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src/graph/dijkstra.cr
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- Last update: 2022-04-16 16:23:13+09:00
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require "../datastructure/binary_heap"
require "../graph"
module Graph(Edge, Edge2)
# Returns the array of distance of each node from *start* or `nil`.
def dijkstra(start : Int)
raise ArgumentError.new unless 0 <= start < size
que = BinaryHeap({Int32, typeof(first.cost)}).new { |(v1, d1), (v2, d2)| d1 <=> d2 }
que << {start, typeof(first.cost).zero}
dist = Array(typeof(first.cost)?).new(size, nil)
dist[start] = typeof(first.cost).zero
until que.empty?
v, d = que.pop
next if dist[v].try { |dist_v| dist_v < d }
current_dist = dist[v].not_nil!
graph[v].each do |edge|
next_dist = current_dist + edge.cost
if dist[edge.to].nil? || dist[edge.to].not_nil! > next_dist
dist[edge.to] = next_dist
que << {edge.to, next_dist}
end
end
end
dist
end
# Returns the array of distance of each node from *start*.
def dijkstra!(start : Int)
dijkstra(start).map(&.not_nil!)
end
# Returns the distance of *start* to *goal* or `nil`.
def dijkstra(start : Int, goal : Int)
raise ArgumentError.new unless 0 <= start < size && 0 <= goal < size
que = BinaryHeap({Int32, typeof(first.cost)}).new { |(v1, d1), (v2, d2)| d1 <=> d2 }
que << {start, typeof(first.cost).zero}
dist = Array(typeof(first.cost)?).new(size, nil)
dist[start] = typeof(first.cost).zero
until que.empty?
v, d = que.pop
return d if v == goal
next if dist[v].try { |dist_v| dist_v < d }
current_dist = dist[v].not_nil!
graph[v].each do |edge|
next_dist = current_dist + edge.cost
if dist[edge.to].nil? || dist[edge.to].not_nil! > next_dist
dist[edge.to] = next_dist
que << {edge.to, next_dist}
end
end
end
end
# Returns the distance of *start* to *goal*.
def dijkstra!(start : Int, goal : Int)
dijkstra(start, goal).not_nil!
end
def dijkstra_with_prev(start : Int)
raise ArgumentError.new unless 0 <= start < size
que = BinaryHeap({Int32, typeof(first.cost)}).new { |(v1, d1), (v2, d2)| d1 <=> d2 }
que << {start, typeof(first.cost).zero}
dist = Array(typeof(first.cost)?).new(size, nil)
dist[start] = typeof(first.cost).zero
prev = Array(Int32?).new(size, nil)
until que.empty?
v, d = que.pop
next if dist[v].try { |dist_v| dist_v < d }
current_dist = dist[v].not_nil!
graph[v].each do |edge|
next_dist = current_dist + edge.cost
if dist[edge.to].nil? || dist[edge.to].not_nil! > next_dist
dist[edge.to] = next_dist
prev[edge.to] = v
que << {edge.to, next_dist}
end
end
end
{dist, prev}
end
def dijkstra_with_path(start : Int, goal : Int)
dist, prev = dijkstra_with_prev(start)
if d = dist[goal]
{d, Graph.restore_path(prev, goal)}
end
end
def self.restore_path(prev : Array(Int32?), v : Int) : Array(Int32)
v = v.to_i
path = [v]
while v = prev[v]
path << v
end
path.reverse
end
end# require "../datastructure/binary_heap"
class BinaryHeap(T)
# Creates a new empty heap.
def initialize
@heap = Array(T).new
@compare_proc = nil
end
# Creates a new empty heap backed by a buffer that is initially *initial_capacity* big (default: `0`).
#
# ```
# a = BinaryHeap.new(3)
# a << 3 << 1 << 2
# a.pop # => 1
# a.pop # => 2
# a.pop # => 3
# ```
def initialize(initial_capacity : Int = 0)
@heap = Array(T).new(initial_capacity)
