Problem: Examples

Input

4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1


Output

6


Input




Output

Solution (in CPP):

Solution:

#include <bits/stdc++.h>


using namespace std;

const int INF = (int) 1e5 + 1;
const int MAX_V = (int) 100;

struct edge { int to, cap, cost, rev; };

vector<edge> G[MAX_V];
int dist[MAX_V];
int prevv[MAX_V], preve[MAX_V];

void add_edge(int from, int to, int cap, int cost) {
    G[from].push_back( (edge) { to, cap, cost, (int) G[to].size() });
    G[to].push_back( (edge) { from, 0, -cost, (int) G[from].size() - 1});
}

int dfs(int v, int t, int f) {
    if (v == t) return f;
    dist[v] = true;
    for (auto &e: G[v]) {
        if (!dist[e.to] && e.cap > 0) {
            int d = dfs(e.to, t, min(f, e.cap));
            if (d > 0) {
                e.cap -= d;
                G[e.to][e.rev].cap += d;
                return d;
            }
        }
    }
    return 0;
}

int main() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);

    int V, E, f;
    cin >> V >> E >> f;

    for (int i = 0; i < E; ++i) {
        int u, v, c, d;
        cin >> u >> v >> c >> d;
        add_edge(u, v, c, d);
    }

    int s = 0;
    int t = V -1;
    int res = 0;
    while (f > 0) {
        fill(dist, dist + V, INF);
        dist[s] = 0;
        bool update = true;
        while (update) {
            update = false;
            for (int v = 0; v < V; ++v) {
                if (dist[v] == INF) continue;
                for (int i = 0; i < G[v].size(); ++i) {
                    edge &e = G[v][i];
                    if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {
                        dist[e.to] = dist[v] + e.cost;
                        prevv[e.to] = v;
                        preve[e.to] = i;
                        update = true;
                    }
                }
            }
        }
        if (dist[t] == INF) {
            res = -1;
            break;
        }
        
        int d = f;
        for (int v = t; v != s; v = prevv[v]) {
            d = min(d, G[prevv[v]][preve[v]].cap);    
        }
        f -= d;
        res += d * dist[t];
        for (int v = t; v != s; v = prevv[v]) {
            edge &e = G[prevv[v]][preve[v]];
            e.cap -= d;
            G[v][e.rev].cap += d;
        }
    }

    cout << res << '\n';

    return 0;
}