UVA-10480-Sabotage(最大流最小割,打印路径)

链接:

https://vjudge.net/problem/UVA-10480

题意:

The regime of a small but wealthy dictatorship has been abruptly overthrown by an unexpected rebellion. Because of the enormous disturbances this is causing in world economy, an imperialist military
super power has decided to invade the country and reinstall the old regime.
For this operation to be successful, communication between the capital and the largest city must
be completely cut. This is a difficult task, since all cities in the country are connected by a computer
network using the Internet Protocol, which allows messages to take any path through the network.
Because of this, the network must be completely split in two parts, with the capital in one part and
the largest city in the other, and with no connections between the parts.
There are large differences in the costs of sabotaging different connections, since some are much
more easy to get to than others.
Write a program that, given a network specification and the costs of sabotaging each connection,
determines which connections to cut in order to separate the capital and the largest city to the lowest
possible cost.

思路:

求最少花费不联通,最小割,不过打印路径是最小割的一条边,不是全部边.
所有在最后一次增广后,bfs可以得到跟源点联通和跟汇点联通的边,打印对应的即可.

代码:

#include <iostream>
#include <cstdio>
#include <cstring>
#include <vector>
//#include <memory.h>
#include <queue>
#include <set>
#include <map>
#include <algorithm>
#include <math.h>
#include <stack>
#include <string>
#define MINF 0x3f3f3f3f
using namespace std;
typedef long long LL;

const int MAXN = 200+10;
const int INF = 1e9;

struct Edge
{
    int from, to, cap;
};
vector<Edge> edges;
vector<int> G[MAXN*4];
int Dis[MAXN*4];
int a[MAXN*4], b[MAXN*4];
int n, m, s, t;

void AddEdge(int from, int to, int cap)
{
    edges.push_back(Edge{from, to, cap});
    edges.push_back(Edge{to, from, cap});
    G[from].push_back(edges.size()-2);
    G[to].push_back(edges.size()-1);
}

bool Bfs()
{
    memset(Dis, -1, sizeof(Dis));
    queue<int> que;
    que.push(s);
    Dis[s] = 0;
    while (!que.empty())
    {
        int u = que.front();
        que.pop();
//        cout << u << endl;
        for (int i = 0;i < G[u].size();i++)
        {
            Edge &e = edges[G[u][i]];
            if (e.cap > 0 && Dis[e.to] == -1)
            {
                Dis[e.to] = Dis[u]+1;
                que.push(e.to);
            }
        }
    }
    return Dis[t] != -1;
}

int Dfs(int u, int flow)
{
    if (u == t)
        return flow;
    int res = 0;
    for (int i = 0;i < G[u].size();i++)
    {
        Edge &e = edges[G[u][i]];
        if (e.cap > 0 && Dis[u]+1 == Dis[e.to])
        {
            int tmp = Dfs(e.to, min(flow, e.cap));
//            cout << "flow:" << e.from << ' ' << e.to << ' ' << tmp << endl;
            e.cap -= tmp;
            flow -= tmp;
            edges[G[u][i]^1].cap += tmp;
            res += tmp;
            if (flow == 0)
                break;
        }
    }
    if (res == 0)
        Dis[u] = -1;
    return res;
}

int MaxFlow()
{
    int res = 0;
    while (Bfs())
    {
        res += Dfs(s, INF);
    }
    return res;
}

int main()
{
//    freopen("test.in", "r", stdin);
    ios::sync_with_stdio(false);
    cin.tie(0);
    while (cin >> n >> m && n)
    {
        for (int i = 1;i <= n;i++)
            G[i].clear();
        edges.clear();
        s = 1, t = 2;
        int u, v, w;
        for (int i = 1;i <= m;i++)
        {
            cin >> u >> v >> w;
            AddEdge(u, v, w);
            a[i] = u, b[i] = v;
        }
        int res = MaxFlow();
        for (int i = 1;i <= m;i++)
        {
            if ((Dis[a[i]] >= 0 && Dis[b[i]] == -1) || (Dis[b[i]] >= 0 && Dis[a[i]] == -1))
                cout << a[i] << ' ' << b[i] << endl;
        }
        cout << endl;
    }

    return 0;
}