我正在使用以下网站的Dijkstra算法代码：https://rosettacode.org/wiki/Dijkstra%27s_algorithm#Lua
不幸的是，它不适用于当前的边表。
我确定从35-> 36删除连接后问题消失了，但是并不能解决问题。
-- Graph definition
local edges = {
[34] = {[35] = 1,[37] = 1,},
[35] = {[34] = 1,[36] = 1,[46] = 1,},
[36] = {[35] = 1,[37] = 1,},
[37] = {[34] = 1,[36] = 1,},
[38] = {[46] = 1,},
[46] = {[35] = 1,[38] = 1,},
}
-- Fill in paths in the opposite direction to the stated edges
function complete (graph)
for node, edges in pairs(graph) do
for edge, distance in pairs(edges) do
if not graph[edge] then graph[edge] = {} end
graph[edge][node] = distance
end
end
end
-- Create path string from table of previous nodes
function follow (trail, destination)
local path, nextStep = destination, trail[destination]
while nextStep do
path = nextStep .. " " .. path
nextStep = trail[nextStep]
end
return path
end
-- Find the shortest path between the current and destination nodes
function dijkstra (graph, current, destination, directed)
if not directed then complete(graph) end
local unvisited, distanceTo, trail = {}, {}, {}
local nearest, nextNode, tentative
for node, edgeDists in pairs(graph) do
if node == current then
distanceTo[node] = 0
trail[current] = false
else
distanceTo[node] = math.huge
unvisited[node] = true
end
end
repeat
nearest = math.huge
for neighbour, pathDist in pairs(graph[current]) do
if unvisited[neighbour] then
tentative = distanceTo[current] + pathDist
if tentative < distanceTo[neighbour] then
distanceTo[neighbour] = tentative
trail[neighbour] = current
end
if tentative < nearest then
nearest = tentative
nextNode = neighbour
end
end
end
unvisited[current] = false
current = nextNode
until unvisited[destination] == false or nearest == math.huge
return distanceTo[destination], follow(trail, destination)
end
-- Main procedure
print("Directed:", dijkstra(edges, 34, 38, true))
print("Undirected:", dijkstra(edges, 34, 38, false))
我使用当前egdes表内容接收了inf, 38的输出，但是当我删除35-> 36之间的连接时，它给出了很好的输出-3, 34 35 46 38
为便于理解，我上传了边表的图形表示：https://i.imgur.com/FFF22C1.png
正如您所见，当我们从34-> 35-> 46-> 38开始时，该路线是正确的，但令人遗憾的是，仅当从35到36的连接不存在时，该路线才有效。
为什么在我的代码所示的情况下它不起作用？
答案 0 :(得分：0)
这是Dijkstra算法实现的示例
-- Graph definition
local edges = {
[34] = {[35] = 1,[37] = 1,},
[35] = {[34] = 1,[36] = 1,[46] = 1,},
[36] = {[35] = 1,[37] = 1,},
[37] = {[34] = 1,[36] = 1,},
[38] = {[46] = 1,},
[46] = {[35] = 1,[38] = 1,},
}
local starting_vertex, destination_vertex = 34, 38
local function create_dijkstra(starting_vertex)
local shortest_paths = {[starting_vertex] = {full_distance = 0}}
local vertex, distance, heap_size, heap = starting_vertex, 0, 0, {}
return
function (adjacent_vertex, edge_length)
if adjacent_vertex then
-- receiving the information about adjacent vertex
local new_distance = distance + edge_length
local adjacent_vertex_info = shortest_paths[adjacent_vertex]
local pos
if adjacent_vertex_info then
if new_distance < adjacent_vertex_info.full_distance then
adjacent_vertex_info.full_distance = new_distance
adjacent_vertex_info.previous_vertex = vertex
pos = adjacent_vertex_info.index
else
return
end
else
adjacent_vertex_info = {full_distance = new_distance, previous_vertex = vertex, index = 0}
shortest_paths[adjacent_vertex] = adjacent_vertex_info
heap_size = heap_size + 1
pos = heap_size
end
while pos > 1 do
local parent_pos = (pos - pos % 2) / 2
local parent = heap[parent_pos]
local parent_info = shortest_paths[parent]
if new_distance < parent_info.full_distance then
heap[pos] = parent
parent_info.index = pos
pos = parent_pos
else
break
end
end
heap[pos] = adjacent_vertex
adjacent_vertex_info.index = pos
elseif heap_size > 0 then
-- which vertex neighborhood to ask for?
vertex = heap[1]
local parent = heap[heap_size]
heap[heap_size] = nil
heap_size = heap_size - 1
if heap_size > 0 then
local pos = 1
local last_node_pos = heap_size / 2
local parent_info = shortest_paths[parent]
local parent_distance = parent_info.full_distance
while pos <= last_node_pos do
local child_pos = pos + pos
local child = heap[child_pos]
local child_info = shortest_paths[child]
local child_distance = child_info.full_distance
if child_pos < heap_size then
local child_pos2 = child_pos + 1
local child2 = heap[child_pos2]
local child2_info = shortest_paths[child2]
local child2_distance = child2_info.full_distance
if child2_distance < child_distance then
child_pos = child_pos2
child = child2
child_info = child2_info
child_distance = child2_distance
end
end
if child_distance < parent_distance then
heap[pos] = child
child_info.index = pos
pos = child_pos
else
break
end
end
heap[pos] = parent
parent_info.index = pos
end
local vertex_info = shortest_paths[vertex]
vertex_info.index = nil
distance = vertex_info.full_distance
return vertex
end
end,
shortest_paths
end
local vertex, dijkstra, shortest_paths = starting_vertex, create_dijkstra(starting_vertex)
while vertex and vertex ~= destination_vertex do
-- send information about all adjacent vertexes of "vertex"
for adjacent_vertex, edge_length in pairs(edges[vertex]) do
dijkstra(adjacent_vertex, edge_length)
end
vertex = dijkstra() -- now dijkstra is asking you about the neighborhood of another vertex
end
if vertex then
local full_distance = shortest_paths[vertex].full_distance
local path = vertex
while vertex do
vertex = shortest_paths[vertex].previous_vertex
if vertex then
path = vertex.." "..path
end
end
print(full_distance, path)
else
print"Path not found"
end