无权图深度，广度优先搜索

# 无权无向图，无权有向图都可以

# dfs和bfs都可以知道是否可达

# dfs和bfs都可以获取两点之间的路径, 但bfs的路径是最短路径

 

【深度优先搜索bfs】

local Dfs = {}
Dfs.__index = Dfs

function Dfs.new(g)
    local obj = {}
    setmetatable(obj, Dfs)

    obj:ctor(g)
    return obj
end

function Dfs:ctor(g)
    if nil == g then
        print("ctor g nil")
    end
    self.graph = g
    self.startVertex = nil
    self.visited = {}
    self.visitFromMap = {} --通过目标点获取访问源点
end

---到另一个点是否可达
function Dfs:IsReachable(endVertex)
    return true == self.visited[endVertex]
end

---遍历所有可达的顶点
function Dfs:VisitAllReachable(startVertex)
    self.startVertex = startVertex
    self.visited = {}
    self.visitFromMap = {}

    function dfs(v)
        self.visited[v] = true

        local list = self.graph:GetAdjacent(v)
        for i=1,#list do
            local adjV = list[i]
            if not self.visited[adjV] then
                self.visitFromMap[adjV] = v
                dfs(adjV)
            end
        end
    end

    dfs(startVertex)
end

---两个点之间的路径
function Dfs:GetPath(endVertex)
    if not self:IsReachable(endVertex) then return nil end

    local pathQueue = {}
    --从目标点, 反向一步一步算出起点
    local v = endVertex
    while v ~= self.startVertex do
        table.insert(pathQueue, 1, v)
        v = self.visitFromMap[v]
    end
    table.insert(pathQueue, 1, v)
    return pathQueue
end

测试代码:

function TestDfs1()
    local g = CreateDGraph()
    local dfs = Dfs.new(g)
    dfs:VisitAllReachable("3")
    print(dfs:IsReachable("4"))
    print(dfs:IsReachable("0"))
    print(table.concat(dfs:GetPath("4"), "->"))
end
TestDfs1()

 

【广度优先搜索bfs】

local Bfs = {}
Bfs.__index = Bfs

function Bfs.new(g)
    local obj = {}
    setmetatable(obj, Bfs)

    obj:ctor(g)
    return obj
end

function Bfs:ctor(g)
    self.graph = g
    self.startVertex = nil
    self.visited = {}
    self.visitFrom = {} --从哪个点访问的key对应的点
end

function Bfs:IsReachable(endVertex)
    return true == self.visited[endVertex]
end

function Bfs:VisitAllReachable(startVertex)
    self.startVertex = startVertex
    self.visited = {}
    self.visitFrom = {}

    local queue = {}
    self.visited[startVertex] = true
    table.insert(queue, startVertex)

    while #queue > 0 do
        local v = queue[1]
        table.remove(queue, 1)

        local list = self.graph:GetAdjacent(v)
        for i=1,#list do
            local adjV = list[i]
            if not self.visited[adjV] then
                self.visitFrom[adjV] = v
                self.visited[adjV] = true
                table.insert(queue, adjV)
            end
        end
    end
end

function Bfs:GetPath(endVertex)
    if not self:IsReachable(endVertex) then return nil end

    local pathQueue = {}
    local v = endVertex
    while v ~= self.startVertex do
        table.insert(pathQueue, 1, v)
        v = self.visitFrom[v]
    end
    table.insert(pathQueue, 1, v)
    return pathQueue
end

测试代码：

function CreateDGraph2()
    local g = DGraph.new()
    g:AddVertex("0")
    g:AddVertex("1")
    g:AddVertex("2")
    g:AddVertex("3")
    g:AddVertex("4")
    g:AddVertex("5")

    g:AddEdge("0", "2")
    g:AddEdge("2", "0")
    g:AddEdge("2", "1")
    g:AddEdge("2", "3")
    g:AddEdge("2", "5")
    g:AddEdge("3", "2")
    g:AddEdge("3", "4")
    g:AddEdge("3", "5")

    return g
end

function TestBfs1()
    local g = CreateDGraph2()

    local dfs = Bfs.new(g)
    dfs:VisitAllReachable("0")
    print(dfs:IsReachable("3"))
    print(dfs:IsReachable("5"))
    print(table.concat(dfs:GetPath("5"), "->"))
end
TestBfs1()

 

【参考】

图论算法——有向图的可达性与寻路_日积月累，天道酬勤-CSDN博客_图可达算法