普里姆算法 [英] Prim's Algorithm

问题描述

我正在使用带有Java中PriorityQueue的 Prim算法来研究最小生成树.但是，我弄错了totalWeight(树的最小权重).

I am working on a minimum spanning tree using Prim's Algorithm with PriorityQueue in Java. However, I am getting the totalWeight (the minimum weight of the tree) wrong.

我是否误解了总重量的概念，还是我的代码有问题?

Did I misunderstand the concept behind total weight, or is there some problem with my code?

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;
}

推荐答案

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.

The problem is you do not remove all instances of vertex from the queue => the same vertex can be added several times into the result.

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).

After the "FIRST ITERATION" the queue contains PriorityVertex(1, 1), PriortyVertex(2, 2).

while循环的迭代次数:

Iterations of while cycle:

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!

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