算法导论：堆排序

堆排序

代码（python 2）只是实现了堆排序的核心代码：堆维护性质（max_heapify）,而后的建堆、及排序都是基于堆得维护性质算法进行调用即可，暂时不做详解。

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注意：
为了和书中的伪代码一致，对堆（以数组的形式表示）的操作从数组的第二个元素array[1]开始，第一个元素不作处理初始为0。

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堆维护性质算法

1、基于递归实现：

"""warning:    1, This codes are based on chapter 6 of Introduction to Algorithms, so the array[0] to be    initialized 0, and ignore array[0].    2, The second element, array[1], will be treated as the root of the heap.    3, At beginning, the heap_size = len(array)-1 because we don't operate array[0]."""'''此时的Heap类暂时使用不到'''class Heap:    def __init__(self, array, list_length, heap_size):        self.A = array        self.list_length = list_length        self.heap_size = heap_size    def heap_size_del(self):        self.heap_size -= 1def left(i):    return 2*idef right(i):    return 2*i + 1def max_heapify_recursion(array, i, heap_size):    if (i > heap_size/2) or (array[i] > array[left(i)] and array[i] > array[right(i)]):        return    largest = i    if i <= heap_size / 2 and array[i] < array[left(i)]:        largest = left(i)    if i <= heap_size / 2 and array[largest] < array[right(i)]:        largest = right(i)    if largest != i:        temp = array[i]        array[i] = array[largest]        array[largest] = temp    max_heapify_recursion(array, largest, heap_size)

实验如下：

heap = [0, 16, 4, 10, 14, 7, 9, 3, 2, 8, 1]print heapmax_heapify_recursion(heap, 2, 10)print heap

结果：

[0, 16, 4, 10, 14, 7, 9, 3, 2, 8, 1][0, 16, 14, 10, 8, 7, 9, 3, 2, 4, 1]

2、非递归实现：

def max_heapify(array, i, heap_size):    check = True    if (i > heap_size/2) or (array[i] > array[left(i)] and array[i] > array[right(i)]):        return    while check:        largest = i        if (i > heap_size/2) or (array[i] > array[left(i)] and array[i] > array[right(i)]):            break        elif i <= heap_size/2 and array[i] < array[left(i)]:            largest = left(i)        elif i <= heap_size/2 and array[largest] < array[right(i)]:            largest = right(i)        if largest != i:            temp = array[i]            array[i] = array[largest]            array[largest] = temp        i = largest

实验相同略过。