#683759 (Crystal) No.470 Inverse S+T Problem

• 問題: No.470 Inverse S+T Problem
• ユーザー: yuruhiya
• 提出日時: 2021-07-29 13:08:54
• 言語: Crystal (1.11.2)
• 結果: AC
• 実行時間: 11 ms / 2,000 ms
• コード長: 11,605 bytes
• コンパイル時間: 22,303 ms
• コンパイル使用メモリ: 264,768 KB
• 実行使用メモリ: 9,368 KB
• 最終ジャッジ日時: 2023-08-24 01:45:30
• 合計ジャッジ時間: 24,071 ms
• ジャッジサーバーID （参考情報）: judge12 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	3 ms; 5,048 KB
testcase_01	AC	3 ms; 5,104 KB
testcase_02	AC	3 ms; 5,020 KB
testcase_03	AC	3 ms; 4,988 KB
testcase_04	AC	4 ms; 5,028 KB
testcase_05	AC	3 ms; 4,988 KB
testcase_06	AC	11 ms; 9,220 KB
testcase_07	AC	11 ms; 9,292 KB
testcase_08	AC	11 ms; 9,368 KB
testcase_09	AC	4 ms; 4,988 KB
testcase_10	AC	3 ms; 4,944 KB
testcase_11	AC	3 ms; 5,040 KB
testcase_12	AC	4 ms; 4,964 KB
testcase_13	AC	4 ms; 5,028 KB
testcase_14	AC	4 ms; 4,948 KB
testcase_15	AC	4 ms; 5,072 KB
testcase_16	AC	3 ms; 5,020 KB
testcase_17	AC	4 ms; 4,956 KB
testcase_18	AC	3 ms; 5,044 KB
testcase_19	AC	4 ms; 5,048 KB
testcase_20	AC	4 ms; 4,884 KB
testcase_21	AC	4 ms; 4,960 KB
testcase_22	AC	4 ms; 4,892 KB
testcase_23	AC	4 ms; 5,036 KB
testcase_24	AC	4 ms; 5,048 KB
testcase_25	AC	4 ms; 5,024 KB
testcase_26	AC	4 ms; 4,884 KB
testcase_27	AC	4 ms; 5,100 KB
testcase_28	AC	4 ms; 5,820 KB
testcase_29	AC	4 ms; 5,160 KB
testcase_30	AC	4 ms; 5,328 KB

コンパイルメッセージ

In Main.cr:418:17

 418 | chars2 = chars1.product(chars1).map { |c1, c2| "#{c1}#{c2}" }
                       ^------
Warning: Deprecated Array(Char)#product. Use `Indexable#cartesian_product(*others : Indexable)` instead

A total of 1 warnings were found.

ソースコード

# require "/scanner"
# ### Specifications
#
# ```plain
# Inside input macro                            | Expanded code
# ----------------------------------------------+---------------------------------------
# Uppercase string: Int32, Int64, Float64, etc. | {}.new(Scanner.s)
# s                                             | Scanner.s
# c                                             | Scanner.c
# Other lowercase string: i, i64, f, etc.       | Scanner.s.to_{}
# operator[]: type[size]                        | Array.new(input(size)) { input(type) }
# Tuple literal: {t1, t2, t3}                   | {input(t1), input(t2), input(t3)}
# Array literal: [t1, t2, t3]                   | [input(t1), input(t2), input(t3)]
# Range literal: t1..t2                         | input(t1)..input(t2)
# If: cond ? t1 : t2                            | cond ? input(t1) : input(t2)
# Assign: target = value                        | target = input(value)
# ```
#
# ### Examples
#
# Input:
# ```plain
# 5 3
# foo bar
# 1 2 3 4 5
# ```
# ```
# n, m = input(Int32, Int64) # => {5, 10i64}
# input(String, Char[m])     # => {"foo", ['b', 'a', 'r']}
# input(Int32[n])            # => [1, 2, 3, 4, 5]
# ```
# ```
# n, m = input(i, i64) # => {5, 10i64}
# input(s, c[m])       # => {"foo", ['b', 'a', 'r']}
# input(i[n])          # => [1, 2, 3, 4, 5]
# ```
#
# Input:
# ```plain
# 2 3
# 1 2 3
# 4 5 6
# ```
#
# ```
# h, w = input(i, i) # => {2, 3}
# input(i[h, w])     # => [[1, 2, 3], [4, 5, 6]]
# ```
# ```
# input(i[i][i]) # => [[1, 2, 3], [4, 5, 6]]
# ```
#
# Input:
# ```plain
# 5 3
# 3 1 4 2 5
# 1 2
# 2 3
# 3 1
# ```
# ```
# n, m = input(i, i)       # => {5, 3}
# input(i.pred[n])         # => [2, 0, 3, 1, 4]
# input({i - 1, i - 1}[m]) # => [{0, 1}, {1, 2}, {2, 0}]
# ```
#
# Input:
# ```plain
# 3
# 1 2
# 2 2
# 3 2
# ```
# ```
# input({tmp = i, tmp == 1 ? i : i.pred}[i]) # => [{1, 2}, {2, 1}, {3, 1}]
# ```
#
# Input:
# ```plain
# 3
# 1 2
# 2 3
# 3 1
# ```
# ```
# n = input(i)
# input_column({Int32, Int32}, n) # => {[1, 2, 3], [2, 3, 1]}
# ```
class Scanner
  private def self.skip_to_not_space
    peek = STDIN.peek
    not_space = peek.index { |x| x != 32 && x != 10 } || peek.size
    STDIN.skip(not_space)
  end

