无向图的连通分量计算

# 从某个顶点出发，访问到其能访问的所有其他顶点，这些顶点是属于一个连通分量的。

# 以此类推，将图的每个顶点都作为出发点一次。

local ConnectedComponent = {}
ConnectedComponent.__index = ConnectedComponent

function ConnectedComponent.new()
    local obj = {}
    setmetatable(obj, ConnectedComponent)
    obj:ctor()
    return obj
end

function ConnectedComponent:ctor()
    self.graph = nil
    self.vertexComponent = nil ---顶点所属的连通分量
    self.componentId = 0
end

function ConnectedComponent:Calc(graph)
    self.graph = graph
    self.vertexComponent = {}
    self.componentId = 0
    local visited = {}

    local function dfsVisitAllReachable(v)
        visited[v] = true
        self.vertexComponent[v] = self.componentId

        local adjList = graph:GetAdjacent(v)
        for i=1,#adjList do
            local adjV = adjList[i]
            if not visited[adjV] then
                dfsVisitAllReachable(adjV)
            end
        end
    end

    for i=1,graph:GetVertexCount() do
        local v = graph:GetVertex(i)
        if not visited[v] then
            dfsVisitAllReachable(v) --这个顶点能访问到的所有顶点属于同一个连通分量
            self.componentId = self.componentId + 1
        end
    end
end

function ConnectedComponent:IsConnected(v1, v2)
    return self.vertexComponent[v1] == self.vertexComponent[v2] --是否属于同一个连通分量
end

---连通分量数量
function ConnectedComponent:GetCount()
    return self.componentId
end

---顶点所属连通分量id
function ConnectedComponent:GetComponentId(v)
    return self.vertexComponent[v]
end

function ConnectedComponent:Dump()
    local ccVertexListTb = {} ---连通分量的顶点队列

    for i=1,self.graph:GetVertexCount() do
        local v = self.graph:GetVertex(i)
        local cid = self:GetComponentId(v)
        local queue = ccVertexListTb[cid]
        if nil == queue then
            queue = {}
            ccVertexListTb[cid] = queue
        end
        table.insert(queue, v)
    end

    for k_v, v_list in pairs(ccVertexListTb) do
        print(table.concat(v_list, ","))
    end
end

 

使用下面的图进行测试：

 

 

function CreateGraph()
    local g = Graph.new()

    g:AddVertex("0")
    g:AddVertex("1")
    g:AddVertex("2")
    g:AddEdge("0", "1")
    g:AddEdge("0", "2")

    g:AddVertex("3")

    g:AddVertex("4")
    g:AddVertex("5")
    g:AddVertex("6")
    g:AddVertex("7")
    g:AddEdge("4", "5")
    g:AddEdge("4", "6")
    g:AddEdge("5", "7")

    g:AddVertex("8")
    g:AddVertex("9")
    g:AddEdge("8", "9")

    tostring(g)
    return g
end

function Test1()
    local g = CreateGraph()
    local cc = ConnectedComponent.new()
    cc:Calc(g)
    cc:Dump()
end
Test1()

 

【参考】

图论算法——无向图的连通分量_日积月累，天道酬勤-CSDN博客_无向图的连通分量