This documentation is automatically generated by online-judge-tools/verification-helper
test/graph/namori_decompose_test_.cr
- View this file on GitHub
- Last update: 2022-04-16 16:23:13+09:00
- Problem: https://yukicoder.me/problems/no/1640
Depends on
src/datastructure/union_find.cr
- src/graph.cr
- src/graph/decompose.cr
- src/graph/degree.cr
- src/graph/edge.cr
- src/graph/namori_decompose.cr
- src/scanner.cr
Code
# verification-helper: PROBLEM https://yukicoder.me/problems/no/1640
# verification-helper: IGNORE
require "../../src/graph/namori_decompose"
require "../../src/graph/decompose"
require "../../src/scanner"
def dfs(graph, v, p, dist, a)
a[v] = dist
graph[v].each do |edge|
next if edge.to == p
dfs(graph, edge.to, v, dist + 1, a)
end
end
n = input(i)
edges = input({i - 1, i - 1}[n])
ans = Array(Int32?).new(n, nil)
g = UnGraph.new n, edges.each_with_index.map { |(e, i)| {e[0], e[1], i} }
graphs, _, normalize = g.decompose
graphs.zip(normalize) do |graph, normalize|
if graph.size != graph.graph.sum(&.size) // 2
puts "No"; exit
end
forest, cycle = graph.namori_decompose
dist = [0] * graph.size
cycle_index = [nil.as Int32?] * graph.size
cycle.each_with_index do |v, i|
cycle_index[v] = i
dfs(forest, v, -1, 0, dist)
end
flag = false
graph.each do |edge|
d_from, d_to = dist[edge.from], dist[edge.to]
c_from, c_to = cycle_index[edge.from], cycle_index[edge.to]
if d_from < d_to
ans[edge.cost] = normalize[edge.to]
elsif d_from == d_to && c_from.not_nil! <= c_to.not_nil!
if {edge.from, edge.to} == {cycle.first, cycle.last}
if cycle.size == 2
ans[edge.cost] = normalize[flag ? edge.to : edge.from]
flag = true
else
ans[edge.cost] = normalize[edge.to]
end
else
ans[edge.cost] = normalize[edge.from]
end
end
end
end
puts "Yes", ans.join('\n', &.not_nil!.succ)# verification-helper: PROBLEM https://yukicoder.me/problems/no/1640
# verification-helper: IGNORE
# require "../../src/graph/namori_decompose"
# 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 "./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)
# Returns forest and cycle of the undirected graph with equal number of vertices and edges.
def namori_decompose : {self, Array(Int32)}
raise ArgumentError.new if self.class.directed?
raise ArgumentError.new unless size == graph.sum(&.size) // 2
deg = Array.new(size) { |i| self[i].size }
que = Deque(Int32).new
flag = Array.new(size, false)
(0...size).each do |i|
if deg[i] == 1
que << i
flag[i] = true
end
end
forest = self.class.new(size)
while v = que.shift?
self[v].each do |edge|
next if flag[edge.to]
deg[edge.to] -= 1
forest << Edge2.new(v, edge)
if deg[edge.to] == 1
que << edge.to
flag[edge.to] = true
end
end
end
cycle = [] of Int32
(0...size).each do |i|
que << i unless flag[i]
while v = que.pop?
next if flag[v]
cycle << v
flag[v] = true
self[v].each do |edge|
que << edge.to unless flag[edge.to]
end
end
end
{forest, cycle}
end
end
# require "../../src/graph/decompose"
# require "../graph"
# 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
# require "../../src/scanner"
module Scanner
extend self
private def skip_to_not_space(io)
peek = io.peek
not_space = peek.index { |x| x != 32 && x != 10 } || peek.size
io.skip(not_space)
end
def c(io = STDIN)
skip_to_not_space(io)
io.read_char.not_nil!
end
private def int(int_type : T.class, io = STDIN) : T forall T
skip_to_not_space(io)
value = T.zero
signed = false
case x = io.read_byte
when nil
raise IO::EOFError.new
when 45
signed = true
when 48..57
value = T.new 48 &- x
else
raise "Unexpected char: #{x.chr}"
end
loop do
peek = io.peek
return signed ? value : -value if peek.empty?
i = 0
while i < peek.size
c = peek.unsafe_fetch(i)
if 48 <= c <= 57
value = value &* 10 &- c &+ 48
i &+= 1
elsif c == 32 || c == 10
io.skip(i &+ 1)
return signed ? value : -value
else
raise "Unexpected char: #{c.chr}"
end
end
io.skip(i)
end
end
private def uint(uint_type : T.class, io = STDIN) : T forall T
skip_to_not_space(io)
value = T.zero
found_digit = false
loop do
peek = io.peek
if peek.empty?
