需要帮助计算MaxHeap中的交换次数

Question

我目前正在开发一个我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有点看起来像：

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;

}

我是否应该计算多个地方的掉期并打印总金额，如果是这样，我会在哪里计算它们？我之前曾尝试在add方法中枚举swaps ++，但我不认为这是正确的方法。

Answer 1

您必须计算add(T newEntry)方法和reHeap方法中的交换，该方法是从removeMax mathod调用的。

在reHeap中，你从顶部开始，当你从removeMax中调用它时，删除max（在Max Heap情况下）你用最后一个元素替换root，然后你需要平衡堆。因此堆递归地下降到最后一级以平衡可能需要交换。

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++
 }

Answer 2

这些是正确的实施方式吗？

所以add方法是：

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;
    swap++;
}
heap[newIndex] = newEntry;
lastIndex++;
ensureCapacity();
}

而重播将是：

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;
        swap++;
    } else
        done = true;
}
heap[rootIndex] = orphan;

}