@compare_proc = nil
end
# Creates a new heap from the elements in *enumerable*.
#
# ```
# a = BinaryHeap.new [3, 1, 2]
# a.pop # => 1
# a.pop # => 2
# a.pop # => 3
# ```
def initialize(enumerable : Enumerable(T))
initialize
enumerable.each { |x| add(x) }
end
# Creates a new empty heap with the custom comperator.
#
# The block must implement a comparison between two elements *a* and *b*, where `a < b` returns `-1`,
# `a == b` returns `0`, and `a > b` returns `1`. The comparison operator `#<=>` can be used for this.
#
# ```
# a = BinaryHeap.new [3, 1, 2]
# a.pop # => 1
# b = BinaryHeap.new [3, 1, 2] { |a, b| b <=> a }
# b.pop # => 3
# ```
def initialize(initial_capacity : Int = 0, &block : T, T -> Int32?)
@heap = Array(T).new(initial_capacity)
@compare_proc = block
end
# :ditto:
def initialize(enumerable : Enumerable(T), &block : T, T -> Int32?)
initialize &block
enumerable.each { |x| add(x) }
end
include Enumerable(T)
include Iterable(T)
def_clone
# Returns true if both heap have the same elements.
def ==(other : BinaryHeap(T)) : Bool
return false if size != other.size
@heap.sort == other.@heap.sort
end
# Returns the number of elements in the heap.
def size : Int32
@heap.size
end
# Returns `true` if `self` is empty, `false` otherwise.
def empty? : Bool
@heap.empty?
end
# Removes all elements from the heap and returns `self`.
def clear : self
@heap.clear
self
end
# Returns the lowest value in the `self`.
# If the `self` is empty, calls the block and returns its value.
def top(&block)
@heap.first { yield }
end
# Returns the lowest value in the `self`.
# If the `self` is empty, returns `nil`.
def top? : T?
top { nil }
end
# Returns the lowest value in the `self`.
# If the `self` is empty, raises `IndexError`.
def top : T
top { raise IndexError.new }
end
# Requires `0 <= i < size`, `0 <= j < size`.
private def compare(i : Int32, j : Int32)
x, y = @heap.unsafe_fetch(i), @heap.unsafe_fetch(j)
if @compare_proc
v = @compare_proc.not_nil!.call(x, y)
raise ArgumentError.new("Comparison of #{x} and #{y} failed") if v.nil?
v > 0
else
x > y
end
end
# Adds *object* to the heap and returns `self`.
def add(object : T) : self
@heap << object
i = size - 1
parent = i.pred // 2
while i > 0 && compare(parent, i)
@heap.swap(parent, i)
i, parent = parent, parent.pred // 2
end
self
end
# :ditto:
def <<(object : T) : self
add(object)
end
# Removes the lowest value from `self` and returns the removed value.
# If the array is empty, the given block is called.
def pop(&block)
case size
when 0
yield
when 1
@heap.pop
else
value = @heap.unsafe_fetch(0)
@heap[0] = @heap.pop
i = 0
loop do
left, right = i * 2 + 1, i * 2 + 2
j = if right < size && compare(i, right)
compare(left, right) ? right : left
elsif left < size && compare(i, left)
left
else
break
end
@heap.swap(i, j)
i = j
end
value
end
end
# Like `#pop`, but returns `nil` if `self` is empty.
def pop? : T?
pop { nil }
end
# Removes the lowest value from `self` and returns the removed value.
# Raises `IndexError` if heap is of 0 size.
def pop : T
pop { raise IndexError.new }
end
# Removes the last *n* values from `self` ahd returns the removed values.
def pop(n : Int) : Array(T)
raise ArgumentError.new unless n >= 0
n = Math.min(n, size)
Array.new(n) { pop }
end
# Yields each element of the heap, and returns `nil`.
def each(&) : Nil
@heap.each { |elem| yield elem }
end
# Returns an iterator for each element of the heap.
def each
@heap.each
end
# Returns a new array with all elements sorted.
#
# ```
# a = BinaryHeap.new [3, 1, 2]
# a.sort # => [1, 2, 3]
# b = BinaryHeap.new [3, 1, 2] { |a, b| b <=> a }
# b.sort # => [3, 2, 1]
# ```
def sort : Array(T)
