820 - Internet Bandwidth

#pragma GCC optimize("Ofast,unroll-loops")
#include <bits/stdc++.h>

#define sz(a) ((int)(a).size())
#define all(a) (a).begin(), (a).end()

#define fi first
#define se second

using namespace std;

#ifndef LOCAL
#define endl '\n'
#endif

typedef long long ll;
typedef pair<int, int> pii;

const int NMAX = 105;
const int INF = 2e9+5;

struct Edge {
    int dest, flow, rev;
};

int n, s, t, m;
vector<Edge> g[NMAX];
int d[NMAX], last[NMAX];

void io() {
#ifdef LOCAL
    freopen("input.txt", "r", stdin);
#else
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
#endif
}

void add_edge(int x, int y, int c) {
    g[x].push_back({ y, c, sz(g[y]) });
    g[y].push_back({ x, 0, sz(g[x]) - 1 });
}

void read() {
    cin >> n;
    if (n == 0) exit(0);
    cin >> s >> t >> m;
    for (int i = 1, x, y, c; i <= m; i++) {
        cin >> x >> y >> c;
        add_edge(x, y, c);
        add_edge(y, x, c);
    }
}

bool bfs() {
    memset(d, 0, sizeof(d));
    memset(last, 0, sizeof(last));

    queue<int> q;
    q.push(s);
    d[s] = 1;

    while (!q.empty()) {
        int u = q.front();
        q.pop();
        if (u == t) continue;
        for (auto &it : g[u]) {
            if (!d[it.dest] && it.flow > 0) {
                d[it.dest] = d[u] + 1;
                q.push(it.dest);
            }
        }
    }

    return d[t];
}

int dfs(int x, int flow = INF) {
    if (x == t) return flow;

    for (; last[x] < sz(g[x]); last[x]++) {
        Edge &e = g[x][last[x]];
        if (e.flow > 0 && d[e.dest] == d[x] + 1) {
            if (int ret = dfs(e.dest, min(flow, e.flow))) {
                e.flow -= ret;
                g[e.dest][e.rev].flow += ret;
                return ret;
            }
        }
    }

    return 0;
}

int dinic() {
    int max_flow = 0;
    while (bfs()) {
        while (int flow = dfs(s))
            max_flow += flow;
    }
    for (int i = 1; i <= n; i++) g[i].clear();
    return max_flow;
}

signed main() {
    io();
    for (int i = 1; ; i++) {
        read();
        cout << "Network " << i << endl << "The bandwidth is " << dinic() << '.' << endl << endl;
    }
    return 0;
}