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 = STDIN.gets.to_i
matrix = Array.new(n) { Array.new(n) }
n.times do
	vertex, degree, *adjacent_info = STDIN.gets.split.map(&:to_i)
	degree.times do
		adjacency, weight = adjacent_info.shift(2)
		matrix[vertex][adjacency] = weight
	end
end

# ダイクストラ法
MAX_WEIGHT = 100_001
distances = Array.new(n)
visited   = Array.new(n, false)
parent    = Array.new(n)

distances[0] = 0
loop do
	vertex = matrix.each_index.
		select { |i| !visited[i] }.
		min_by { |i| distances[i] || MAX_WEIGHT }

	break if vertex.nil?
	visited[vertex] = true

	matrix.each_index do |i|
		next if visited[i] || matrix[vertex][i].nil?

		tmp_distance = distances[vertex] + matrix[vertex][i]
		if distances[i].nil? || tmp_distance < distances[i]
			distances[i] = tmp_distance
			parent[i] = vertex
		end
	end
end

matrix.each_index { |i| puts "#{i} #{distances[i]}" }