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 Scala (judge verdict: Accepted)

import java.util.Scanner

import scala.collection.mutable
import scala.collection.mutable.ArrayBuffer

object Main extends App {
  val in = new Scanner(System.in)
  val V = in.nextInt()
  val E = in.nextInt()
  val dinitz = new Dinitz(V)
  for (_ <- 0 until E) {
    val s = in.nextInt()
    val t = in.nextInt()
    val c = in.nextInt()
    dinitz.addEdge(s, t, c)
  }

  val f = dinitz.maxFlow(0, V - 1)
  println(f)
}

import java.util

class Dinitz(val V: Int) {

  class Edge(var to: Int, var cap: Long, var rev: Int)

  private val graph = (for (_ <- 0 until V) yield new ArrayBuffer[Edge]()).toArray
  private val level = new Array[Int](V)
  private val iter = new Array[Int](V)


  def addEdge(from: Int, to: Int, cap: Long): Unit = {
    graph(from).append(new Edge(to, cap, graph(to).size))
    graph(to).append(new Edge(from, 0, graph(from).size - 1))
  }

  def maxFlow(source: Int, sink: Int): Long = {
    var flow = 0L

    while (true) {
      val queue = new mutable.Queue[Int]()
      util.Arrays.fill(level, -1)
      level(source) = 0
      queue.enqueue(source)
      while (queue.nonEmpty) {
        val v = queue.dequeue()
        for (e <- graph(v)) {
          if (e.cap > 0 && level(e.to) < 0) {
            level(e.to) = level(v) + 1
            queue.enqueue(e.to)
          }
        }
      }

      if (level(sink) < 0) return flow
      util.Arrays.fill(iter, 0)

      def dfs(v: Int, t: Int, f: Long): Long = {
        if (v == t) return f

        while (iter(v) < graph(v).size) {
          val e = graph(v)(iter(v))
          if (e.cap > 0 && level(v) < level(e.to)) {
            val d = dfs(e.to, t, Math.min(f, e.cap))
            if (d > 0) {
              e.cap -= d
              graph(e.to)(e.rev).cap += d
              return d
            }
          }

          iter(v) += 1
        }
        0
      }
      
      var f = 1L
      while (f > 0) {
        f = dfs(source, sink, Long.MaxValue)
        flow += f
      }
    }

    throw new IllegalStateException()
  }
}