  def self.c
    skip_to_not_space
    STDIN.read_char.not_nil!
  end

  def self.s
    skip_to_not_space

    peek = STDIN.peek
    if index = peek.index { |x| x == 32 || x == 10 }
      STDIN.skip(index + 1)
      return String.new(peek[0, index])
    end

    String.build do |buffer|
      loop do
        buffer.write peek
        STDIN.skip(peek.size)
        peek = STDIN.peek
        break if peek.empty?
        if index = peek.index { |x| x == 32 || x == 10 }
          buffer.write peek[0, index]
          STDIN.skip(index)
          break
        end
      end
    end
  end
end

macro internal_input(type, else_ast)
  {% if Scanner.class.has_method?(type.id) %}
    Scanner.{{type.id}}
  {% elsif type.stringify == "String" %}
    Scanner.s
  {% elsif type.stringify == "Char" %}
    Scanner.c
  {% elsif type.stringify =~ /[A-Z][a-z0-9_]*/ %}
    {{type.id}}.new(Scanner.s)
  {% elsif String.has_method?("to_#{type}".id) %}
    Scanner.s.to_{{type.id}}
  {% else %}
    {{else_ast}}
  {% end %}
end

macro internal_input_array(type, args)
  {% for i in 0...args.size %}
    %size{i} = input({{args[i]}})
  {% end %}
  {% begin %}
    {% for i in 0...args.size %} Array.new(%size{i}) { {% end %}
      input({{type.id}})
    {% for i in 0...args.size %} } {% end %}
  {% end %}
end

macro input(type)
  {% if type.is_a?(Call) %}
    {% if type.receiver.is_a?(Nop) %}
      internal_input(
        {{type.name}}, {{type.name}}(
          {% for argument in type.args %} input({{argument}}), {% end %}
        )
      )
    {% elsif type.name.stringify == "[]" %}
      internal_input_array({{type.receiver}}, {{type.args}})
    {% else %}
      input({{type.receiver}}).{{type.name.id}}(
        {% for argument in type.args %} input({{argument}}), {% end %}
      ) {{type.block}}
    {% end %}
  {% elsif type.is_a?(TupleLiteral) %}
    { {% for i in 0...type.size %} input({{type[i]}}), {% end %} }
  {% elsif type.is_a?(ArrayLiteral) %}
    [ {% for i in 0...type.size %} input({{type[i]}}), {% end %} ]
  {% elsif type.is_a?(RangeLiteral) %}
    Range.new(input({{type.begin}}), input({{type.end}}), {{type.excludes_end?}})
  {% elsif type.is_a?(If) %}
    {{type.cond}} ? input({{type.then}}) : input({{type.else}})
  {% elsif type.is_a?(Assign) %}
    {{type.target}} = input({{type.value}})
  {% else %}
    internal_input({{type.id}}, {{type.id}})
  {% end %}
end

macro input(*types)
  { {% for type in types %} input({{type}}), {% end %} }
end

macro input_column(types, size)
  {% for type, i in types %}
    %array{i} = Array({{type}}).new({{size}})
  {% end %}
  {{size}}.times do
    {% for type, i in types %}
      %array{i} << input({{type}})
    {% end %}
  end
  { {% for type, i in types %} %array{i}, {% end %} }
end

# require "atcoder/TwoSat"
# ac-library.cr by hakatashi https://github.com/google/ac-library.cr
#
# Copyright 2021 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

# require "./SCC.cr"
# ac-library.cr by hakatashi https://github.com/google/ac-library.cr
#
# Copyright 2021 Google LLC
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#      https://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.

module AtCoder
  # Implements [atcoder::scc_graph](https://atcoder.github.io/ac-library/master/document_en/scc.html).
  #
  # ```
  # scc = AtCoder::SCC.new(3_i64)
  # scc.add_edge(0, 1)
  # scc.add_edge(1, 0)
  # scc.add_edge(2, 0)
  # scc.scc # => [Set{2}, Set{0, 1}]
  # ```
  class SCC
    alias Adjacency = NamedTuple(in: Array(Int64), out: Array(Int64))

    getter size : Int64
    getter adjacencies : Array(Adjacency)

    def initialize(@size)
      @adjacencies = Array(Adjacency).new(@size) { {in: [] of Int64, out: [] of Int64} }

      @topological_order = Array(Int64).new(@size)
      @visit_counts = Array(Int64).new(@size, 0_i64)
      @visited = Set(Int64).new
      @stack = Deque(Int64).new
      @groups = Array(Set(Int64)).new
    end

