test/graph/lca_test.cr

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• Last update: 2022-04-16 16:23:13+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/GRL_5_C

Depends on

• src/graph.cr
• src/graph/edge.cr
• src/graph/lca.cr
• src/scanner.cr

Code

# verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/GRL_5_C
require "../../src/graph/lca"
require "../../src/scanner"
n = input(i)

g1 = UnweightedUnGraph.new(n)
g2 = UnGraph(Int32).new(n)
n.times do |u|
  input(i[i]).each do |v|
    g1 << {u, v}
    g2 << {u, v, 42}
  end
end

lca1 = LCA.new(g1, 0)
lca2 = LCA.new(g2, 0)

input(i).times do
  u, v = input(i, i)
  a1, a2 = lca1.lca(u, v), lca2.lca(u, v)
  raise "" unless a1 == a2
  puts a1
end

# verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/GRL_5_C
# require "../../src/graph/lca"
# require "../graph"
# require "./graph/edge"
struct WeightedEdge(T)
  include Comparable(WeightedEdge(T))

  property to : Int32, cost : T

  def initialize(@to, @cost : T)
  end

  def <=>(other : WeightedEdge(T))
    {cost, to} <=> {other.cost, other.to}
  end

  def to_s(io) : Nil
    io << '(' << to << ", " << cost << ')'
  end

  def inspect(io) : Nil
    io << "->" << to << '(' << cost << ')'
  end
end

struct WeightedEdge2(T)
  include Comparable(WeightedEdge2(T))

  property from : Int32, to : Int32, cost : T

  def initialize(@from, @to, @cost : T)
  end

  def initialize(@from, edge : WeightedEdge(T))
    @to, @cost = edge.to, edge.cost
  end

  def <=>(other : WeightedEdge2(T))
    {cost, from, to} <=> {other.cost, other.from, other.to}
  end

  def reverse : self
    WeightedEdge2(T).new(to, from, cost)
  end

  def sort : self
    WeightedEdge2(T).new(*{to, from}.minmax, cost)
  end

  def to_s(io) : Nil
    io << '(' << from << ", " << to << ", " << cost << ')'
  end

  def inspect(io) : Nil
    io << from << "->" << to << '(' << cost << ')'
  end
end

struct UnweightedEdge
  property to : Int32

  def initialize(@to)
  end

  def initialize(@to, cost)
  end

  def cost : Int32
    1
  end

  def to_s(io) : Nil
    io << to
  end

  def inspect(io) : Nil
    io << "->" << to
  end
end

struct UnweightedEdge2
  property from : Int32, to : Int32

  def initialize(@from, @to)
  end

  def initialize(@from, @to, cost)
  end

  def initialize(@from, edge : UnweightedEdge)
    @to = edge.to
  end

  def cost : Int32
    1
  end

  def reverse : self
    UnweightedEdge2.new(to, from)
  end

  def sort : self
    UnweightedEdge2.new(*{to, from}.minmax)
  end

  def to_s(io) : Nil
    io << '(' << from << ", " << to << ')'
  end

  def inspect(io) : Nil
    io << from << "->" << to
  end
end

module Graph(Edge, Edge2)
  include Enumerable(Edge2)

  getter graph : Array(Array(Edge))

  def initialize(size : Int)
    @graph = Array(Array(Edge)).new(size) { [] of Edge }
  end

  def initialize(size : Int, edges : Enumerable)
    initialize(size)
    add_edges(edges)
  end

  # Add *edge*.
  abstract def <<(edge : Edge2)

  # :ditto:
  def <<(edge : Tuple) : self
    self << Edge2.new(*edge)
  end

  def add_edges(edges : Enumerable) : self
    edges.each { |edge| self << edge }
    self
  end

  delegate size, :[], to: @graph

  # Yields each edge of the graph, ans returns `nil`.
  def each(&) : Nil
    (0...size).each do |v|
      graph[v].each do |edge|
        yield Edge2.new(v, edge)
      end
    end
  end

  def each_child(vertex : Int, parent, &block) : Nil
    graph[vertex].each do |edge|
      yield edge if edge.to != parent
    end
  end

  def each_child(vertex : Int, parent)
    graph[vertex].each.reject(&.to.== parent)
  end

  def reverse : self
    if self.class.directed?
      each_with_object(self.class.new(size)) do |edge, reversed|
        reversed << edge.reverse
      end
    else
      dup
    end
  end

  def to_undirected : self
    if self.class.directed?
      each_with_object(self.class.new(size)) do |edge, graph|
        graph << edge << edge.reverse
      end
    else
      dup
    end
  end

