首都间通过其他首都的最短路径

Question

我正在尝试为一项大学工作开发一些代码，我有一个算法，可以为我提供图形中两个节点之间的最短路径。请注意，节点是有资本的国家。

有谁能解释一下，我怎样才能开发出一条从A国到B国的最短路径，通过一系列的首都（国家）吗？

我已经实现了一种方法，该方法还提供了两个地理点之间的距离。

我最初的想法是，根据首都到A国的距离排列首都列表，然后将A国到列表第一个国家、列表第一个国家和列表第三个国家之间最短路径的所有距离相加，依此类推。显然这是不对的。

    public double shortestPathCapitals2(List<String> capitais, Pais pOrig, Pais pDest) {
    double dist = 0;
    LinkedList<Pais> shortPath = new LinkedList<Pais>();
    LinkedList<String> temp = new LinkedList<>(capitais);

    temp.addFirst(pOrig.getCapital());
    temp.addLast(pDest.getCapital());

    Collections.sort(temp, (c1, c2) -> (int) (distance(pOrig, shortestPathCapitals2(c2)) - distance(pOrig, obterPaisPorCapital(c1))));

    for (int i = 0; i < temp.size() - 1; i++) {
        Pais p1 = obterPaisPorCapital(temp.get(i));
        Pais p2 = obterPaisPorCapital(temp.get(i + 1));
        dist += shortestPath(p1, p2, shortPath);
        shortPath.clear();
    }

    return dist;
}

谢谢你。

Answer 1

问题描述：

给定一个顶点为V、边为E的图。我们希望在Va和Vb之间找到路径P，以便：

• 路径包含{V0， V1，...}（V的某个子集）
• P中边的权重之和最小

伪代码：

function findPath(startVertex, endVertex, verticesToBeVisited, currentPath)

    // check if we have reached the destination
    if startVertex == endVertex:

          /*
           * there are multiple ways of reaching the destination
           * calculate the length of the past (also called the cost)
           * if the cost is lower than the current minimum, store the path
           */
          cost = calculateCost(currentPath)
          if cost  < currentMinCost:
              currentMinCost = cost
              currentMinPath = currentPath            

    else:

        /*
         * if we have not reached the destination
         * we need to try all possible next hops
         * this algorithm uses recursion to do so
         */
        for every vertex Vn that is a neighbour of startVertex:

            /*
             * this check prevents us from going
             * Paris --> Rome --> Paris --> Rome (endlessly)
             */
            if currentPath contains Vn:
                 continue

            // add the next hop to our path
            currentPath += Vn

            // if this vertex needed to be visit, cross it out in the list
            if verticesToBeVisited contains Vn:
                verticesToBeVisited -= Vn

            // recursion
            findPath(Vn, endVertex, verticesToBeVisited, currentPath)

            // clean up
            if verticesToBeVisited contained Vn:
                verticesToBeVisited += Vn

            currentPath -= Vn