if found_digit
return value
else
raise IO::EOFError.new
end
end
i = 0
while i < peek.size
c = peek.unsafe_fetch(i)
if 48 <= c <= 57
found_digit = true
value = value &* 10 &+ c &- 48
i &+= 1
elsif c == 32 || c == 10
io.skip(i &+ 1)
return value
else
raise "Unexpected char: #{c.chr}"
end
end
io.skip(i)
end
end
def i(io = STDIN)
int(Int32, io)
end
{% for n in [8, 16, 32, 64, 128] %}
def i{{n}}(io = STDIN)
int(Int{{n}}, io)
end
def u{{n}}(io = STDIN)
uint(UInt{{n}}, io)
end
{% end %}
{% for method in [:f, :f32, :f64] %}
def {{method.id}}(io = STDIN)
s(io).to_{{method.id}}
end
{% end %}
def s(io = STDIN)
skip_to_not_space(io)
peek = io.peek
if peek.empty?
raise IO::EOFError.new
end
if index = peek.index { |x| x == 32 || x == 10 }
io.skip(index + 1)
return String.new(peek[0, index])
end
String.build do |buffer|
loop do
buffer.write peek
io.skip(peek.size)
peek = io.peek
break if peek.empty?
if index = peek.index { |x| x == 32 || x == 10 }
buffer.write peek[0, index]
io.skip(index + 1)
break
end
end
end
end
end
macro internal_input(type, else_ast, io)
{% if Scanner.class.has_method?(type.id) %}
Scanner.{{type.id}}({{io}})
{% elsif type.stringify == "String" %}
Scanner.s({{io}})
{% elsif type.stringify == "Char" %}
Scanner.c({{io}})
{% elsif type.is_a?(Path) %}
{% if type.resolve.class.has_method?(:scan) %}
{{type}}.scan(Scanner, {{io}})
{% else %}
{{type}}.new(Scanner.s({{io}}))
{% end %}
{% elsif String.has_method?("to_#{type}".id) %}
Scanner.s({{io}}).to_{{type.id}}
{% else %}
{{else_ast}}
{% end %}
end
macro internal_input_array(type, args, io)
{% for i in 0...args.size %}
%size{i} = input({{args[i]}}, io: {{io}})
{% end %}
{% begin %}
{% for i in 0...args.size %} Array.new(%size{i}) { {% end %}
input({{type.id}}, io: {{io}})
{% for i in 0...args.size %} } {% end %}
{% end %}
end
# Inputs from *io*.
#
# ### Specifications
#
# ```plain
# AST | Example | Expanded code
# ------------------+---------------------+---------------------------------------
# Uppercase string | Int32, Int64, etc. | {}.new(Scanner.s)
# | s, c, i, iN, uN | Scanner.{}
# | f, big_i, etc. | Scanner.s.to_{}
# Call [] | type[size] | Array.new(input(size)) { input(type) }
# TupleLiteral | {t1, t2, t3} | {input(t1), input(t2), input(t3)}
# ArrayLiteral | [t1, t2, t3] | [input(t1), input(t2), input(t3)]
# HashLiteral | {t1 => t2} | {input(t1) => input(t2)}
# NamedTupleLiteral | {a: t1, b: t2} | {a: input(t1), b: input(t2)}
# RangeLiteral | t1..t2 | input(t1)..input(t2)
# Expressions | (exp1; exp2) | (input(exp1); input(exp2);)
# If | cond ? t1 : t2 | input(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, 5i64}
# input(String, Char[m]) # => {"foo", ['b', 'a', 'r']}
# input(Int32[n]) # => [1, 2, 3, 4, 5]
# ```
# ```
# n, m = input(i, i64) # => {5, 5i64}
# 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 1
# 2 1 2
# 5 1 2 3 4 5
# ```
# ```
# n = input(i) # => 3
# input(i[i][n]) # => [[1], [1, 2], [1, 2, 3, 4, 5]]
# ```
#
# Input:
# ```plain
# 3
# 1 2
# 2 3
# 3 1
# ```
# ```
# n = input(i)
# input_column({Int32, Int32}, n) # => {[1, 2, 3], [2, 3, 1]}
# ```
macro input(ast, *, io = STDIN)
{% if ast.is_a?(Call) %}
{% if ast.receiver.is_a?(Nop) %}
internal_input(
