HDU 3549 Flow Problem 網絡最大流問題 Edmonds_Karp算法

 

 

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)
題意：

 

純求網絡最大流，用EK算法就可以實現。

 

代碼：

 

#include 
#include 
#include 
#include 
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 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找增光路徑
        {

            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])  //改進網絡流
        {
            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
, cas, ans);
    }
    return 0;
}