我正在实施斐波那契堆以改进我的 Dijkstra 的最短路径算法。我的 insert 方法工作正常，接下来我需要做的是 extract-min。我正在关注 CLRS。请注意本书中提到的一些属性还没有在我的实现中，因为到目前为止这些功能都不需要它们，但我稍后会添加它们。
private static class FibonacciHeap {
/**
* Implementation of the node used in
* fibonacci heap. The nodes are stored
* as a circular doubly-linked list, making
* delete and insert operations easy, as
* well as being able to iterate through
* without being forced to keep track of the
* head
*/
private class Node {
/**
* The vertex this node is storing
*/
Vertex val;
/**
* Key used to know the order of vertices
*/
int key;
/**
* The left and right sibling in the list
*/
Node left, right;
/**
* Pointer to one of the child's
*/
Node child;
/**
* The amount of children this node has
*/
int degree;
/**
* Constructs a node with a value and key
*
* @param val the value of this node
* @param key the key of this node
*/
public Node(Vertex val, int key) {
this.val = val;
this.key = key;
}
/**
* Inserts a new node into this node's list.
* Inserts it to the left of this node, while
* maintaining the fact that it's circular
*
* @param newNode The new node to be inserted
*/
public void insert(Node newNode) {
newNode.left = left;
left.right = newNode;
newNode.right = this;
left = newNode;
if(newNode.key < min.key) {
min = newNode;
}
size++;
}
/**
* Removes this node from it's list
*/
public void remove() {
right.left = left;
left.right = right;
}
/**
* Inserts a new child into this nodes
* child list
*
* @param child The new node to be added as a child
*/
public void link(Node child) {
child.remove();
if(this.child == null) {
this.child = child;
} else {
this.child.insert(child);
}
degree ++;
}
/**
* Used for debugging. Will be removed after
* all operations work fine
*
* @return A string representation of this node
*/
@Override
public String toString() {
Node dummy = right;
StringBuilder sb = new StringBuilder();
sb.append(key).append(" -> (");
sb.append(dummy.child);
sb.append(") ");
while(dummy != this) {
sb.append(dummy.key).append(" -> (");
sb.append(dummy.child);
sb.append(") ");
dummy = dummy.right;
}
return sb.toString();
}
}
/**
* Pointer to the node with the smallest key
*/
private Node min;
/**
* Stores the number of nodes in the heap
*/
private int size;
/**
* Creates an empty Fibonacci Heap
*/
public FibonacciHeap() { }
/**
* Gets and returns the key with the
* smallest value
*
* @return the key with the smallest value
*/
public int getMin() {
if(min == null) {
throw new NoSuchElementException("Empty Fibonacci Heap");
}
return min.key;
}
/**
* Inserts a vertex along with a key. The
* key is the one used to measure whether
* this vertex is lesser than another
*
* @param vertex vertex to be added
* @param key key of the vertex
*/
public void insert(Vertex vertex, int key) {
if(min == null) {
min = new Node(vertex, key);
min.left = min;
min.right = min;
size = 1;
} else {
min.insert(new Node(vertex, key));
}
}
/**
* Removes the node with the smallest key from
* the heap, and updates the minimum node if needed
*
* @return The node with the smallest key prior to this method call
*/
public Vertex extractMin() {
if(isEmpty()) {
throw new NoSuchElementException("Empty Fibonacci Heap");
}
Vertex toReturn;
if(min == null) {
toReturn = null;
} else {
toReturn = min.val;
if(min.right == min) {
min = null;
} else {
min.remove();
min = min.right;
consolidate();
}
}
return toReturn;
}
/**
* Consolidates the heap. Consolidation is the process
* making every node in the root list have it's own
* unique degree. That is, every node in the top most
* layer has a unique amount of children
*/
private void consolidate() {
Node[] degrees = new Node[size];
degrees[min.degree] = min;
Node tempMin, dummy = (tempMin = min).right;
while(dummy != tempMin) {
if(dummy.key < min.key) {
min = dummy;
}
while(degrees[dummy.degree] != null) {
Node other = degrees[dummy.degree];
if(other.key < dummy.key) {
Node temp = dummy;
dummy = other;
other = temp;
}
dummy.link(other);
degrees[dummy.degree - 1] = null;
}
degrees[dummy.degree] = dummy;
}
}
/**
* Returns true if and only if the
* heap is empty
*
* @return if the heap is empty
*/
public boolean isEmpty() {
return min == null;
}
/**
* A string representation of this
* heap. Format of string is:
* node1 -> (node1.child.toString()) node2 -> (node2.child.toString()) ... noden -> (noden.child.toString())
* The string representation of the
* heap is the string representation of
* the minimum node
*
* @return A string representation of this heap
*/
@Override
public String toString() {
return min.toString();
}
}
这是它提供的堆栈跟踪：
Exception in thread "main" java.lang.ArrayIndexOutOfBoundsException: Index 10 out of bounds for length 10
at GraphTheory.ShortestPathAlgorithms.DijkstraShortestPath$FibonacciHeap.consolidate(DijkstraShortestPath.java:362)
at GraphTheory.ShortestPathAlgorithms.DijkstraShortestPath$FibonacciHeap.extractMin(DijkstraShortestPath.java:338)
at GraphTheory.ShortestPathAlgorithms.DijkstraShortestPath.main(DijkstraShortestPath.java:104)
主要错误在 consolidate 函数的内部 while 循环的条件语句中给出。我还在代码中注释了这一行。出了什么问题？我的主要测试方法是从 1 - 10 中插入 10 个随机数，然后提取最小值直到它为空。第一次调用 extract-min 时发生错误。
public static void main(String[] args) {
FibonacciHeap f = new FibonacciHeap();
StringBuilder sb = new StringBuilder();
for(int i = 0; i < 10; i ++) {
f.insert(new Vertex(i), (int) (Math.random() * 10));
}
while(!f.isEmpty()) {
System.out.println(f.extractMin());
}
}