verify/graph/bfs_graph.test.cr

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• Last update: 2024-07-28 06:26:08+09:00
• Problem: http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_11_C

Depends on

• src/nglib/constants.cr
• src/nglib/graph/bfs.cr

Code

# verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_11_C

require "../../src/nglib/graph/bfs"

n = read_line.to_i64
graph = NgLib::BfsGraph.new(n)
n.times do
  line = read_line.split.map &.to_i64.pred
  u = line[0]
  vs = line[2...]

  vs.each do |v|
    graph.add_edge(u, v, directed: true)
  end
end

dist = graph.shortest_path(start: 0)

n.times do |i|
  puts "#{i + 1} #{dist[i] >= n + 1 ? -1 : dist[i]}"
end

# verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=ALDS1_11_C

# require "../../src/nglib/graph/bfs"
# require "../constants"
OO = (1_i64 << 62) - (1_i64 << 31)

module NgLib
  # $n$ 頂点 $m$ 辺からなるグラフに対して、幅優先探索によって最短経路を求めます。
  #
  # 経路の復元も可能です。
  class BfsGraph
    getter size : Int32
    getter graph : Array(Array(Int32))

    # $n$ 頂点 $0$ 辺からなるグラフを作成します。
    #
    # ```
    # graph = BfsGraph.new(n)
    # ```
    def initialize(n : Int)
      @size = n.to_i64.to_i32
      @graph = Array.new(@size) { Array(Int32).new }
    end

    # 辺 $(u, v)$ を追加します。
    #
    # `directed` が `true` の場合、
    # 有向辺とみなして、$u$ から $v$ への辺のみ生やします。
    #
    # ```
    # graph = BfsGraph.new(n)
    # graph.add_edge(u, v)                 # => (u) <---w---> (v)
    # graph.add_edge(u, v, directed: true) # => (u) ----w---> (v)
    # ```
    def add_edge(u : Int, v : Int, directed : Bool = true)
      @graph[u.to_i32] << v.to_i32
      @graph[v.to_i32] << u.to_i32 unless directed
    end

    # 全点対間の最短経路長を返します。
    #
    # ```
    # dists = graph.shortest_path
    # dists # => [[0, 1, 3], [1, 0, 2], [1, 1, 0]]
    # ```
    def shortest_path
      (0...@size).map { |start| shortest_path(start) }
    end

    # 始点 `start` から各頂点への最短経路長を返します。
    #
    # ```
    # dist = graph.shortest_path(start: 2)
    # dist # => [3, 8, 0, 7, 1]
    # ```
    def shortest_path(start : Int)
      queue = Deque.new([start.to_i32])
      dist = Array.new(@size) { |i| i == start ? 0_i64 : OO }
      until queue.empty?
        from = queue.shift
        @graph[from].each do |adj|
          next if dist[adj] != OO
          dist[adj] = dist[from] + 1
          queue << adj
        end
      end
      dist
    end

    # 始点 `start` から終点 `dest` への最短経路長を返します。
    #
    # ```
    # dist = graph.shortest_path(start: 2, dest: 0)
    # dist # => 12
    # ```
    def shortest_path(start : Int, dest : Int)
      shortest_path(start)[dest]
    end
  end
end

n = read_line.to_i64
graph = NgLib::BfsGraph.new(n)
n.times do
  line = read_line.split.map &.to_i64.pred
  u = line[0]
  vs = line[2...]

  vs.each do |v|
    graph.add_edge(u, v, directed: true)
  end
end

dist = graph.shortest_path(start: 0)

n.times do |i|
  puts "#{i + 1} #{dist[i] >= n + 1 ? -1 : dist[i]}"
end

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