#682366 (Crystal) No.922 東北きりきざむたん

提出ソース
結果

問題	No.922 東北きりきざむたん
ユーザー	yuruhiya
提出日時	2021-07-23 16:36:47
言語	Crystal (1.14.0)
結果	AC
実行時間	217 ms / 2,000 ms
コード長	16,115 bytes
コンパイル時間	13,700 ms
コンパイル使用メモリ	305,176 KB
実行使用メモリ	69,088 KB
最終ジャッジ日時	2024-07-18 12:00:39
合計ジャッジ時間	19,115 ms
ジャッジサーバーID （参考情報）	judge3 / judge4
このコードへのチャレンジ
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ファイルパターン	結果
sample	AC * 4
other	AC * 26
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ソースコード

raw source code
# 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({i, i}, 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 %}
    first_value = input({{type}})
    %array{i} = Array(typeof(first_value)).new({{size}})
    %array{i} << first_value
  {% end %}
  {{size}}.pred.times do
    {% for type, i in types %}
      %array{i} << input({{type}})
    {% end %}
  end
  {
    {% for type, i in types %}
      %array{i},
    {% end %}
  }
end

# 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
    WeightedEdge2(T).new(to, from, cost)
  end

  def sort
    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 cost
    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, edge : UnweightedEdge)
    @to = edge.to
  end

  def cost
    1
  end

  def reverse
    UnweightedEdge2.new(to, from)
  end

  def sort
    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 << Edge2.new(*edge)
  end

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

  delegate size, to: @graph
  delegate :[], to: @graph

  def each : Nil
    (0...size).each do |v|
      self[v].each do |edge|
        yield Edge2.new(v, edge)
      end
    end
  end

  def reverse
    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
    if self.class.directed?
      each_with_object(self.class.new(size)) do |edge, graph|
        graph << edge
        graph << edge.reverse if self.class.directed?
      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
    to_s(io)
  end
end

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

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

  def self.weighted?
    true
  end

  def self.directed?
    true
  end
end

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

  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))
    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

  def self.weighted?
    true
  end

  def self.directed?
    false
  end
end

class UnweightedDirectedGraph
  include Graph(UnweightedEdge, UnweightedEdge2)

  def initialize(size : Int)
    super
  end

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

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

  def self.weighted?
    false
  end

  def self.directed?
    true
  end
end

class UnweightedUndirectedGraph
  include Graph(UnweightedEdge, UnweightedEdge2)

  def initialize(size : Int)
    super
  end

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

  def <<(edge : UnweightedEdge2)
    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

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

  def each_child(vertex : Int, parent)
    graph[vertex].each.select { |u| u != parent }
  end

  def self.weighted?
    false
  end

  def self.directed?
    false
  end
end

# require "/graph/re_rooting"
# require "../graph"

# Example of T:
# ```
# struct DP
#   getter val : Int64, cnt : Int32
#
#   def initialize
#     @val, @cnt = 0i64, 0
#   end
#
#   def initialize(@val, @cnt)
#   end
#
#   def +(other : self) : self
#     DP.new(val + other.val, cnt + other.cnt)
#   end
#
#   def add_root(v : Int32) : self
#     DP.new(val + cnt, cnt + 1)
#   end
# end
# ```
class ReRooting(T, GraphType)
  getter graph : GraphType

  def initialize(size : Int)
    @graph = GraphType.new(size)
    @dp = Array(Array(T)).new
    @result = Array(T).new
  end

  def initialize(@graph : GraphType)
    @dp = Array(Array(T)).new
    @result = Array(T).new
  end

  delegate size, to: @graph
  delegate :<<, to: @graph
  delegate add_edges, to: @graph

  private def dfs(v : Int32, p : Int32) : T
    graph[v].each_with_index.select { |(edge, i)| edge.to != p }.reduce(T.new) { |acc, (edge, i)|
      acc + (@dp[v][i] = dfs(edge.to, v))
    }.add_root(v)
  end

  private def bfs(v : Int32, p : Int32, dp_par : T) : Nil
    graph[v].each_with_index do |edge, i|
      @dp[v][i] = dp_par if edge.to == p
    end

    n = graph[v].size
    dp_left = Array.new(n + 1, T.new)
    (0...n).each do |i|
      dp_left[i + 1] = dp_left[i] + @dp[v][i]
    end
    dp_right = Array.new(n + 1, T.new)
    (0...n).reverse_each do |i|
      dp_right[i] = dp_right[i + 1] + @dp[v][i]
    end
    @result[v] = dp_left.last.add_root(v)

    graph[v].each_with_index do |edge, i|
      bfs(edge.to, v, (dp_left[i] + dp_right[i + 1]).add_root(v)) if edge.to != p
    end
  end

  def solve : Array(T)
    @dp = Array.new(size) { |i| Array.new(@graph[i].size, T.new) }
    @result = Array.new(size, T.new)
    dfs(0, -1)
    bfs(0, -1, T.new)
    @result
  end
end

