This documentation is automatically generated by online-judge-tools/verification-helper
src/graph/decompose.cr
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- Last update: 2022-04-16 16:23:13+09:00
Depends on
Required by
test/graph/namori_decompose_test_.cr
Verified with
Code
require "../graph"
require "../datastructure/union_find"
module Graph(Edge, Edge2)
# Decomposes the graph into each conected components.
def decompose : {Array(self), Array({Int32, Int32}), Array(Array(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
normalize = Array.new(groups.size) { |i| Array.new(groups[i].size, -1) }
index.each_with_index { |(i, j), k| normalize[i][j] = k }
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, edge.cost}
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, edge.cost}
end
end
end
{graphs, index, normalize}
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 : 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
# require "../datastructure/union_find"
class UnionFind
@d : Array(Int32)
getter count_components : Int32
def initialize(n : Int)
@d = Array.new(n, -1)
@count_components = n
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
@count_components -= 1
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)
# Decomposes the graph into each conected components.
def decompose : {Array(self), Array({Int32, Int32}), Array(Array(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
normalize = Array.new(groups.size) { |i| Array.new(groups[i].size, -1) }
index.each_with_index { |(i, j), k| normalize[i][j] = k }
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, edge.cost}
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, edge.cost}
end
end
end
{graphs, index, normalize}
end
end