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: Time Limit Exceeded)

$n = gets.to_i
INF = 1 << 30
$m = Array.new($n){ Array.new }
$n.times do
  l = gets.split.map(&:to_i)
  (1..l[1]).each{ |i| $m[l[0]] << l[2*i,2] }
end
def dijkstra(x)
  $heap = Hash.new
  $heap[0] = 0
  (1..$n-1).each{ |i| $heap[i] = INF }
  d = Array.new($n, INF)
  d[x] = 0
  while $heap.size > 0
    t = $heap.sort_by{ |k, v| v }[0][0]
    $heap.delete(t)
    $m[t].each do |r|
      u, w = r
      if d[t] + w < d[u]
        d[u] = d[t] + w 
        $heap[u] = d[u]
      end
    end
  end
  d
end
ret = dijkstra(0)
ret.each_index{ |i| puts "#{i} #{ret[i]}" }