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: Wrong Answer)

class MaxFlow
  def initialize
    @node={}#Hash.new{|h,k|h[k]=[]}
  end

  def add_node(name)
    @node[name]||=Hash.new{0}
  end

  def add_edge(src,dst,cost)
    add_node(src)
    add_node(dst)
    @node[src][dst]=cost
  end

  def maxflow(src,dst)
    residual=Hash[@node.map{|k,v|[k,v.dup]}]
    while true
      #p residual
      pre={}
      q=[src]
      while q[0] && !pre[dst]
        sr=q.shift
        residual[sr]&&residual[sr].each{|d,c|
          pre[d]||=(q << d;sr)
        }
      end
      break if !pre[dst]
      path=[]
      ds=dst
      co=residual.values.flat_map(&:values).max
      while ds!=src
        #p ds
        sr=pre[ds]
        co=[residual[sr][ds],co].min
        path.unshift [sr,ds]
        ds=sr
      end
      path.each{|s,d|
        if (residual[s][d]-=co)==0
          residual[s].delete(d)
        end
        residual[d][s]+=co
      }
    end
    Hash[@node.map{|k,v|[k,Hash[v.map{|d,c|[d,c-residual[k][d]]}]]}]
  end
end

#def g;gets.split.map(&:to_i)end
#v,e=g;l=(1..e).map{g}
(v,_),*l=$<.map{|t|t.split.map &:to_i}
mf=MaxFlow.new
l.each{|s,d,c|
  mf.add_edge(s,d,c)
}
p mf.maxflow(0,v-1).fetch(0,{0=>0}).values.inject(:+)