# require "/graph/bfs01" # require "../graph" struct Edge(T) include Comparable(Edge(T)) property to : Int32, cost : T def initialize(@to : Int32, @cost : T) end def <=>(other : Edge(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 Edge2(T) include Comparable(Edge2(T)) property from : Int32, to : Int32, cost : T def initialize(@from : Int32, @to : Int32, @cost : T) end def <=>(other : Edge2(T)) {cost, from, to} <=> {other.cost, other.from, other.to} end def reverse Edge2(T).new(to, from, cost) end def sort Edge2(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 UnweightedEdge2 property from : Int32, to : Int32 def initialize(@from, @to) 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 abstract class Graph(T) getter graph : Array(Array(Edge(T))) def initialize(size : Int) raise ArgumentError.new("Negative graph size: #{size}") unless size >= 0 @graph = Array.new(size) { Array(Edge(T)).new } end def add_edge(from : Int, to : Int, cost : T) add_edge(Edge2.new(from, to, cost)) end def add_edge(from_to_cost : {Int32, Int32, T}) add_edge(Edge2.new(*from_to_cost)) end def add_edges(edges) edges.each { |edge| add_edge(edge) } self end delegate size, to: @graph delegate :[], to: @graph def each_edge : Nil (0...size).each do |v| graph[v].each do |edge| yield Edge2(T).new(v, edge.to, edge.cost) end end end def edges result = [] of Edge2(T) each_edge do |edge| result << edge end result end def reverse result = self.class.new(size) each_edge do |edge| result.add_edge(edge.reverse) end result end end class DirectedGraph(T) < Graph(T) def initialize(size : Int) super end def initialize(size : Int, edges : Enumerable(Edge2(T))) super(size) add_edges(edges) end def initialize(size : Int, edges : Enumerable({Int32, Int32, T})) super(size) add_edges(edges) end def add_edge(edge : Edge2(T)) raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size @graph[edge.from] << Edge.new(edge.to, edge.cost) self end end class UndirectedGraph(T) < Graph(T) def initialize(size : Int) super end def initialize(size : Int, edges : Enumerable(Edge2(T))) super(size) add_edges(edges) end def initialize(size : Int, edges : Enumerable({Int32, Int32, T})) super(size) add_edges(edges) end def add_edge(edge : Edge2(T)) raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size @graph[edge.from] << Edge.new(edge.to, edge.cost) @graph[edge.to] << Edge.new(edge.from, edge.cost) self end end abstract class UnweightedGraph getter graph : Array(Array(Int32)) def initialize(size : Int) raise ArgumentError.new("Negative graph size: #{size}") unless size >= 0 @graph = Array.new(size) { Array(Int32).new } end def add_edge(from : Int, to : Int) add_edge(UnweightedEdge2.new(from, to)) end def add_edge(from_to : {Int32, Int32}) add_edge(*from_to) end def add_edges(edges) edges.each { |edge| add_edge(edge) } self end delegate size, to: @graph delegate :[], to: @graph def each_edge : Nil (0...size).each do |v| graph[v].each do |u| yield UnweightedEdge2.new(v, u) end end end def edges result = [] of UnweightedEdge2 each_edge do |edge| result << edge end result end def reverse result = self.class.new(size) each_edge do |edge| result.add_edge(edge.reverse) end result end end class UnweightedDirectedGraph < UnweightedGraph def initialize(size : Int) super end def initialize(size : Int, edges) super(size) add_edges(edges) end def add_edge(edge : UnweightedEdge2) raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size @graph[edge.from] << edge.to self end def to_undirected : self result = UnweightedDirectedGraph.new(size) each_edge do |edge| result.add_edge(edge) result.add_edge(edge.reverse) end result end end class UnweightedUndirectedGraph < UnweightedGraph def initialize(size : Int) super end def initialize(size : Int, edges) super(size) add_edges(edges) end def add_edge(edge : UnweightedEdge2) raise IndexError.new unless 0 <= edge.from < size && 0 <= edge.to < size @graph[edge.from] << edge.to @graph[edge.to] << 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 to_undirected : self self end end class Graph(T) def bfs01(start : Int, &block) raise ArgumentError.new unless 0 <= start < size queue = Deque{start} dist = Array(Int32?).new(size, nil) dist[start] = 0 while v = queue.shift? current_dist = dist[v].not_nil! graph[v].each do |edge| cost = yield(edge) raise ArgumentError.new("Unexpected cost: #{cost}") unless cost == 0 || cost == 1 next_dist = current_dist + cost if (d = dist[edge.to]).nil? || next_dist < d dist[edge.to] = next_dist if cost == 0 que.unshift edge.to else que.push edge.to end end end end dist end def bfs01(start : Int) bfs01(start, &.cost) end def bfs01!(start : Int32, &block) bfs01(start) { |edge| yield edge }.map(&.not_nil!) end def bfs01!(start : Int) bfs01!(start, &.cost) end def bfs01_st(start : Int, goal : Int) : Int32? raise ArgumentError.new unless 0 <= start < size queue = Deque{start} dist = Array(Int32?).new(size, nil) dist[start] = 0 while v = queue.shift? current_dist = dist[v].not_nil! return current_dist if v == goal graph[v].each do |edge| cost = yield(edge) raise ArgumentError.new("Unexpected cost: #{cost}") unless cost == 0 || cost == 1 next_dist = current_dist + cost if (d = dist[edge.to]).nil? || next_dist < d dist[edge.to] = next_dist if cost == 0 queue.unshift edge.to else queue.push edge.to end end end end nil end end n, m, k = read_line.split.map(&.to_i) graph = UndirectedGraph.new n, Array.new(m) { u, v, c = read_line.split.map(&.to_i) {u - 1, v - 1, c} } puts (0..2*10**5).bsearch { |x| graph.bfs01_st(0, n - 1) { |edge| edge.cost > x ? 1 : 0 }.not_nil! < k }