This documentation is automatically generated by online-judge-tools/verification-helper
test/graph/decompose_test.cr
- View this file on GitHub
- Last update: 2022-04-16 16:23:13+09:00
- Problem: https://yukicoder.me/problems/no/922
Depends on
- src/datastructure/union_find.cr
- src/graph.cr
- src/graph/decompose.cr
- src/graph/edge.cr
- src/graph/lca.cr
- src/graph/re_rooting.cr
- src/scanner.cr
Code
# verification-helper: PROBLEM https://yukicoder.me/problems/no/922
require "../../src/scanner"
require "../../src/graph/re_rooting"
require "../../src/graph/decompose"
require "../../src/graph/lca"
struct DP
getter sum : Int64, cnt : Int32
class_property! k : Array(Int32)
def initialize
@sum, @cnt = 0i64, 0
end
def initialize(@sum, @cnt)
end
def +(other : self) : self
DP.new(sum + other.sum, cnt + other.cnt)
end
def add_root(v : Int32) : self
DP.new(sum + cnt, cnt + DP.k[v])
end
end
n, m, q = input(i, i, i)
g = UnweightedUnGraph.new n, input({i - 1, i - 1}[m])
graphs, index, _ = g.decompose
lcas = graphs.map { |graph| LCA.new(graph, 0) }
ans = 0i64
cnts = Array.new(graphs.size) { |i| Array.new(graphs[i].size, 0) }
q.times do
a, b = input(i - 1, i - 1)
ai, aj = index[a]
bi, bj = index[b]
if ai == bi
ans += lcas[ai].dist(aj, bj)
else
cnts[ai][aj] += 1
cnts[bi][bj] += 1
end
end
graphs.each_with_index do |graph, i|
DP.k = cnts[i]
dp = ReRooting(DP, UnweightedUnGraph).new(graph)
ans += dp.solve.min_of(&.sum)
end
puts ans# verification-helper: PROBLEM https://yukicoder.me/problems/no/922
# 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
# require "../../src/graph/re_rooting"
# 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
# Example of `T`:
# ```
# struct DP
# getter val : Int64, cnt : Int32
#
# def initialize
# @val, @cnt = 0i64, 0
# end
#
# def initialize(@val, @cnt)
# end
#
# def +(other : self) : self
# DP.new(val + other.val, cnt + other.cnt)
# end
#
# def add_root(v : Int32) : self
# DP.new(val + cnt, cnt + 1)
# end
# end
# ```
class ReRooting(T, GraphType)
getter graph : GraphType
def initialize(size : Int)
initialize(GraphType.new(size))
end
def initialize(@graph : GraphType)
@dp = Array(Array(T)).new
@result = Array(T).new
end
def initialize(size : Int, edges : Enumerable)
initialize(GraphType.new(size, edges))
end
delegate size, :<<, add_edges, to: @graph
private def dfs(v : Int32, p : Int32) : T
acc = T.new
graph[v].each_with_index do |edge, i|
if edge.to != p
acc += (@dp[v][i] = dfs(edge.to, v))
end
end
acc.add_root(v)
end
private def bfs(v : Int32, p : Int32, dp_p : T) : Nil
graph[v].each_with_index do |edge, i|
@dp[v][i] = dp_p if edge.to == p
end
n = graph[v].size
dp_left = Array.new(n + 1, T.new)
(0...n).each do |i|
dp_left[i + 1] = dp_left[i] + @dp[v][i]
end
dp_right = Array.new(n + 1, T.new)
(0...n).reverse_each do |i|
dp_right[i] = dp_right[i + 1] + @dp[v][i]
end
@result[v] = dp_left.last.add_root(v)
graph[v].each_with_index do |edge, i|
bfs(edge.to, v, (dp_left[i] + dp_right[i + 1]).add_root(v)) if edge.to != p
end
end
def solve : Array(T)
@dp = Array.new(size) { |i| Array.new(@graph[i].size, T.new) }
@result = Array.new(size, T.new)
dfs(0, -1)
bfs(0, -1, T.new)
@result
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/graph/lca"
# require "../graph"
class LCA(Edge, Edge2)
getter graph : Graph(Edge, Edge2), depth : Array(Int32), log2 : Int32
private def dfs(vertex : Int32, par : Int32, dep : Int32) : Nil
@parent[0][vertex] = par
@depth[vertex] = dep
@graph[vertex].each do |edge|
dfs(edge.to, vertex, dep + 1) if edge.to != par
end
end
def initialize(@graph : Graph(Edge, Edge2), root : Int32)
@log2 = Math.log2(size).to_i.succ
@depth = Array(Int32).new(size, -1)
@parent = Array(Array(Int32)).new(log2) { Array.new(size, 0) }
dfs(root, -1, 0)
(0...log2 - 1).each do |k|
(0...size).each do |v|
@parent[k + 1][v] = @parent[k][v] < 0 ? -1 : @parent[k][@parent[k][v]]
end
end
end
delegate size, to: @graph
def depth(v : Int32) : Int32
@depth[v]
end
def parent_p2(v : Int32, k : Int32) : Int32?
