java - Prim 算法

Question

我正在使用Prim 算法和 Java 中的 PriorityQueue来研究最小生成树。但是，我弄错了总重量（树的最小重量）。

我是否误解了总重量背后的概念，还是我的代码有问题？

public int getMinSpanningTree(Graph g) {
    int[][] matrix = g.getEdgeMatrix();
    int totalVertices = g.getNumberOfVertices();
    boolean[] visit = new boolean[totalVertices];
    int visitNum = 1;
    int totalWeight = 0;
    PriorityQueue<PriorityVertex> queue = new PriorityQueue<PriorityVertex>();

    //FIRST ITERATION
    visit[0] = true;
    for (int i = 0; i < totalVertices; i++) {
        if(matrix[0][i] > 0) {
            PriorityVertex temp = new PriorityVertex(i, g.getWeight(0,i));
            queue.add(temp);
        } 
    }

    while (visitNum < totalVertices) {
        PriorityVertex temp = queue.poll();
        visit[temp.vertex] = true;
        visitNum++;
        totalWeight = temp.priority + totalWeight;
        //RUN NEIGHBOUR VERTICES
        for (int k = 0; k < totalVertices; k++) {
           if(matrix[temp.vertex][k] > 0 && visit[k] == false) {
               PriorityVertex vertex = new PriorityVertex(k, g.getWeight(temp.vertex, k));
               queue.add(vertex);
           } 
        }
    }
    return totalWeight;
}

Answer 1

问题是您没有从队列中删除所有顶点实例=>同一顶点可以多次添加到结果中。

假设下图：

weight(0,1) = 1
weight(0,2) = 2
weight(1,2) = 3
weight(1,3) = 4
weight(2,3) = 5

在“FIRST ITERATION”之后，队列包含 PriorityVertex(1, 1)、PriortyVertex(2, 2)。

while循环的迭代：

1) removed: PriorityVertex(1, 1) - edge (0,1) 
   added: PriorityVerterx(2, 3) and PriorityVertex(3, 4)
   queue: PriorityVertex(2, 2), PriorityVertex(2, 3), PriorityVertex(3, 4)

2) removed: PriorityVertex(2, 2) - edge (0,2)
   added: PriorityVertex(3, 5)
   queue: PriorityVertex(2, 3), PriorityVertex(3, 4), PriorityVertex(3, 5)

3) removed: PriorityVertex(2, 3) - edge (1,2), cycle in the result!