问题描述
我正在使用 BFS 在 ruby 中实现一个函数，我想知道如何在无向图中打印起始值和结束值之间的最短路径
图表 在这个例子中，图有十个顶点。每个节点代表一个顶点，它有一个存储相邻节点（边）的数组。
$ irb
graph.to_s
1. 1 -> [2 3 4 5 8 9 10]
2. 2 -> [1 4 5 6 7 8 10]
3. 3 -> [1 4 6]
4. 4 -> [1 2 3 6 7 8 9 10]
5. 5 -> [1 2 8 9 10]
6. 6 -> [2 3 4 7 8 9 10]
7. 7 -> [2 4 6 8 9]
8. 8 -> [1 2 4 5 6 7 9 10]
9. 9 -> [1 4 5 6 7 8]
10. 10 -> [1 2 4 5 6 8]
=> [1,2,3,4,5,6,7,8,9,10]
预期产出
2,1,9 或 2,9 等
BFS
def bfs_shortest_path(graph,start=2,search=9)
if graph.nodes[start].nil? || graph.nodes[search].nil?
return nil
end
visited = Set.new
search_queue = Queue.new
search_queue.enq(start)
while !search_queue.empty? do
current_node_key = search_queue.deq
current_node = graph.nodes[current_node_key]
visited.add(current_node_key)
if current_node.value == search
return current_node # I would like to return the PATH Eg. 2,9
end
adjacent_nodes_array = current_node.adjacent_nodes.map{|x| x.value}
adjacent_nodes_array.each do |value|
if !visited.include?(value)
search_queue.enq(value)
graph.nodes[value].concat_to_path(current_node.path_from_start)
end
end
end
end
节点
class Node
attr_reader :value
attr_reader :adjacent_nodes
def initialize(value)
@value = value
@adjacent_nodes = []
end
def add_edge(node)
@adjacent_nodes.push(node)
end
def to_s
"#{@value} -> [#{@adjacent_nodes.map(&:value).sort.join(" ")}]"
end
end
图表
class Graph
attr_reader :nodes
def initialize
@nodes = {}
end
def add_node(node)
@nodes[node.value] = node
end
def add_edge(node1,node2)
if @nodes[node1.value].adjacent_nodes.map(&:value).include? (node2.value)
puts "#{node1.value} and #{node2.value} already have an edge"
elsif node1.value == node2.value
puts "node1.value == node2.value"
else
@nodes[node1.value].add_edge(@nodes[node2.value])
@nodes[node2.value].add_edge(@nodes[node1.value])
end
end
def to_s
@nodes.keys.sort.each_with_index do |key,index|
puts "#{index + 1}. #{@nodes[key].to_s}"
end
end
end
生成图表
def generate_random_graph
g = Graph.new
[*1..10].shuffle.each do |node_value|
g.add_node(Node.new(node_value))
end
40.times do
key1 = g.nodes.keys.sample
key2 = g.nodes.keys.sample
g.add_edge(g.nodes[key1],g.nodes[key2])
end
return g
end
测试
graph = generate_random_graph
graph.to_s
bfs_shortest_path(graph,9)
解决方法
要保留您去过的地方的历史记录，以便您可以重建路径，而不是使用 visited 集，请使用哈希。哈希跟踪哪个节点是每个访问节点的前驱。当您将邻居推入队列时，通过 came_from[neighbor] = current 添加我们正在远离的当前节点作为父节点/前驱节点。
这个哈希也可以像 visited 一样消除循环。
当你达到目标时，你可以通过重复键入这个 came_from 哈希来重建路径，直到你用完前辈。反转数组（线性时间）并作为最终路径返回。
这是一个最小的、可运行的示例，您可以适应您的类结构：
def reconstruct_path(tail,came_from)
path = []
while !tail.nil?
path << tail
tail = came_from[tail]
end
path.reverse
end
def bfs(graph,start,goal)
q = Queue.new
q.enq(start)
came_from = {start => nil}
while !q.empty?
curr = q.deq
if graph.key? curr
return reconstruct_path(goal,came_from) if curr == goal
graph[curr].each do |neighbor|
if !came_from.key?(neighbor)
came_from[neighbor] = curr
q.enq(neighbor)
end
end
end
end
end
graph = {
"A" => ["B","C"],"B" => ["A","F"],"C" => ["D"],"D" => ["E","E" => [],"F" => []
}
=begin
+----+
v |
A--->B--->F
| ^
V |
C--->D----+
|
v
E
=end
p bfs(graph,"A","F") # => ["A","B","F"]
p bfs(graph,"E") # => ["A","C","D","E"]
p bfs(graph,"E") # => ["B","E"]
感谢评论
工作版本
class Node
attr_reader :value
attr_reader :adjacent_nodes
attr_reader :path_from_start
def initialize(value)
@value = value
@adjacent_nodes = []
@path_from_start = []
end
def add_edge(node)
@adjacent_nodes.push(node)
end
def add_to_path(value)
@path_from_start.push(value)
end
def concat_to_path(value_array)
@path_from_start.concat(value_array)
end
def to_s
"#{@value} -> [#{@adjacent_nodes.map(&:value).sort.join(" ")}]"
end
end
class Graph
attr_reader :nodes
def initialize
@nodes = {}
end
def add_node(node)
@nodes[node.value] = node
end
def add_edge(node1,node2)
if @nodes[node1.value].adjacent_nodes.map(&:value).include? (node2.value)
puts "#{node1.value} and #{node2.value} already have an edge"
elsif node1.value == node2.value
puts "node1.value == node2.value"
else
@nodes[node1.value].add_edge(@nodes[node2.value])
@nodes[node2.value].add_edge(@nodes[node1.value])
end
end
def to_s
@nodes.keys.sort.each_with_index do |key,index|
puts "#{index + 1}. #{@nodes[key].to_s}"
end
end
end
def generate_random_graph
g = Graph.new
[*1..10].shuffle.each do |node_value|
g.add_node(Node.new(node_value))
end
40.times do
key1 = g.nodes.keys.sample
key2 = g.nodes.keys.sample
g.add_edge(g.nodes[key1],g.nodes[key2])
end
return g
end
def bfs(graph,start_node_value=2,search_value=9)
if graph.nodes[start_node_value].nil? || graph.nodes[search_value].nil?
return nil
end
visited = Set.new
search_queue = Queue.new
search_queue.enq(graph.nodes[start_node_value])
while !search_queue.empty? do
current_node = search_queue.deq
visited.add(current_node)
if current_node.value == search_value
return current_node
end
current_node.adjacent_nodes.each do |node|
if !visited.include?(graph.nodes[node.value])
search_queue.enq(graph.nodes[node.value])
end
end
end
end
def bfs_shortest_path(graph,start=2,search=9)
if graph.nodes[start].nil? || graph.nodes[search].nil?
return nil
end
visited = Set.new
visited.add(start)
search_queue = Queue.new
search_queue.enq(start)
while !search_queue.empty? do
current_node_key = search_queue.deq
current_node = graph.nodes[current_node_key]
current_node.add_to_path(current_node.value)
if current_node.value == search
return current_node.path_from_start
end
adjacent_nodes_array = current_node.adjacent_nodes.map{|x| x.value}
adjacent_nodes_array.each do |value|
if !visited.include?(value)
search_queue.enq(value)
visited.add(value)
graph.nodes[value].concat_to_path(current_node.path_from_start)
end
end
end
end
def test_graph
graph = generate_random_graph
graph.to_s
bfs_shortest_path(graph,2,9)
end