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 + " ");
        }
    }

}