  def to_s(io : IO) : Nil
    io << '['
    join(", ", io) do |edge, io|
      edge.inspect io
    end
    io << ']'
  end

  def inspect(io : IO) : Nil
    io << "[\n"
    graph.each do |edges|
      io << "  " << edges << ",\n"
    end
    io << ']'
  end
end

class DiGraph(T)
  include Graph(WeightedEdge(T), WeightedEdge2(T))

  def self.weighted?
    true
  end

  def self.directed?
    true
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable(WeightedEdge2(T)))
    super
  end

  def initialize(size : Int, edges : Enumerable({Int32, Int32, T}))
    super
  end

  def <<(edge : WeightedEdge2(T)) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << WeightedEdge.new(edge.to, edge.cost)
    self
  end
end

class UnGraph(T)
  include Graph(WeightedEdge(T), WeightedEdge2(T))

  def self.weighted?
    true
  end

  def self.directed?
    false
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable(WeightedEdge2(T)))
    super
  end

  def initialize(size : Int, edges : Enumerable({Int32, Int32, T}))
    super
  end

  def <<(edge : WeightedEdge2(T)) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << WeightedEdge.new(edge.to, edge.cost)
    @graph[edge.to] << WeightedEdge.new(edge.from, edge.cost)
    self
  end
end

class UnweightedDiGraph
  include Graph(UnweightedEdge, UnweightedEdge2)

  def self.weighted?
    false
  end

  def self.directed?
    true
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable)
    super
  end

  def <<(edge : UnweightedEdge2) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << UnweightedEdge.new(edge.to)
    self
  end
end

class UnweightedUnGraph
  include Graph(UnweightedEdge, UnweightedEdge2)

  def self.weighted?
    false
  end

  def self.directed?
    false
  end

  def initialize(size : Int)
    super
  end

  def initialize(size : Int, edges : Enumerable)
    super
  end

  def <<(edge : UnweightedEdge2) : self
    raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size
    @graph[edge.from] << UnweightedEdge.new(edge.to)
    @graph[edge.to] << UnweightedEdge.new(edge.from)
    self
  end
end

class LCA(Edge, Edge2)
  getter graph : Graph(Edge, Edge2), depth : Array(Int32), log2 : Int32

  private def dfs(vertex : Int32, par : Int32, dep : Int32) : Nil
    @parent[0][vertex] = par
    @depth[vertex] = dep
    @graph[vertex].each do |edge|
      dfs(edge.to, vertex, dep + 1) if edge.to != par
    end
  end

  def initialize(@graph : Graph(Edge, Edge2), root : Int32)
    @log2 = Math.log2(size).to_i.succ
    @depth = Array(Int32).new(size, -1)
    @parent = Array(Array(Int32)).new(log2) { Array.new(size, 0) }
    dfs(root, -1, 0)
    (0...log2 - 1).each do |k|
      (0...size).each do |v|
        @parent[k + 1][v] = @parent[k][v] < 0 ? -1 : @parent[k][@parent[k][v]]
      end
    end
  end

  delegate size, to: @graph

  def depth(v : Int32) : Int32
    @depth[v]
  end

  def parent_p2(v : Int32, k : Int32) : Int32?
    p = @parent[k][v]
    p >= 0 ? p : nil
  end

  def parent_p2!(v : Int32, k : Int32) : Int32
    parent_p2(v, k).not_nil!
  end

  def parent(v : Int32) : Int32?
    parent_p2(v, 0)
  end

  def parent!(v : Int32) : Int32
    parent(v).not_nil!
  end

  def parent(v : Int32, up : Int32) : Int32?
    log2.times do |k|
      v = @parent[k][v] if up.bit(k) == 1
      return nil if v < 0
    end
    v
  end

  def parent!(v : Int32, up : Int32) : Int32
    parent(v, up).not_nil!
  end

  def lca(u : Int32, v : Int32) : Int32
    raise IndexError.new unless 0 <= u < size && 0 <= v < size
    u, v = v, u if @depth[u] > @depth[v]
    (0...log2).each do |k|
      v = @parent[k][v] if (@depth[v] - @depth[u]).bit(k) == 1
    end

    return u if u == v

    (0...log2).reverse_each do |k|
      u, v = @parent[k][u], @parent[k][v] if @parent[k][u] != @parent[k][v]
    end
    @parent[0][u]
  end

  def dist(u : Int32, v : Int32) : Int32
    depth(u) + depth(v) - depth(lca(u, v)) * 2
  end

  def path(start : Int32, goal : Int32, &) : Nil
    lca = lca(start, goal)
    {start, goal}.each do |first|
      if first != lca
        yield v = first
        while (v = parent!(v)) != lca
          yield v
        end
      end
    end
    yield lca
  end

  def path(start : Int32, goal : Int32) : Array(Int32)
    path = [] of Int32
    path(start, goal) { |v| path << v }
    path
  end
end

