算法导论Java实现-MAX-HEAPIFY算法(6.2章节)

package lhz.algorithm.chapter.six;

/**
* MAX-HEAPIFY,《算法导论》第六章
* 算法导论原文：
* MAX-HEAPIFY is an important subroutine for manipulating max-heaps. Its inputs are an
* array A and an index i into the array. When MAX-HEAPIFY is called, it is assumed that the
* binary trees rooted at LEFT(i) and RIGHT(i) are max-heaps, but that A[i] may be smaller than
* its children, thus violating the max-heap property. The function of MAX-HEAPIFY is to let
* the value at A[i] "float down" in the max-heap so that the subtree rooted at index i becomes a
* max-heap.
* 伪代码：
* MAX-HEAPIFY(A, i)
* 1 l ← LEFT(i)
* 2 r ← RIGHT(i)
* 3 if l ≤ heap-size[A] and A[l] > A[i]
* 4 then largest ← l
* 5 else largest ← i
* 6 if r ≤ heap-size[A] and A[r] > A[largest]
* 7 then largest ← r
* 8 if largest ≠ i
* 9 then exchange A[i] ↔ A[largest] 10 MAX-HEAPIFY(A, largest)
* @author lihzh(苦逼coder)
* 本文地址：http://mushiqianmeng.blog.51cto.com/3970029/736717
*/
public class MaxHeapify {

private static int[] input = new int[] { 16, 4, 10, 14, 7, 9, 3, 2, 8, 1 };
private static int heapSize = input.length;

public static void main(String[] args) {
maxHeapify(input, 2);//此处，2对于二叉树中的索引值，对应数组中的4
//打印数组
printArray();
}

/**
* MaxHeap，调整算法，前提是假设所有的子二叉树已经是max-heap。
* 复杂度：
* 因为：T (n) ≤ T(2n/3) + Θ(1)
* 所以有：  * T (n) = O(lgn)
* @param array
* @param index
*/
private static void maxHeapify(int[] array, int index) {
int l = index * 2;
int r = l + 1;
int largest;
//如果左叶子节点索引小于堆大小，比较当前值和左叶子节点的值，取值大的索引值
if (l <= heapSize && array[l-1] > array[index-1]) {
largest = l;
} else {
largest = index;
}
//如果右叶子节点索引小于堆大小，比较右叶子节点和之前比较得出的较大值，取大的索引值
if (r <= heapSize && array[r-1] > array[largest-1]) {
largest = r;
}
//交换位置，并继续递归调用该方法调整位置。
if (largest != index) {
int temp = array[index-1];
array[index-1] = array[largest-1];
array[largest-1] = temp;
maxHeapify(array,largest);
}
}

private static void printArray() {
for (int i : input) {
System.out.print(i + " ");
}
}

}
图示：