while(int flow=dfs(s,inf)) ans+=flow;
    	return ans;
    }
    
    signed main(){
    	read(n),read(m),read(s),read(t);
    	for(int i=1;i<=m;i++){
    		read(u),read(v),read(w);
    		add(u,v,w);
    		add(v,u,0);
    	}
    	cout<<dinic()<<endl;
    	return 0;
    }
    

    orz lhm_,orz i207M,orz AWR2020,orz XiEn1847,orz wsy_jim

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  • 原文地址:https://www.cnblogs.com/DReamLion/p/14732921.html
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