# require "../../src/scanner"
module Scanner
  extend self

  private def skip_to_not_space(io)
    peek = io.peek
    not_space = peek.index { |x| x != 32 && x != 10 } || peek.size
    io.skip(not_space)
  end

  def c(io = STDIN)
    skip_to_not_space(io)
    io.read_char.not_nil!
  end

  private def int(int_type : T.class, io = STDIN) : T forall T
    skip_to_not_space(io)

    value = T.zero
    signed = false
    case x = io.read_byte
    when nil
      raise IO::EOFError.new
    when 45
      signed = true
    when 48..57
      value = T.new 48 &- x
    else
      raise "Unexpected char: #{x.chr}"
    end

    loop do
      peek = io.peek
      return signed ? value : -value if peek.empty?
      i = 0
      while i < peek.size
        c = peek.unsafe_fetch(i)
        if 48 <= c <= 57
          value = value &* 10 &- c &+ 48
          i &+= 1
        elsif c == 32 || c == 10
          io.skip(i &+ 1)
          return signed ? value : -value
        else
          raise "Unexpected char: #{c.chr}"
        end
      end
      io.skip(i)
    end
  end

  private def uint(uint_type : T.class, io = STDIN) : T forall T
    skip_to_not_space(io)
    value = T.zero
    found_digit = false
    loop do
      peek = io.peek
      if peek.empty?
        if found_digit
          return value
        else
          raise IO::EOFError.new
        end
      end
      i = 0
      while i < peek.size
        c = peek.unsafe_fetch(i)
        if 48 <= c <= 57
          found_digit = true
          value = value &* 10 &+ c &- 48
          i &+= 1
        elsif c == 32 || c == 10
          io.skip(i &+ 1)
          return value
        else
          raise "Unexpected char: #{c.chr}"
        end
      end
      io.skip(i)
    end
  end

  def i(io = STDIN)
    int(Int32, io)
  end

  {% for n in [8, 16, 32, 64, 128] %}
    def i{{n}}(io = STDIN)
      int(Int{{n}}, io)
    end

    def u{{n}}(io = STDIN)
      uint(UInt{{n}}, io)
    end
  {% end %}

  {% for method in [:f, :f32, :f64] %}
    def {{method.id}}(io = STDIN)
      s(io).to_{{method.id}}
    end
  {% end %}

  def s(io = STDIN)
    skip_to_not_space(io)

    peek = io.peek
    if peek.empty?
      raise IO::EOFError.new
    end
    if index = peek.index { |x| x == 32 || x == 10 }
      io.skip(index + 1)
      return String.new(peek[0, index])
    end

    String.build do |buffer|
      loop do
        buffer.write peek
        io.skip(peek.size)
        peek = io.peek
        break if peek.empty?
        if index = peek.index { |x| x == 32 || x == 10 }
          buffer.write peek[0, index]
          io.skip(index + 1)
          break
        end
      end
    end
  end
end

macro internal_input(type, else_ast, io)
  {% if Scanner.class.has_method?(type.id) %}
    Scanner.{{type.id}}({{io}})
  {% elsif type.stringify == "String" %}
    Scanner.s({{io}})
  {% elsif type.stringify == "Char" %}
    Scanner.c({{io}})
  {% elsif type.is_a?(Path) %}
    {% if type.resolve.class.has_method?(:scan) %}
      {{type}}.scan(Scanner, {{io}})
    {% else %}
      {{type}}.new(Scanner.s({{io}}))
    {% end %}
  {% elsif String.has_method?("to_#{type}".id) %}
    Scanner.s({{io}}).to_{{type.id}}
  {% else %}
    {{else_ast}}
  {% end %}
end

