java - 需要帮助计算 MaxHeap 中的交换数量

Question

我目前正在开发一个必须创建最大堆的项目。我目前正在使用我的教科书版本的堆，它看起来像:

public MaxHeap(int initialCapacity) {
    if (initialCapacity < DEFAULT_CAPACITY)
        initialCapacity = DEFAULT_CAPACITY;
    else
        checkCapacity(initialCapacity);

    @SuppressWarnings("unchecked")
    T[] tempHeap = (T[]) new Comparable[initialCapacity + 1];
    heap = tempHeap;
    lastIndex = 0;
    initialized = true;
}

public T getMax() {
    checkInitialization();
    T root = null;
    if (!isEmpty())
        root = heap[1];
    return root;
}

public boolean isEmpty() {
    return lastIndex < 1;
}

public int getSize() {
    return lastIndex;
}

public void clear() {
    checkInitialization();
    while (lastIndex > -1) {
        heap[lastIndex] = null;
        lastIndex--;
    }
    lastIndex = 0;
}

public void add(T newEntry) {
    checkInitialization();
    int newIndex = lastIndex + 1;
    int parentIndex = newIndex / 2;
    while ((parentIndex > 0) && newEntry.compareTo(heap[parentIndex]) > 0) {
        heap[newIndex] = heap[parentIndex];
        newIndex = parentIndex;
        parentIndex = newIndex / 2;
    }
    heap[newIndex] = newEntry;
    lastIndex++;
    ensureCapacity();
}

public int getSwaps()
{
    return swaps;
}

public T removeMax() {
    checkInitialization();
    T root = null;
    if (!isEmpty()) {
        root = heap[1];
        heap[1] = heap[lastIndex];
        lastIndex--;
        reheap(1);
    }
    return root;
}

private void reheap(int rootIndex) {
    boolean done = false;
    T orphan = heap[rootIndex];
    int leftChildIndex = 2 * rootIndex;

    while (!done && (leftChildIndex <= lastIndex)) {
        int largerChildIndex = leftChildIndex;
        int rightChildIndex = leftChildIndex + 1;
        if ((rightChildIndex <= lastIndex) && heap[rightChildIndex].compareTo(heap[largerChildIndex]) > 0) {
            largerChildIndex = rightChildIndex;
        }
        if (orphan.compareTo(heap[largerChildIndex]) < 0) {
            heap[rootIndex] = heap[largerChildIndex];
            rootIndex = largerChildIndex;
            leftChildIndex = 2 * rootIndex;
        } else
            done = true;
    }
    heap[rootIndex] = orphan;

}

我是否应该在多个地方计算掉期并打印总金额，如果是的话我会在哪里计算它们？我之前曾尝试在 add 方法中枚举 swaps++，但我认为这不是正确的方法。

Answer 1

您必须计算 add(T newEntry) 方法和从 removeMax 方法调用的 reHeap 方法中的交换。

在reHeap中，您从顶部开始，当您从removeMax调用它时，在删除最大值(在最大堆情况下)后，您将根替换为最后一个元素，然后您需要平衡堆。因此堆递归地下降到最后一层以达到平衡，这可能需要交换。

编辑:

在reHeap的以下代码块中添加交换:

if (orphan.compareTo(heap[largerChildIndex]) < 0) {
        heap[rootIndex] = heap[largerChildIndex];
        rootIndex = largerChildIndex;
        leftChildIndex = 2 * rootIndex;
        // increment the swap here as inside this block of reHeap only swap takes place.
        swap++
 }