# require "/graph/topological_sort" # 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 # require "./degree" # require "../graph" module Graph(Edge, Edge2) # Returns table of indegree. def indegree : Array(Int32) each_with_object(Array.new(size, 0)) do |edge, cnt| cnt[edge.to] += 1 end end # Returns table of outdegree. def outdegree : Array(Int32) each_with_object(Array.new(size, 0)) do |edge, cnt| cnt[edge.from] += 1 end end end module Graph(Edge, Edge2) def topological_sort : Array(Int32)? deg = indegree que = Deque(Int32).new size.times { |i| que << i if deg[i] == 0 } result = Array(Int32).new(size) while v = que.shift? result << v self[v].each do |edge| que << edge.to if (deg[edge.to] -= 1) == 0 end end deg.any? { |x| x > 0 } ? nil : result end end n, m = read_line.split.map(&.to_i) a = read_line.split.map(&.to_i.pred) if a.each_cons(3).any? { |(x, y, z)| x == y || x == z || y == z } puts "No" else graph = UnweightedDirectedGraph.new(m) (0...n - 1).each do |i| if i.even? graph << {a[i], a[i + 1]} else graph << {a[i + 1], a[i]} end end if order = graph.topological_sort ans = [-1] * m order.each_with_index { |x, i| ans[x] = i } puts "Yes", ans.join(' ', &.succ) else puts "No" end end