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 Ruby (judge verdict: Accepted)

class EdmondsKarp
  def initialize(n)
    @n = n
    @flow = Array.new(n) { Array.new(n, 0) }
    @cap = Array.new(n) { Array.new(n, 0) }
  end

  def add_edge(s, t, w)
    @cap[s][t] = w
  end

  def max_flow(start, goal)
    inf = 2 ** 30
    sum = 0
    while true
      que = [start]
      prev = Array.new(@n, -1)
      prev[start] = start
      while !que.empty? && prev[goal] == -1
        u = que.shift
        @n.times do |i|
          if prev[i] == -1 && @cap[u][i] - @flow[u][i] > 0
            prev[i] = u
            que.push(i)
          end
        end
      end
      return sum if (prev[goal] == -1)
      inc = inf
      c = goal
      while c != start
        inc = [inc, @cap[prev[c]][c] - @flow[prev[c]][c]].min
        c = prev[c]
      end
      c = goal
      while c != start
        @flow[prev[c]][c] += inc
        @flow[c][prev[c]] -= inc
        c = prev[c]
      end
      sum += inc
    end
  end
end



vn, en = gets.split.map(&:to_i)
g = EdmondsKarp.new(vn)

en.times do |i|
  s, t, w = gets.split.map(&:to_i)
  g.add_edge(s, t, w)
end

puts g.max_flow(0, vn - 1)