Problem:
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Maximum Flow

A flow network is a directed graph which has a $source$ and a $sink$. In a flow network, each edge $(u, v)$ has a capacity $c(u, v)$. Each edge receives a flow, but the amount of flow on the edge can not exceed the corresponding capacity. Find the maximum flow from the $source$ to the $sink$.

Input

A flow network is given in the following format.

$|V|\;|E|$

$u_0\;v_0\;c_0$

$u_1\;v_1\;c_1$

:

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

$|V|$, $|E|$ is the number of vertices and edges 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 $|V|-1$.

$u_i$, $v_i$, $c_i$ 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 $c_i$ is the capacity of $i$-th edge.

Output

Print the maximum flow.

Constraints

$2 \leq |V| \leq 100$

$1 \leq |E| \leq 1000$

$0 \leq c_i \leq 10000$

Sample Input 1

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

Sample Output 1

3

Solution in JAVA (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    int v, e;

    public static void main(String args[]) {
        new Main().run();
    }

    void run() {
        FastReader sc = new FastReader();
        v = sc.nextInt();
        e = sc.nextInt();
        Dinic d = new Dinic(v);
        for (int i = 0; i < e; i++) {
            int from = sc.nextInt();
            int to = sc.nextInt();
            int capacity = sc.nextInt();
            d.addEdge(from, to, capacity);
        }
        long ans = d.maximumFlow(0, v - 1);
        System.out.println(ans);
    }

    public class Dinic {
        ArrayList<ArrayList<DinicEdge>> graph;
        // distances from s
        int[] levels;
        int[] iters;

        Dinic(int n) {
            graph = new ArrayList<>();
            for (int i = 0; i < n; i++) {
                graph.add(new ArrayList<>());
            }
            levels = new int[n];
            iters = new int[n];
            // manually add edges by using addEdge
        }

        void bfs(int s) {
            Arrays.fill(levels, -1);
            Queue<Integer> queue = new LinkedList<>();
            levels[s] = 0;
            queue.offer(s);
            while (!queue.isEmpty()) {
                int v = queue.poll();
                for (DinicEdge e : graph.get(v)) {
                    if (e.capacity > 0 && levels[e.to] < 0) {
                        levels[e.to] = levels[v] + 1;
                        queue.offer(e.to);
                    }
                }
            }
        }

        long dfs(int v, int t, long f) {
            if (v == t) {
                return f;
            }
            for (int i = iters[v]; i < graph.get(v).size(); i++) {
                DinicEdge e = graph.get(v).get(i);
                if (e.capacity > 0 && levels[v] < levels[e.to]) {
                    long d = dfs(e.to, t, Math.min(f, e.capacity));
                    if (d > 0) {
                        e.capacity -= d;
                        graph.get(e.to).get(e.reverse).capacity += d;
                        return d;
                    }
                }
            }
            return 0;
        }

        long maximumFlow(int s, int t) {
            long flow = 0;
            while (true) {
                bfs(s);
                if (levels[t] < 0) {
                    return flow;
                }
                Arrays.fill(iters, 0);
                long f;
                while ((f = dfs(s, t, Long.MAX_VALUE)) > 0) {
                    flow += f;
                }
            }
        }

        void addEdge(int from, int to, int capacity) {
            graph.get(from).add(new DinicEdge(to, capacity, graph.get(to).size()));
            graph.get(to).add(new DinicEdge(from, 0, graph.get(from).size() - 1));
        }
    }

    class DinicEdge {
        int to;
        int capacity;
        int reverse;

        DinicEdge(int to, int capacity, int reverse) {
            this.to = to;
            this.capacity = capacity;
            this.reverse = reverse;
        }
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}