    # Implements atcoder::scc_graph.add_edge(from, to).
    def add_edge(from, to)
      @adjacencies[from][:out] << to.to_i64
      @adjacencies[to][:in] << from.to_i64
    end

    private def dfs(start)
      @stack << start
      @visited << start

      until @stack.empty?
        node = @stack.last
        children = @adjacencies[node][:out]

        if @visit_counts[node] < children.size
          child = children[@visit_counts[node]]
          @visit_counts[node] += 1

          unless @visited.includes?(child)
            @visited << child
            @stack << child
          end
        else
          @topological_order << node
          @stack.pop
        end
      end
    end

    private def reverse_dfs(start)
      @stack << start
      @visited << start
      group = Set{start}

      until @stack.empty?
        node = @stack.pop
        children = @adjacencies[node][:in]

        children.each do |child|
          unless @visited.includes?(child)
            @stack << child
            @visited << child
            group << child
          end
        end
      end

      @groups << group
    end

    # Implements atcoder::scc_graph.scc().
    def scc
      @visited = Set(Int64).new
      @stack = Deque(Int64).new
      @visit_counts = Array(Int64).new(@size, 0_i64)
      @topological_order = Array(Int64).new(@size)
      @groups = Array(Set(Int64)).new

      @size.times do |node|
        unless @visited.includes?(node)
          dfs(node)
        end
      end

      @visited = Set(Int64).new

      @topological_order.reverse_each do |node|
        unless @visited.includes?(node)
          reverse_dfs(node)
        end
      end

      @groups
    end
  end
end

module AtCoder
  # Implements [atcoder::two_sat](https://atcoder.github.io/ac-library/master/document_en/twosat.html)
  #
  # ```
  # twosat = AtCoder::TwoSat.new(2_i64)
  # twosat.add_clause(0, true, 1, false)
  # twosat.add_clause(1, true, 0, false)
  # twosat.add_clause(0, false, 1, false)
  # twosat.satisfiable? # => true
  # twosat.answer       # => [false, false]
  # ```
  class TwoSat
    getter size : Int64

    class NotSatisfiableError < Exception
      def initialize
        super("The formula is not satisfiable")
      end
    end

    def initialize(@size)
      @scc = AtCoder::SCC.new(@size * 2)
      @solved = false
      @satisfiable = false
      @group_list = Array(Int64).new(@size * 2, 0_i64)
    end

    @[AlwaysInline]
    private def var(i, f)
      if f
        i.to_i64
      else
        i.to_i64 + @size
      end
    end

    # Implements atcoder::two_sat.add_clause(i, f, j, g).
    def add_clause(i, f, j, g)
      @scc.add_edge(var(i, !f), var(j, g))
      @scc.add_edge(var(j, !g), var(i, f))
    end

    # Implements atcoder::two_sat.satisfiable().
    def satisfiable?
      @satisfiable = false

      groups = @scc.scc
      @group_list = Array(Int64).new(@size * 2, 0_i64)
      groups.each_with_index do |group, i|
        group.each do |item|
          @group_list[item] = i.to_i64
        end
      end

      @size.times do |i|
        if @group_list[i] == @group_list[i + @size]
          return false
        end
      end

      @satisfiable = true
    end

    # Implements atcoder::two_sat.answer().
    #
    # This method will raise `NotSatisfiableError` if it's not satisfiable.
    def answer
      unless @satisfiable
        raise NotSatisfiableError.new
      end

      Array(Bool).new(@size) do |i|
        @group_list.not_nil![i] > @group_list.not_nil![i + @size]
      end
    end
  end
end

n = input(Int64)
s = input(String[n])

chars1 = ('a'..'z').to_a + ('A'..'Z').to_a
chars2 = chars1.product(chars1).map { |c1, c2| "#{c1}#{c2}" }
index1 = chars1.zip(0..).to_h
index2 = chars2.zip(0..).to_h

if n > 52
  puts "Impossible"
  exit
end

two_sat = AtCoder::TwoSat.new(n)
(0...n).each do |i|
  (i + 1...n).each do |j|
    if s[i][0] == s[j][0] || s[i][1..2] == s[j][1..2]
      two_sat.add_clause(i, false, j, false)
    end
    if s[i][0] == s[j][2] || s[i][1..2] == s[j][0..1]
      two_sat.add_clause(i, false, j, true)
    end
    if s[i][2] == s[j][0] || s[i][0..1] == s[j][1..2]
      two_sat.add_clause(i, true, j, false)
    end
    if s[i][2] == s[j][2] || s[i][0..1] == s[j][0..1]
      two_sat.add_clause(i, true, j, true)
    end
  end
end
if two_sat.satisfiable?
  two_sat.answer.each_with_index do |f, i|
    if f
      puts [s[i][0], s[i][1..2]].join(' ')
    else
      puts [s[i][0..1], s[i][2]].join(' ')
    end
  end
else
  puts "Impossible"
end