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: Accepted)

module Color
  WHITE = 0
  GRAY = 1
  BLACK = 2
end

def dijkstra(s)
  d = Array.new($n, Float::INFINITY)
  color = Array.new($n, Color::WHITE)
  
  d[s] = 0

  while true
    # puts d.join(' ')
    mincost = Float::INFINITY
    u = nil
    $n.times do |i|
      if color[i] != Color::BLACK && d[i] < mincost
        mincost = d[i]
        u = i
      end
    end

    if mincost == Float::INFINITY
      break
    end

    color[u] = Color::BLACK

    $n.times do |v|
      if color[v] != Color::BLACK && $m[u][v]
        if d[u] + $m[u][v] < d[v]
          d[v] = d[u] + $m[u][v]
          color[v] = Color::GRAY
        end
      end
    end
  end
  d
end

$n = gets.to_i
$m = Array.new($n) { Array.new($n) }
$n.times do |i|
  u, k, *arr = gets.split.map(&:to_i)
  arr.each_slice(2) do |v, c|
    $m[u][v] = c
  end
end
# puts "====="
# $m.each do |k|
#   puts k.join(' ')
# end
# puts "====="

d = dijkstra(0)
d.each_with_index do | v, i |
  puts "#{i} #{v}"
end