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HDU 3549 Flow Problem 网络最大流问题 Edmonds_Karp算法

2024-07-23 21:29:41   222人阅读

题目链接：HDU 3549 Flow Problem

Flow Problem

Time Limit: 5000/5000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others)
Total Submission(s): 8218    Accepted Submission(s): 3824


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
 

Source
HyperHexagon‘s Summer Gift (Original tasks)
 

题意：

纯求网络最大流，用EK算法就可以实现。


代码：

#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;

#define maxn 20
#define INF 0x3f3f3f3f
int ans, s, t, n;
int a[maxn], pre[maxn];
int flow[maxn][maxn];
int cap[maxn][maxn];

void Edmonds_Karp()
{
    queue<int> q;
    memset(flow, 0, sizeof(flow));
    ans = 0;
    while(1)
    {
        memset(a, 0, sizeof(a));
        a[s] = INF;
        q.push(s);
        while(!q.empty())   //bfs找增光路径
        {

            int u = q.front();
            q.pop();
            for(int v = 1; v <= n; v++)
                if(!a[v] && cap[u][v] > flow[u][v])
                {
                    pre[v] = u;
                    q.push(v);
                    a[v] = min(a[u], cap[u][v]-flow[u][v]);
                }
        }
        if(a[t] == 0) break;
        for(int u = t; u != s; u = pre[u])  //改进网络流
        {
            flow[pre[u]][u] += a[t];
            flow[u][pre[u]] -= a[t];
        }
        ans += a[t];
    }
}

int main()
{
    //freopen("hdu_3549.txt", "r", stdin);
    int T, m, u, v, c;
    scanf("%d", &T);
    for(int cas = 1; cas <= T; cas++)
    {
        scanf("%d%d", &n, &m);
        memset(cap, 0, sizeof(cap));
        while(m--)
        {
            scanf("%d%d%d", &u, &v, &c);
            cap[u][v] += c;
        }
        s = 1, t = n;
        Edmonds_Karp();
        printf("Case %d: %d\n", cas, ans);
    }
    return 0;
}





HDU 3549 Flow Problem 网络最大流问题 Edmonds_Karp算法


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