p = @parent[k][v]
p >= 0 ? p : nil
end
def parent_p2!(v : Int32, k : Int32) : Int32
parent_p2(v, k).not_nil!
end
def parent(v : Int32) : Int32?
parent_p2(v, 0)
end
def parent!(v : Int32) : Int32
parent(v).not_nil!
end
def parent(v : Int32, up : Int32) : Int32?
log2.times do |k|
v = @parent[k][v] if up.bit(k) == 1
return nil if v < 0
end
v
end
def parent!(v : Int32, up : Int32) : Int32
parent(v, up).not_nil!
end
def lca(u : Int32, v : Int32) : Int32
raise IndexError.new unless 0 <= u < size && 0 <= v < size
u, v = v, u if @depth[u] > @depth[v]
(0...log2).each do |k|
v = @parent[k][v] if (@depth[v] - @depth[u]).bit(k) == 1
end
return u if u == v
(0...log2).reverse_each do |k|
u, v = @parent[k][u], @parent[k][v] if @parent[k][u] != @parent[k][v]
end
@parent[0][u]
end
def dist(u : Int32, v : Int32) : Int32
depth(u) + depth(v) - depth(lca(u, v)) * 2
end
def path(start : Int32, goal : Int32, &) : Nil
lca = lca(start, goal)
{start, goal}.each do |first|
if first != lca
yield v = first
while (v = parent!(v)) != lca
yield v
end
end
end
yield lca
end
def path(start : Int32, goal : Int32) : Array(Int32)
path = [] of Int32
path(start, goal) { |v| path << v }
path
end
end
struct DP
getter sum : Int64, cnt : Int32
class_property! k : Array(Int32)
def initialize
@sum, @cnt = 0i64, 0
end
def initialize(@sum, @cnt)
end
def +(other : self) : self
DP.new(sum + other.sum, cnt + other.cnt)
end
def add_root(v : Int32) : self
DP.new(sum + cnt, cnt + DP.k[v])
end
end
n, m, q = input(i, i, i)
g = UnweightedUnGraph.new n, input({i - 1, i - 1}[m])
graphs, index, _ = g.decompose
lcas = graphs.map { |graph| LCA.new(graph, 0) }
ans = 0i64
cnts = Array.new(graphs.size) { |i| Array.new(graphs[i].size, 0) }
q.times do
a, b = input(i - 1, i - 1)
ai, aj = index[a]
bi, bj = index[b]
if ai == bi
ans += lcas[ai].dist(aj, bj)
else
cnts[ai][aj] += 1
cnts[bi][bj] += 1
end
end
graphs.each_with_index do |graph, i|
DP.k = cnts[i]
dp = ReRooting(DP, UnweightedUnGraph).new(graph)
ans += dp.solve.min_of(&.sum)
end
puts ans