if @compare_proc
@heap.sort { |a, b| @compare_proc.not_nil!.call(a, b) }
else
@heap.sort
end
end
# Returns the elements as an Array.
#
# ```
# BinaryHeap{3, 1, 2}.to_a # => [1, 3, 2]
# ```
def to_a : Array(T)
@heap.dup
end
# Writes a string representation of the heap to `io`.
#
# ```
# BinaryHeap{1, 2}.to_s # => "BinaryHeap{1, 2}"
# ```
def to_s(io : IO) : Nil
io << "BinaryHeap{"
# TODO: use join
each_with_index do |x, i|
io << ", " if i > 0
io << x
end
io << '}'
end
# Writes a string representation of the heap to `io`.
#
# ```
# BinaryHeap{1, 2}.inspect # => "BinaryHeap{1, 2}"
# ```
def inspect(io : IO) : Nil
to_s(io)
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
module Graph(Edge, Edge2)
# Returns the array of distance of each node from *start* or `nil`.
def dijkstra(start : Int)
raise ArgumentError.new unless 0 <= start < size
que = BinaryHeap({Int32, typeof(first.cost)}).new { |(v1, d1), (v2, d2)| d1 <=> d2 }
que << {start, typeof(first.cost).zero}
dist = Array(typeof(first.cost)?).new(size, nil)
dist[start] = typeof(first.cost).zero
until que.empty?
v, d = que.pop
next if dist[v].try { |dist_v| dist_v < d }
current_dist = dist[v].not_nil!
graph[v].each do |edge|
next_dist = current_dist + edge.cost
if dist[edge.to].nil? || dist[edge.to].not_nil! > next_dist
dist[edge.to] = next_dist
que << {edge.to, next_dist}
end
end
end
dist
end
# Returns the array of distance of each node from *start*.
def dijkstra!(start : Int)
dijkstra(start).map(&.not_nil!)
end
# Returns the distance of *start* to *goal* or `nil`.
def dijkstra(start : Int, goal : Int)
raise ArgumentError.new unless 0 <= start < size && 0 <= goal < size
que = BinaryHeap({Int32, typeof(first.cost)}).new { |(v1, d1), (v2, d2)| d1 <=> d2 }
que << {start, typeof(first.cost).zero}
dist = Array(typeof(first.cost)?).new(size, nil)
dist[start] = typeof(first.cost).zero
until que.empty?
v, d = que.pop
return d if v == goal
next if dist[v].try { |dist_v| dist_v < d }
current_dist = dist[v].not_nil!
graph[v].each do |edge|
next_dist = current_dist + edge.cost
if dist[edge.to].nil? || dist[edge.to].not_nil! > next_dist
dist[edge.to] = next_dist
que << {edge.to, next_dist}
end
end
end
end
# Returns the distance of *start* to *goal*.
def dijkstra!(start : Int, goal : Int)
dijkstra(start, goal).not_nil!
end
def dijkstra_with_prev(start : Int)
raise ArgumentError.new unless 0 <= start < size
que = BinaryHeap({Int32, typeof(first.cost)}).new { |(v1, d1), (v2, d2)| d1 <=> d2 }
que << {start, typeof(first.cost).zero}
dist = Array(typeof(first.cost)?).new(size, nil)
dist[start] = typeof(first.cost).zero
prev = Array(Int32?).new(size, nil)
until que.empty?
v, d = que.pop
next if dist[v].try { |dist_v| dist_v < d }
current_dist = dist[v].not_nil!
graph[v].each do |edge|
next_dist = current_dist + edge.cost
if dist[edge.to].nil? || dist[edge.to].not_nil! > next_dist
dist[edge.to] = next_dist
prev[edge.to] = v
que << {edge.to, next_dist}
end
end
end
{dist, prev}
end
def dijkstra_with_path(start : Int, goal : Int)
dist, prev = dijkstra_with_prev(start)
if d = dist[goal]
{d, Graph.restore_path(prev, goal)}
end
end
def self.restore_path(prev : Array(Int32?), v : Int) : Array(Int32)
v = v.to_i
path = [v]
while v = prev[v]
path << v
end
path.reverse
end
end