Problem:
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Single Source Shortest Path

For a given weighted graph $G = (V, E)$, find the shortest path from a source to each vertex. For each vertex $u$, print the total weight of edges on the shortest path from vertex $0$ to $u$.

Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, adjacency lists for each vertex $u$ are respectively given in the following format:

$u$ $k$ $v_1$ $c_1$ $v_2$ $c_2$ ... $v_k$ $c_k$

Vertices in $G$ are named with IDs $0, 1, ..., n-1$. $u$ is ID of the target vertex and $k$ denotes its degree. $v_i (i = 1, 2, ... k)$ denote IDs of vertices adjacent to $u$ and $c_i$ denotes the weight of a directed edge connecting $u$ and $v_i$ (from $u$ to $v_i$).

Output

For each vertex, print its ID and the distance separated by a space character in a line respectively. Print in order of vertex IDs.

Constraints

$1 \leq n \leq 100$

$0 \leq c_i \leq 100,000$

$|E| \leq 10,000$

All vertices are reachable from vertex $0$

Sample Input 1

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

Sample Output 1

0 0
1 2
2 2
3 1
4 3

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Ruby (judge verdict: Wrong Answer)

def calc(vertices)
  result = Hash.new(-1)
  result[0] = 0
  queue = [0] 
  
  until queue.empty? do
    current = queue.shift

    vertices[current].each do |neighbor|
      target = neighbor[0]
      length = neighbor[1]
      if (result[target] > 0) then
        if (result[current] > result[target] + length) then
          result[current] = result[target] + length
        end
      end
    end

    vertices[current].each do |neighbor|
      target = neighbor[0]
      length = neighbor[1]
      if (result[target] < 0) then
        result[target] = result[current] + length
        queue.push(target)
      else
        cand_route_len = result[current] + length
        result[target] = cand_route_len if cand_route_len < result[target]
      end
    end
  end

  return result 
end


# main
n = gets.chomp.to_i
vertices = {}
n.times do
  inputs = gets.chomp.split.map(&:to_i)
  neighbors = []
  2.step(2+inputs[1]*2-1, 2) do |i|
    neighbors << [inputs[i], inputs[i+1]]
  end
  vertices[inputs[0]] = neighbors
end

result = calc(vertices)
result.sort_by{|key, value| key}.each do |key, value|
  puts "#{key} #{value}"
end