网络流板子

Posted 2020-12-18 vikyanite

Dinic模板

#pragma GCC optimize(2)
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
//const int maxm = 1e3 * 2 + 10;
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;

struct Edge{
    int to;
    int next;
    int w;
}edge[maxn*2];
int head[maxn];
int cur[maxn];//当前弧优化数组
int n, m, s, t;//点数，边数，源点，汇点
int dis[maxn];//Bfs深度
int cnt = 0;//边数
int x;

inline void init(){
    cnt = 0;
    memset(head, -1, sizeof head);
}

inline void Add_Edge(int u, int v, int w){
    edge[cnt].next = head[u];
    edge[cnt].to = v;
    edge[cnt].w = w;
    head[u] = cnt++;
}

inline bool Bfs(){
    for(int i = 1; i <= n; ++i) dis[i] = -1;
    dis[s] = 0;
    queue<int> q;
    q.push(s);
    while(!q.empty()){
        int u = q.front(); q.pop();
        for(int i = head[u]; i != -1; i = edge[i].next){
            int v = edge[i].to;
            if(dis[v] == -1 && edge[i].w){//没有标记深度并且有残量
                dis[v] = dis[u] + 1;
                q.push(v);
            }
        }
    }
    return dis[t] != -1;
}

inline int dfs(int u, int flow){
    if(u == t) return flow;
    int del = flow;
    for(int i = cur[u]; i != -1; i = edge[i].next){
        cur[u] = edge[i].next;//当前弧优化，下次直接从cur[u]开始增广，节省时间
        int v = edge[i].to;
        if(dis[v] == dis[u] + 1 && edge[i].w > 0){//深度+1且残量大于0
            int ans = dfs(v, min(del, edge[i].w));//木桶原理
            edge[i].w -= ans;//正向弧减增广流量
            edge[i ^ 1].w += ans;//反向弧加增广流量
            del -= ans;//总流量减增广流量
            if(del == 0) break;//总流量为0则不继续增广
        }
    }
    return flow - del;//返回本次增广的流量
}

inline int Dinic(){
    int ans = 0;
    while(Bfs()){
        for(int i = 1; i <= n; ++i) cur[i] = head[i];
        ans += dfs(s, inf);
    }
    return ans;
}

int main(){

    scanf("%d %d %d", &n, &m, &x);
    s = 1, t = n;
    init();
    for(int i = 1; i <= m; ++i){
        int u, v, w;
        scanf("%d %d %d", &u, &v, &w);
        Add_Edge(u, v, w);
        Add_Edge(v, u, 0);
    }
    int ans = Dinic();
    if (!ans) cout << "Orz Ni Jinan Saint Cow!" << endl;
    else {
        int ans1 = ceil(x*1./ans);
        printf("%d %d
", ans, ans1);
    }
    return 0;
}

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ISAP模板

#pragma GCC optimize(2)
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1e5 + 10;
//const int maxm = 1e3 * 2 + 10;
const int inf = 0x3f3f3f3f;
const int mod = 1e9 + 7;
int m,n,s,t, x, head[maxn], num_edge;
int cur[maxn],deep[maxn],last[maxn],num[maxn];
//cur当前弧优化； last该点的上一条边； num桶 用来GAP优化
struct Edge{
    int next,to,dis;
}edge[maxn*2];

void add_edge(int from,int to,int dis)
{
    edge[num_edge].to=to;
    edge[num_edge].dis=dis;
    edge[num_edge].next=head[from];
    head[from]=num_edge++;
}
//bfs仅用于更新deep
void bfs(int t)
{
    queue<int>q;
    for (int i=0; i<=n; i++) cur[i]=head[i];
    for (int i=1; i<=n; i++) deep[i]=n;
    deep[t]=0;
    q.push(t);
    while (!q.empty())
    {
        int now=q.front(); q.pop();
        for (int i=head[now]; i != -1; i=edge[i].next)
        {
            if (deep[edge[i].to]==n && edge[i^1].dis)//i^1是为了找反边
            {
                deep[edge[i].to] = deep[now]+1;
                q.push(edge[i].to);
            }
        }
    }
}

int add_flow(int s,int t)
{
    int ans=inf,now=t;
    while (now!=s)
    {
        ans=min(ans,edge[last[now]].dis);
        now=edge[last[now]^1].to;
    }
    now=t;
    while (now!=s)
    {
        edge[last[now]].dis-=ans;
        edge[last[now]^1].dis+=ans;
        now=edge[last[now]^1].to;
    }
    return ans;
}
int isap(int s,int t)
{
    int now=s;
    int maxflow = 0;
    bfs(t);//搜出一条增广路
    for (int i=1; i<=n; i++) num[deep[i]]++;
    while (deep[s]<n)
    {
        if (now==t)
        {//如果到达汇点就直接增广，重新回到源点进行下一轮增广
            maxflow+=add_flow(s,t);
            now=s;//回到源点
        }
        bool has_find=0;
        for (int i=cur[now]; i!=-1; i=edge[i].next)
        {
            if (deep[now]==deep[edge[i].to]+1 && edge[i].dis)//找到一条增广路
            {
                has_find=true;
                cur[now]=i;//当前弧优化
                now=edge[i].to;
                last[edge[i].to]=i;
                break;
            }
        }
        if (!has_find)//没有找到出边，重新编号
        {
            int minn=n-1;
            for (int i=head[now]; i!=-1; i=edge[i].next)//回头找路径
                if (edge[i].dis)
                    minn=min(minn,deep[edge[i].to]);
            if ((--num[deep[now]])==0) break;//GAP优化 出现了断层
            num[deep[now]=minn+1]++;
            cur[now]=head[now];
            if (now!=s)
                now=edge[last[now]^1].to;
        }
    }
    return maxflow;
}
int main(){
    num_edge = 0;
    memset(head,-1,sizeof(head));
    scanf("%d%d%d",&n,&m,&x);
    for(int i=0;i<m;i++){
            int u,v,cap;
            scanf("%d%d%d",&u,&v,&cap);
            add_edge(u,v,cap);
            add_edge(v,u,0);
    }
    s = 1, t = n;
    int ans = isap(s,t);
    if (!ans) cout << "Orz Ni Jinan Saint Cow!" << endl;
    else {
        int ans2 = ceil(x*1./ans);
        printf("%d %d
", ans, ans2);
    }

    return 0;
}

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