HDU3549最大流多路增广(Ford-Fulkerson邻接矩阵)

最新推荐文章于 2021-02-27 08:13:16 发布

Rain722

最新推荐文章于 2021-02-27 08:13:16 发布

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本文解析了HDU3549最大流问题，提供了两种不同的深度优先搜索算法实现方法，并通过具体代码示例展示了如何解决从1号点到N号点的最大流问题。

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HDU 3549 Flow Problem(最大流入门)

http://acm.hdu.edu.cn/showproblem.php?pid=3549

题意:

给你一个N个顶点M条边的有向图,要你求1号点到N号点的最大流.

分析:

注意本题有重边.

code 1:

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
using namespace std;
#define INF 0x3f3f3f3f
const int maxn = 16;
int cap[maxn][maxn];
bool vis[maxn];
int n, m, s, t, maxflow;
int dfs(int u, int low)
{
    int flow;
    if(u == t)
        return low;
    vis[u] = true;
    for(int v = 1; v <= n; v++)
    {
        if(!vis[v] && cap[u][v] && (flow = dfs(v, min(low, cap[u][v]))))
        {
            cap[u][v] -= flow;
            cap[v][u] += flow;
            return flow;
        }
    }
    return 0;
}
int main()
{
    int T, u, v, w, flow;
    scanf("%d", &T);
    for(int kase = 1; kase <= T; kase++)
    {
        scanf("%d%d", &n, &m);
        memset(cap, 0, sizeof(cap));
        memset(vis, false, sizeof(vis));
        for(int i = 1; i <= m ; i++)
        {
            scanf("%d%d%d", &u, &v, &w);
            cap[u][v] += w;
        }
        s = 1, t = n;
        maxflow = 0;
        while(flow = dfs(s, INF))
        {
            maxflow += flow;
            memset(vis, false, sizeof(vis));
        }
        printf("Case %d: %d\n", kase, maxflow);
    }
    return 0;
}

code2: 多路增广

#include<iostream>
#include<cstring>
#include<cstdio>
#include<queue>
using namespace std;
#define INF 0x3f3f3f3f
const int maxn = 16;
int cap[maxn][maxn];
bool vis[maxn];
int n, m, s, t, maxflow;
int dfs(int u, int low)
{
    int flow, sum = 0;
    if(u == t)
        return low;
    vis[u] = true;
    for(int v = 1; v <= n; v++)
    {
        if(!vis[v] && cap[u][v] && (flow = dfs(v, min(low, cap[u][v]))))
        {
            sum += flow;
            low -= flow;
            cap[u][v] -= flow;
            cap[v][u] += flow;
            if(!low)
                break;
        }
    }
    return sum;
}
int main()
{
    int T, u, v, w, flow;
    scanf("%d", &T);
    for(int kase = 1; kase <= T; kase++)
    {
        scanf("%d%d", &n, &m);
        memset(cap, 0, sizeof(cap));
        memset(vis, false, sizeof(vis));
        for(int i = 1; i <= m ; i++)
        {
            scanf("%d%d%d", &u, &v, &w);
            cap[u][v] += w;
        }
        s = 1, t = n;
        maxflow = 0;
        while(flow = dfs(s, INF))
        {
            maxflow += flow;
            memset(vis, false, sizeof(vis));
        }
        printf("Case %d: %d\n", kase, maxflow);
    }
    return 0;
}