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)

INF = 1<<29

def dfs(v, f)
  return f if v == $goal
  $used[v] = true
  $g[v].each do |u, c|
    if !$used[u] && c > 0
      d = dfs(u, [f, c].min)
      if d > 0
        $g[v][u] -= d
        $g[u][v] += d
        return d
      end
    end
  end
  0
end

def max_flow(size)
  flow = 0
  loop do
    $used =  [false] * size
    f = dfs($start, INF)
    return flow if f == 0
    flow += f
  end
end

v, e = gets.split.map(&:to_i)
$g = v.times.map { {} }
$start = 0
$goal = v - 1

e.times do
  s, t, c = gets.split.map(&:to_i)
  $g[s][t] = c
  $g[t][s] = 0
end

p max_flow(v)