多個未加權圖上的 Dijkstra 最短路徑？

Question

我試圖弄清楚如何實現 djiktra 算法來找到2 個未加權圖之間的最短路徑。 我得到的建議是使用兩張圖表，一張用於紅色，一張用於藍色。 旅行的成本始終是 1，但要在藍色時訪問紅色方塊，則需要支付 2 才能切換圖形。

我主要是在尋找建議和參考有沒有人做過類似的事情？？？

Answer 1

根據原始圖創建一個新的加權圖，其中藍色 -> 紅色路徑花費 3 而不是 1，然后在其上運行 Dijkstra。

編輯：可能沒有必要實際創建新圖表，您可以直接從原始圖表中獲取權重，但首先創建新圖表可能更容易遵循。

頂角看起來像這樣：

A ← 3 → B ← 1 → C ← 1 → D ...
↑       ↑       ↑
1       1       3  
↓       ↓       ↓
E ← 3 → F ← 3 → G...

Answer 2

這只是標准的 Dijkstra。

// Not pure C++

enum Color { Red, Blue};
using Graph = std::vector_like<std::vector_like<Color>>;
using Point = std::pair<int, int>;

int getCost(Graph const& graph, Point src, Point dst)
{
    // Assumes: src and dst are 1 point away from each other.
    //          This assumes that work is done via
    //          getListOfPointsReachable() which only gets nodes
    //          nodes that are adjecent.
    //          
    // Standard movement cost.
    int cost = 1;

    // Add a cost if switching between blue red.
    if (graph[src] !=  graph[dst]) {
        cost += 2;
    }
    return cost;
}

void Dijkstra(Graph const& graph, Point start, Point end)
{
    std::set<Point>  visited;

    // Boundary:  int   => Cost
    //            Point => Point cost applies to.
    // Using tuple as it already has the comparison operator defined.
    using Boundary = std::tuple<int, Point>;
    std:: priority_queue<Boundary>   boundary;

    // Set up the boundary list with a start.
    boundary.emplace(0, start);

    while (!boundary.empty())
    {
        Boundary next = boundry.top();
        boundary.pop();

        int      cost = std::get<0>(next);
        Point    nextP = std::get<1>(next);

        if (nextP == end)
        {
            throw std::runtime_error("Found route to end: Cheapest Route is: " + cost);
        }
        if (visited.find(nextP) != std::end(visited))
        {
            // we already did this node.
            continue;
        }
        visited.insert(nextP);

        std::list<Point> dests = getListOfPointsReachable(graph, nextP);
        for (auto const& dest: dests)
        {
            int extraCost = getCost(graph, nextP, dest);
            boundary.emplace(extraCost + cost, dest);
        }
    }
    throw std::runtime_error("No Route from Start to End");
 }

Answer 3

要創建圖形，請使用此偽代碼在節點之間添加邊

AddEdge( n1, n2 )
SET cost = 1
IF n1color != n2color
   SET cost = 3;
graph.AddEdge( n1, n2, cost );
RUN Dijsktra on graph