Problem:
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Single Source Shortest Path II

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

$1 \leq n \leq 10,000$

$0 \leq c_i \leq 100,000$

$|E| < 500,000$

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)

# Node
class Node
  attr_accessor :id, :edges, :cost, :done

  def initialize(id, edges = [], cost = nil, done = false)
    @id, @edges, @cost, @done = id, edges, cost, done
  end
end

# Edge
class Edge
  attr_accessor :to, :cost

  def initialize(to, cost)
    @to, @cost = to, cost
  end
end

# Dijkstra
class Dijkstra
  attr_accessor :nodes

  def initialize(data)
    @nodes = {}
    data.each do |id, edges|
      edges.map! { |edge| Edge.new(*edge) }
      @nodes[id] = Node.new(id, edges)
    end
  end

  def start(start_id)
    @nodes.each do |id, node|
      node.done = false
      node.cost = node.id == start_id ? 0 : -1
    end

    loop do
      done_node = nil
      @nodes.each do |id, node|
        next if node.done || node.cost < 0
        done_node = node if done_node.nil? || node.cost < done_node.cost
        break
      end
      break if done_node.nil?
      done_node.done = true
      done_node.edges.each do |edge|
        node = @nodes[edge.to]
        cost = done_node.cost + edge.cost
        node.cost = cost if node.cost < 0 || cost < node.cost
      end
    end
  end
end

n = gets.chop.to_i

data = {}

n.times do
  u, k, *edges = gets.split.map(&:to_i)
  data[u] = edges.each_slice(2).to_a
end

d = Dijkstra.new data
d.start(0)
d.nodes.each do |id, node|
  puts "#{id} #{node.cost}"
end