{{ast.name}},
{{ast.name}}({% for argument in ast.args %} input({{argument}}, io: {{io}}), {% end %}),
{{io}},
)
{% elsif ast.receiver.is_a?(Path) && ast.receiver.resolve.class.has_method?(ast.name.symbolize) %}
{{ast.receiver}}.{{ast.name}}(
{% for argument in ast.args %} input({{argument}}, io: {{io}}) {% end %}
) {{ast.block}}
{% elsif ast.name.stringify == "[]" %}
internal_input_array({{ast.receiver}}, {{ast.args}}, {{io}})
{% else %}
input({{ast.receiver}}, io: {{io}}).{{ast.name}}(
{% for argument in ast.args %} input({{argument}}, io: {{io}}), {% end %}
) {{ast.block}}
{% end %}
{% elsif ast.is_a?(TupleLiteral) %}
{ {% for i in 0...ast.size %} input({{ast[i]}}, io: {{io}}), {% end %} }
{% elsif ast.is_a?(ArrayLiteral) %}
[ {% for i in 0...ast.size %} input({{ast[i]}}, io: {{io}}), {% end %} ]
{% elsif ast.is_a?(HashLiteral) %}
{ {% for key, value in ast %} input({{key}}, io: {{io}}) => input({{value}}, io: {{io}}), {% end %} }
{% elsif ast.is_a?(NamedTupleLiteral) %}
{ {% for key, value in ast %} {{key}}: input({{value}}, io: {{io}}), {% end %} }
{% elsif ast.is_a?(RangeLiteral) %}
Range.new(
input({{ast.begin}}, io: {{io}}),
input({{ast.end}}, io: {{io}}),
{{ast.excludes_end?}},
)
{% elsif ast.is_a?(SymbolLiteral) %}
{{ast.id}}
{% elsif ast.is_a?(Expressions) %}
( {% for exp in ast.expressions %} input({{exp}}, io: {{io}}); {% end %} )
{% elsif ast.is_a?(If) %}
input({{ast.cond}}, io: {{io}}) ? input({{ast.then}}, io: {{io}}) : input({{ast.else}}, io: {{io}})
{% elsif ast.is_a?(Assign) %}
{{ast.target}} = input({{ast.value}}, io: {{io}})
{% else %}
internal_input({{ast}}, {{ast}}, io: {{io}})
{% end %}
end
macro input(*asts, io = STDIN)
{ {% for ast in asts %} input({{ast}}, io: {{io}}), {% end %} }
end
macro input_column(types, size, *, io = STDIN)
%size = {{size}}
{% for type, i in types %}
%array{i} = Array({{type}}).new(%size)
{% end %}
%size.times do
{% for type, i in types %}
%array{i} << input({{type}}, io: {{io}})
{% end %}
end
{ {% for type, i in types %} %array{i}, {% end %} }
end
def dfs(graph, v, p, dist, a)
a[v] = dist
graph[v].each do |edge|
next if edge.to == p
dfs(graph, edge.to, v, dist + 1, a)
end
end
n = input(i)
edges = input({i - 1, i - 1}[n])
ans = Array(Int32?).new(n, nil)
g = UnGraph.new n, edges.each_with_index.map { |(e, i)| {e[0], e[1], i} }
graphs, _, normalize = g.decompose
graphs.zip(normalize) do |graph, normalize|
if graph.size != graph.graph.sum(&.size) // 2
puts "No"; exit
end
forest, cycle = graph.namori_decompose
dist = [0] * graph.size
cycle_index = [nil.as Int32?] * graph.size
cycle.each_with_index do |v, i|
cycle_index[v] = i
dfs(forest, v, -1, 0, dist)
end
flag = false
graph.each do |edge|
d_from, d_to = dist[edge.from], dist[edge.to]
c_from, c_to = cycle_index[edge.from], cycle_index[edge.to]
if d_from < d_to
ans[edge.cost] = normalize[edge.to]
elsif d_from == d_to && c_from.not_nil! <= c_to.not_nil!
if {edge.from, edge.to} == {cycle.first, cycle.last}
if cycle.size == 2
ans[edge.cost] = normalize[flag ? edge.to : edge.from]
flag = true
else
ans[edge.cost] = normalize[edge.to]
end
else
ans[edge.cost] = normalize[edge.from]
end
end
end
end
puts "Yes", ans.join('\n', &.not_nil!.succ)