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)

def shortest_path
  cost = Array.new(@n-1, Float::INFINITY).unshift(0)
  node = Marshal.load(Marshal.dump(cost))

  @n.times do
    now = node.index(node.compact.min)
    @graph[now].each_with_index do |x, i|
      unless x == nil
        alt = cost[now] + x
        if cost[i] > alt
          cost[i] = alt
          node[i] = alt
        end
      end
    end
    node[now] = nil
  end
  
  return cost
end


@n = gets.to_i
@graph = Array.new(@n).map{Array.new(@n,nil)}

@n.times do |i|
  input = gets.split(" ").map{|x| x.to_i}
  u = input.shift
  k = input.shift
  k.times do
    @graph[u][input.shift] = input.shift
  end
end

shortest_path.each_with_index do |x, i|
  printf "%d %d\n",i ,x
end