# require "/graph/decompose"
# require "../graph"

# require "../datastructure/union_find"
class UnionFind
  @d : Array(Int32)

  def initialize(n : Int)
    @d = Array.new(n, -1)
  end

  def initialize(n : Int, edges : Enumerable({Int32, Int32}))
    initialize(n)
    edges.each { |u, v| unite(u, v) }
  end

  def root(x : Int)
    @d[x] < 0 ? x : (@d[x] = root(@d[x]))
  end

  def unite(x : Int, y : Int)
    x = root(x)
    y = root(y)
    return false if x == y
    x, y = y, x if @d[x] > @d[y]
    @d[x] += @d[y]
    @d[y] = x
    true
  end

  def same?(x : Int, y : Int)
    root(x) == root(y)
  end

  def size(x : Int)
    -@d[root(x)]
  end

  def groups
    groups = Hash(Int32, Set(Int32)).new { |h, k| h[k] = Set(Int32).new }
    @d.size.times do |i|
      groups[root(i)] << i
    end
    groups.values.to_set
  end
end

module Graph(Edge, Edge2)
  def decompose : {Array(self), Array({Int32, Int32})}
    uf = UnionFind.new(size)
    each do |edge|
      uf.unite(edge.from, edge.to)
    end
    groups = uf.groups.to_a
    index = Array.new(size, {-1, -1})
    groups.each_with_index do |group, i|
      group.each_with_index do |v, j|
        index[v] = {i, j}
      end
    end

    graphs = Array.new(groups.size) { |i| self.class.new(groups[i].size) }
    if self.class.directed?
      each do |edge|
        i1, j1 = index[edge.from]
        _, j2 = index[edge.to]
        graphs[i1] << {j1, j2}
      end
    else
      edge_set = Set(Edge2).new
      each do |edge|
        if edge_set.add?(edge.sort)
          i1, j1 = index[edge.from]
          _, j2 = index[edge.to]
          graphs[i1] << {j1, j2}
        end
      end
    end
    {graphs, index}
  end
end

# require "/graph/lca"
# require "../graph"

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

  private def dfs(vertex : Int, par : Int, dep : Int) : 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 : Int)
    @log2 = Math.log2(size).to_i.succ.as(Int32)
    @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|
        if @parent[k][v] < 0
          @parent[k + 1][v] = -1
        else
          @parent[k + 1][v] = @parent[k][@parent[k][v]]
        end
      end
    end
  end

  delegate size, to: @graph

  def lca(u : Int, v : Int) : Int32
    raise IndexError.new unless 0 <= u < size
    raise IndexError.new unless 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 : Int, v : Int) : Int32
    @depth[u] + @depth[v] - @depth[lca(u, v)] * 2
  end
end

struct DP
  getter sum : Int64, cnt : Int32

  class_property! k : Array(Int32)

  def initialize
    @sum, @cnt = 0i64, 0
  end

  def initialize(@sum, @cnt)
  end

  def +(other : self) : self
    DP.new(sum + other.sum, cnt + other.cnt)
  end

  def add_root(v : Int32) : self
    DP.new(sum + cnt, cnt + DP.k[v])
  end
end

n, m, q = input(i, i, i)
g = UnweightedUndirectedGraph.new n, input({i - 1, i - 1}[m])
graphs, index = g.decompose
lcas = graphs.map { |graph| LCA.new(graph, 0) }
cnts = Array.new(graphs.size) { |i| Array.new(graphs[i].size, 0) }

ans = 0i64
q.times do
  a, b = input(i - 1, i - 1)
  ai, aj = index[a]
  bi, bj = index[b]
  if ai == bi
    ans += lcas[ai].dist(aj, bj)
  else
    cnts[ai][aj] += 1
    cnts[bi][bj] += 1
  end
end

graphs.each_with_index do |graph, i|
  DP.k = cnts[i]
  dp = ReRooting(DP, UnweightedUndirectedGraph).new(graph)
  ans += dp.solve.min_of(&.sum)
end

puts ans
yukicoder

結果

ソースコード
