# 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}] # ``` 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(s, else_ast) {% if Scanner.class.has_method?(s.id) %} Scanner.{{s.id}} {% elsif s.stringify == "String" %} Scanner.s {% elsif s.stringify == "Char" %} Scanner.c {% elsif s.stringify =~ /[A-Z][a-z0-9_]*/ %} {{s.id}}.new(Scanner.s) {% elsif String.has_method?("to_#{s}".id) %} Scanner.s.to_{{s.id}} {% else %} {{else_ast}} {% end %} end macro internal_input_array(s, 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({{s.id}}) {% for i in 0...args.size %} } {% end %} {% end %} end macro input(s) {% if s.is_a?(Call) %} {% if s.receiver.is_a?(Nop) %} internal_input( {{s.name}}, {{s.name}}( {% for argument in s.args %} input({{argument}}), {% end %} ) ) {% elsif s.name.stringify == "[]" %} internal_input_array({{s.receiver}}, {{s.args}}) {% else %} input({{s.receiver}}).{{s.name.id}}( {% for argument in s.args %} input({{argument}}), {% end %} ) {{s.block}} {% end %} {% elsif s.is_a?(TupleLiteral) %} { {% for i in 0...s.size %} input({{s[i]}}), {% end %} } {% elsif s.is_a?(ArrayLiteral) %} [ {% for i in 0...s.size %} input({{s[i]}}), {% end %} ] {% elsif s.is_a?(RangeLiteral) %} Range.new(input({{s.begin}}), input({{s.end}}), {{s.excludes_end?}}) {% elsif s.is_a?(If) %} {{s.cond}} ? input({{s.then}}) : input({{s.else}}) {% elsif s.is_a?(Assign) %} {{s.target}} = input({{s.value}}) {% else %} internal_input({{s.id}}, {{s.id}}) {% end %} end macro input(*s) { {% for s in s %} input({{s}}), {% end %} } end # require "atcoder/SCC" # 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 # require "/graph/components" # 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 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 module Graph(Edge, Edge2) # Returns `{components size, index, groups}`. def components undirected = to_undirected index = Array(Int32?).new(size, nil) groups = [] of Set(Int32) id = 0 size.times do |v| next if index[v] que = Deque{v} groups << Set(Int32).new while u = que.shift? next if index[u] index[u] = id groups[id] << u undirected[u].each do |edge| que << edge.to if index[edge.to].nil? end end id += 1 end {id, index.map(&.not_nil!), groups} end end # 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 n, m = input(i, i) edges = input({i - 1, i - 1}[m]) graph = UnweightedDirectedGraph.new n, edges scc = AtCoder::SCC.new(n.to_i64) graph.each do |edge| scc.add_edge edge.from, edge.to end scc_groups = scc.scc.map &.map(&.to_i) scc_id = [-1] * n scc_groups.each_with_index do |group, id| group.each { |i| scc_id[i] = id } end k, id, groups = graph.components ans = [] of {Int32, Int32} has_cycle = [false] * k scc_groups.each do |group| v = group.first has_cycle[id[v]] = true if group.size > 1 end topo = Array.new(k) { [] of Int32 } scc_groups.each do |group| group.each do |v| topo[id[v]] << v end end (0...k).each do |i| group = groups[i].to_a if has_cycle[i] (0...group.size).each do |i| ans << {group[i], group[i.succ % group.size]} end else topo[i].each_cons_pair do |u, v| ans << {u, v} end end end puts ans.size, ans.join('\n', &.join(' ', &.succ))