Problem:
Single Source Shortest Path (Negative Edges)

Input

An edge-weighted graph G (V, E) and the source r.

|V| |E| r
s0 t0 d0
s1 t1 d1
:
s|E|-1 t|E|-1 d|E|-1

|V| is the number of vertices and |E| is the number of edges in G. The graph vertices are named with the numbers 0, 1,..., |V|-1 respectively. r is the source of the graph.

si and ti represent source and target vertices of i-th edge (directed) and di represents the cost of the i-th edge.

Output

If the graph contains a negative cycle (a cycle whose sum of edge costs is a negative value) which is reachable from the source r, print

NEGATIVE CYCLE

in a line.

Otherwise, print

c0
c1
:
c|V|-1

The output consists of |V| lines. Print the cost of the shortest path from the source r to each vertex 0, 1, ... |V|-1 in order. If there is no path from the source to a vertex, print "INF".

Constraints

1 ≤ |V| ≤ 1000

0 ≤ |E| ≤ 2000

-10000 ≤ di ≤ 10000

There are no parallel edges

There are no self-loops

Sample Input 1

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

Sample Output 1

0
2
-3
-1

Sample Input 2

4 6 0
0 1 2
0 2 3
1 2 -5
1 3 1
2 3 2
3 1 0

Sample Output 2

NEGATIVE CYCLE

Sample Input 3

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

Sample Output 3

INF
0
-5
-3

Solution in Ruby (judge verdict: Accepted)

def bellman_ford(start, edges)
  dist = Array.new(V + 1, Float::INFINITY)
  dist[start] = 0

  V.times do |i|
    update = false

    edges.each do |from, to, cost|
      if dist[to] > dist[from] + cost
        dist[to] = dist[from] + cost
        update = true

        dist[to] = -Float::INFINITY if i == V - 1
      end
    end

    break unless update
  end

  dist
end

V, E, r = gets.split.map(&:to_i)

edges = []

E.times do
  edges << gets.split.map(&:to_i)
end

dist = bellman_ford(r, edges)

if dist.any? { |d| d == -Float::INFINITY }
  puts 'NEGATIVE CYCLE'
else
  V.times do |i|
    if dist[i] == Float::INFINITY
      puts 'INF'
    else
      puts dist[i]
    end
  end
end