Hdu3549 Flow Problem 2017-02-11 16:24 58人阅读 评论(0) 收藏

Flow Problem

Problem Description

Network flow is a well-known difficult problem for ACMers. Given a graph, your task is to find out the maximum flow for the weighted directed graph.

 

Input

The first line of input contains an integer T, denoting the number of test cases.

For each test case, the first line contains two integers N and M, denoting the number of vertexes and edges in the graph. (2 <= N <= 15, 0 <= M <= 1000)

Next M lines, each line contains three integers X, Y and C, there is an edge from X to Y and the capacity of it is C. (1 <= X, Y <= N, 1 <= C <= 1000)

 

Output

For each test cases, you should output the maximum flow from source 1 to sink N.

 

Sample Input

2
3 2
1 2 1
2 3 1
3 3
1 2 1
2 3 1
1 3 1

 

Sample Output

Case 1: 1
Case 2: 2

 

Author

HyperHexagon

 

————————————————————————————————————————————————————————

题目要求很简单，求从第一个点到最后一个点的最大流量。

最大流板子题，直接套模板，

Dinic

#include <iostream>
#include <cstdio>
#include <cstring>
#include <string>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <vector>
#include <bitset>

using namespace std;

#define LL long long
const int INF = 0x3f3f3f3f;
#define MAXN 500

struct node
{
    int u, v, next, cap;
} edge[MAXN*MAXN];
int nt[MAXN], s[MAXN], d[MAXN], visit[MAXN];
int cnt;

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

void add(int u, int v, int c)
{
    edge[cnt].u = u;
    edge[cnt].v = v;
    edge[cnt].cap = c;
    edge[cnt].next = s[u];
    s[u] = cnt++;
    edge[cnt].u = v;
    edge[cnt].v = u;
    edge[cnt].cap = 0;
    edge[cnt].next = s[v];
    s[v] = cnt++;
}

bool BFS(int ss, int ee)
{
    memset(d, 0, sizeof d);
    d[ss] = 1;
    queue<int>q;
    q.push(ss);
    while (!q.empty())
    {
        int pre = q.front();
        q.pop();
        for (int i = s[pre]; ~i; i = edge[i].next)
        {
            int v = edge[i].v;
            if (edge[i].cap > 0 && !d[v])
            {
                d[v] = d[pre] + 1;
                q.push(v);
            }
        }
    }
    return d[ee];
}

int DFS(int x, int exp, int ee)
{
    if (x == ee||!exp) return exp;
    int temp,flow=0;
    for (int i = nt[x]; ~i ; i = edge[i].next, nt[x] = i)
    {
        int v = edge[i].v;
        if (d[v] == d[x] + 1&&(temp = (DFS(v, min(exp, edge[i].cap), ee))) > 0)
        {
            edge[i].cap -= temp;
            edge[i ^ 1].cap += temp;
            flow += temp;
            exp -= temp;
            if (!exp) break;
        }
    }
    if (!flow) d[x] = 0;
    return flow;
}

int Dinic_flow(int ss, int ee)
{
    int ans = 0;
    while (BFS(ss, ee))
    {
        for (int i = 0; i <= ee; i++) nt[i] = s[i];
        ans+= DFS(ss, INF, ee);
    }
    return ans;
}

int main()
{
    int n,m,u,v,c,T;
    int q=1;
    scanf("%d",&T);
    while (T--)
    {
        scanf("%d %d", &n, &m);
        init();
        for(int i=0; i<m; i++)
        {
            scanf("%d%d%d",&u,&v,&c);
            add(u,v,c);
        }
        printf("Case %d: %d\n",q++,Dinic_flow(1,n));

    }
    return 0;
}

isap+bfs

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <string>
#include <queue>
#include <vector>
#include <stack>
#include <set>
#include <map>
using namespace std;
const int MAXN =100010;//点max
const int MAXM=400010;//边max
const int INF=0x3f3f3f3f;
struct Edge
{
    int to,next,cap,flow;
} edge[MAXM];
int tol;
int head[MAXN];
int gap[MAXN],dep[MAXN],cur[MAXN];
void init()
{
    tol=0;
    memset(head,-1,sizeof(head));
}
void addedge(int u,int v,int w,int rw=0)
{
    edge[tol].to=v;
    edge[tol].cap=w;
    edge[tol].flow=0;
    edge[tol].next=head[u];
    head[u]=tol++;
    edge[tol].to=u;
    edge[tol].cap=rw;
    edge[tol].flow=0;
    edge[tol].next=head[v];
    head[v]=tol++;
}

int Q[MAXN];
void BFS(int start,int end)
{
    memset(dep,-1,sizeof(dep));
    memset(gap,0,sizeof(gap));
    gap[0]=1;
    int front=0,rear=0;
    dep[end]=0;
    Q[rear++]=end;
    while(front!=rear)
    {
        int u=Q[front++];
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            int v=edge[i].to;
            if(dep[v]!=-1)
                continue;
            Q[rear++]=v;
            dep[v]=dep[u]+1;
            gap[dep[v]]++;
        }
    }
}

int S[MAXN];
int sap(int start,int end,int N)
{
    BFS(start,end);
    memcpy(cur,head,sizeof(head));
    int top=0;
    int u =start;
    int ans=0;
    while(dep[start]<N)
    {
        if(u==end)
        {
            int Min=INF;
            int inser;
            for(int i=0; i<top; i++)
            {
                if(Min>edge[S[i]].cap-edge[S[i]].flow)
                {
                    Min=edge[S[i]].cap-edge[S[i]].flow;
                    inser=i;
                }
            }

            for(int i=0; i<top; i++)
            {
                edge[S[i]].flow+=Min;
                edge[S[i]^1].flow-=Min;

            }
            ans+=Min;
            top=inser;
            u=edge[S[top]^1].to;
            continue;
        }

        bool flag=false;
        int v;
        for(int i=cur[u]; i!=-1; i=edge[i].next)
        {
            v=edge[i].to;
            if(edge[i].cap-edge[i].flow&&dep[v]+1==dep[u])
            {
                flag=true;
                cur[u]=i;
                break;
            }

        }
        if(flag)
        {
            S[top++]=cur[u];
            u=v;
            continue;
        }
        int Min=N;
        for(int i=head[u]; i!=-1; i=edge[i].next)
        {
            if(edge[i].cap-edge[i].flow&&dep[edge[i].to]<Min)
            {
                Min=dep[edge[i].to];
                cur[u]=i;
            }
        }
        gap[dep[u]]--;
        if(!gap[dep[u]])return ans;
        dep[u]=Min+1;
        gap[dep[u]]++;
        if(u!=start)
            u=edge[S[--top]^1].to;
    }
    return ans;

}

int main()
{
    int n,m,u,v,w,T;
    while(~scanf("%d",&T))
    {
        int q=0;
        while(T--)
        {
            scanf("%d%d",&m,&n);
            init();
            for(int i=0; i<n; i++)
            {
                scanf("%d%d%d",&u,&v,&w);
                addedge(u,v,w,0);
            }
            int ans=sap(1,m,m);
            printf("Case %d: %d\n",++q,ans);
        }
    }

    return 0;
}