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)

n = gets.to_i

# 隣接行列の作成
INF = 100_001 * n
graph = Array.new(n) { [INF] * n }
n.times do
  i, j, *vcs = gets.split.map(&:to_i)
  j.times do
    k = vcs.shift
    c = vcs.shift
    graph[i][k] = c
  end
end

# ダイクストラ
vs = [false] * n # <- verified
ws = [INF] * n   # <- weights

# 開始点を0とする
ws[0] = 0
mv  = -1

# 検証済のノードが無くなるまで実施
while vs.include? false
  min = INF
  mv  = -1

  # もっともコストが低く未検証のノード(minimum vertex)を探す
  ws.each_with_index do |w, i|
    if w < min && vs[i] == false
      min = w
      mv  = i
    end
  end

  # 見つけたらそれは最短経路に含めるので検証済みにする
  vs[mv] = true

  # 見つけたノードから到達可能なネイバーへのコストを調べる
  graph[mv].each_with_index do |costs, i|
    # ネイバーまでの現在のコストの方が大きいようなら更新する
    ws[i] = min + costs if ws[i] > min + costs && vs[i] == false
  end
end

ws.each_with_index { |cost, i| puts "#{i} #{cost}" }