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

# Inputs from *io*.
#
# ### Specifications
#
# ```plain
# AST               | Example             | Expanded code
# ------------------+---------------------+---------------------------------------
# Uppercase string  | Int32, Int64, etc.  | {}.new(Scanner.s)
#                   | s, c, i, iN, uN     | Scanner.{}
#                   | f, big_i, etc.      | Scanner.s.to_{}
# Call []           | type[size]          | Array.new(input(size)) { input(type) }
# TupleLiteral      | {t1, t2, t3}        | {input(t1), input(t2), input(t3)}
# ArrayLiteral      | [t1, t2, t3]        | [input(t1), input(t2), input(t3)]
# HashLiteral       | {t1 => t2}          | {input(t1) => input(t2)}
# NamedTupleLiteral | {a: t1, b: t2}      | {a: input(t1), b: input(t2)}
# RangeLiteral      | t1..t2              | input(t1)..input(t2)
# Expressions       | (exp1; exp2)        | (input(exp1); input(exp2);)
# If                | cond ? t1 : t2      | input(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, 5i64}
# input(String, Char[m])     # => {"foo", ['b', 'a', 'r']}
# input(Int32[n])            # => [1, 2, 3, 4, 5]
# ```
# ```
# n, m = input(i, i64) # => {5, 5i64}
# 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 1
# 2 1 2
# 5 1 2 3 4 5
# ```
# ```
# n = input(i)   # => 3
# input(i[i][n]) # => [[1], [1, 2], [1, 2, 3, 4, 5]]
# ```
#
# Input:
# ```plain
# 3
# 1 2
# 2 3
# 3 1
# ```
# ```
# n = input(i)
# input_column({Int32, Int32}, n) # => {[1, 2, 3], [2, 3, 1]}
# ```
macro input(ast, *, io = STDIN)
  {% if ast.is_a?(Call) %}
    {% if ast.receiver.is_a?(Nop) %}
      internal_input(
        {{ast.name}},
        {{ast.name}}({% for argument in ast.args %} input({{argument}}, io: {{io}}), {% end %}),
        {{io}},
      )
    {% elsif ast.receiver.is_a?(Path) && ast.receiver.resolve.class.has_method?(ast.name.symbolize) %}
      {{ast.receiver}}.{{ast.name}}(
        {% for argument in ast.args %} input({{argument}}, io: {{io}}) {% end %}
      ) {{ast.block}}
    {% elsif ast.name.stringify == "[]" %}
      internal_input_array({{ast.receiver}}, {{ast.args}}, {{io}})
    {% else %}
      input({{ast.receiver}}, io: {{io}}).{{ast.name}}(
        {% for argument in ast.args %} input({{argument}}, io: {{io}}), {% end %}
      ) {{ast.block}}
    {% end %}
  {% elsif ast.is_a?(TupleLiteral) %}
    { {% for i in 0...ast.size %} input({{ast[i]}}, io: {{io}}), {% end %} }
  {% elsif ast.is_a?(ArrayLiteral) %}
    [ {% for i in 0...ast.size %} input({{ast[i]}}, io: {{io}}), {% end %} ]
  {% elsif ast.is_a?(HashLiteral) %}
    { {% for key, value in ast %} input({{key}}, io: {{io}}) => input({{value}}, io: {{io}}), {% end %} }
  {% elsif ast.is_a?(NamedTupleLiteral) %}
    { {% for key, value in ast %} {{key}}: input({{value}}, io: {{io}}), {% end %} }
  {% elsif ast.is_a?(RangeLiteral) %}
    Range.new(
      input({{ast.begin}}, io: {{io}}),
      input({{ast.end}}, io: {{io}}),
      {{ast.excludes_end?}},
    )
  {% elsif ast.is_a?(SymbolLiteral) %}
    {{ast.id}}
  {% elsif ast.is_a?(Expressions) %}
    ( {% for exp in ast.expressions %} input({{exp}}, io: {{io}}); {% end %} )
  {% elsif ast.is_a?(If) %}
    input({{ast.cond}}, io: {{io}}) ? input({{ast.then}}, io: {{io}}) : input({{ast.else}}, io: {{io}})
  {% elsif ast.is_a?(Assign) %}
    {{ast.target}} = input({{ast.value}}, io: {{io}})
  {% else %}
    internal_input({{ast}}, {{ast}}, io: {{io}})
  {% end %}
end

macro input(*asts, io = STDIN)
  { {% for ast in asts %} input({{ast}}, io: {{io}}), {% end %} }
end

macro input_column(types, size, *, io = STDIN)
  %size = {{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}}, io: {{io}})
    {% end %}
  end
  { {% for type, i in types %} %array{i}, {% end %} }
end

n = input(i)

g1 = UnweightedUnGraph.new(n)
g2 = UnGraph(Int32).new(n)
n.times do |u|
  input(i[i]).each do |v|
    g1 << {u, v}
    g2 << {u, v, 42}
  end
end

lca1 = LCA.new(g1, 0)
lca2 = LCA.new(g2, 0)

input(i).times do
  u, v = input(i, i)
  a1, a2 = lca1.lca(u, v), lca2.lca(u, v)
  raise "" unless a1 == a2
  puts a1
end

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