Problem:
MathJax.Hub.Config({ tex2jax: { inlineMath: [["$","$"], ["\\(","\\)"]], processEscapes: true }});

Minimum Cost Flow

Find the minimum cost to send a certain amount of flow through a flow network.

The flow network is a directed graph where each edge $e$ has capacity $c(e)$ and cost $d(e)$. Each edge $e$ can send an amount of flow $f(e)$ where $f(e) \leq c(e)$. Find the minimum value of $\sum_{e} (f(e) \times d(e))$ to send an amount of flow $F$ from source $s$ to sink $t$.

Input

A flow network $G(V,E)$ is given in the following format.

$|V|\;|E|\;F$

$u_0\;v_0\;c_0\;d_0$

$u_1\;v_1\;c_1\;d_1$

:

$u_{|E|1}\;v_{|E|-1}\;c_{|E|-1}\;d_{|E|-1}$

$|V|$, $|E|$, $F$ are the number of vertices, the number of edges, and the amount of flow of the flow network respectively. The vertices in $G$ are named with the numbers $0, 1,..., |V|−1$. The source is $0$ and the sink is $|V|−1$.

$u_i$, $v_i$, $c_i$, $d_i$ represent $i$-th edge of the flow network. A pair of $u_i$ and $v_i$ denotes that there is an edge from $u_i$ to $v_i$, and $c_i$ and $d_i$ are the capacity and the cost of $i$-th edge respectively.

Output

Print the minimum value in a line. If it is impossible to send the flow from the source $s$ to the sink $t$, print -1.

Constraints

2 ≤ $|V|$ ≤ 100

1 ≤ $|E|$ ≤ 1000

0 ≤ $F$ ≤ 1000

0 ≤ $c_i$, $d_i$ ≤ 1000

$u_i$ $\ne$ $v_i$

If there is an edge from vertex $x$ to vertex $y$, there is no edge from vertex $y$ to vertex $x$.

Sample Input

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

Sample Output

6

Solution in JAVA (judge verdict: Accepted)

import java.io.*;
import java.util.*;

public class Main implements Runnable{
    private ArrayList<ArrayList<Integer>> graph;
    private Edge[] edges;
    public static void main(String[] args) throws Exception {
        new Thread(null, new Main(), "bridge", 16 * 1024 * 1024).start();
    }

    @Override
    public void run() {
        try {
            solve();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    private void solve() throws Exception{
        FastScanner scanner = new FastScanner(System.in);

        int V = scanner.nextInt();
        int E = scanner.nextInt();
        int F = scanner.nextInt();

        graph = new ArrayList<>(V);
        edges = new Edge[E * 2];
        for(int i = 0; i < V; ++i){
            graph.add(new ArrayList<Integer>());
        }

        int edgeSize = 0;
        for(int i = 0; i < E; ++i){
            int u = scanner.nextInt();
            int v = scanner.nextInt();
            int cap = scanner.nextInt();
            int cost = scanner.nextInt();

            edges[edgeSize++] = new Edge(v, 0, cap, cost);
            edges[edgeSize++] = new Edge(u, 0, 0, -cost);
            graph.get(u).add(edgeSize - 2);
            graph.get(v).add(edgeSize - 1);
        }

        costOfMaxFlow(F, 0, V - 1);
    }

    private void costOfMaxFlow(int F, int s, int t){
        int V = graph.size();
        int[] dist = new int[V];
        int[] curFlow = new int[V];
        int[] prevNode = new int[V];
        int[] prevEdge = new int[V];

        int totalFlow = 0;
        int totalCost = 0;

        while(totalFlow < F){
            BellmanFord(s, dist, prevNode, prevEdge, curFlow);
            if(dist[t] == Integer.MAX_VALUE){
                break;
            }

            int pathFlow = Math.min(curFlow[t], F - totalFlow);
            totalFlow += pathFlow;

            for(int v = t; v != s; v = prevNode[v]){
                Edge edge = edges[prevEdge[v]];
                totalCost += edge.cost * pathFlow;

                edge.flow += pathFlow;
                edges[prevEdge[v] ^ 1].flow -= pathFlow;
            }
        }

        if(totalFlow < F){
            System.out.println("-1");
        }
        else{
            System.out.println(totalCost);
        }
    }

    private void BellmanFord(int s, int[] dist, int[] prevNode, int[] prevEdge, int[] curFlow) {
        Arrays.fill(dist, Integer.MAX_VALUE);
        dist[s] = 0;
        curFlow[s] = Integer.MAX_VALUE;
        prevNode[s] = -1;
        prevEdge[s] = -1;

        int V = dist.length;
        boolean[] inqueue = new boolean[V];
        int[] q = new int[V];
        int qt = 0;
        q[qt++] = s;
        for (int qh = 0; (qh - qt) % V != 0; qh++) {
            int u = q[qh % V];
            inqueue[u] = false;
            for (int edgeIndex : graph.get(u)) {
                Edge edge = edges[edgeIndex];

                if (edge.flow >= edge.cap) {
                    continue;
                }

                if (dist[edge.v] > dist[u] + edge.cost) {
                    dist[edge.v] = dist[u] + edge.cost;
                    prevNode[edge.v] = u;
                    prevEdge[edge.v] = edgeIndex;
                    curFlow[edge.v] = Math.min(curFlow[u], edge.cap - edge.flow);

                    if(!inqueue[edge.v]){
                        inqueue[edge.v] = true;
                        q[qt++ % V] = edge.v;
                    }
                }
            }

        }
    }

    static class Edge{
        int v;
        int flow;
        int cap;
        int cost;

        public Edge(int v, int flow, int cap, int cost){
            this.v = v;
            this.flow = flow;
            this.cap = cap;
            this.cost = cost;
        }
    }

    static class FastScanner {
        private InputStream in;
        private final byte[] buffer = new byte[1024 * 8];
        private int ptr = 0;
        private int buflen = 0;

        public FastScanner(InputStream in){
            this.in = in;
        }

        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            } else {
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }

        private int readByte() {
            if (hasNextByte()) return buffer[ptr++];
            else return -1;
        }

        private static boolean isPrintableChar(int c) {
            return 33 <= c && c <= 126;
        }

        private void skipUnprintable() {
            while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
        }

        public boolean hasNext() {
            skipUnprintable();
            return hasNextByte();
        }

        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while (isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}