python算法与数据结构（19）堆

堆：一种完全二叉树，有最大堆和最小堆两种。
最大堆：根总是最大值，最小的值存储在叶节点中，
最小堆：每个非叶子节点的两个孩子的值都比它大。
堆的操作：
插入新的值，依然保证堆的最大堆或者最小堆的结构。
删除一个值。
堆的表示：使用数组表示堆。

parent = int(i-1)/2
left = 2i +1
right = 2i+2

class Array(object):
    def __init__(self, size=32):
        self._size = size
        self._items = [None] * size

    def __getitem__(self, index):
        return self._items[index]

    def __setitem__(self, index, value):
        self._items[index] = value

    def __len__(self):
        return self._size

    def clear(self, value=None):
        for i in range(len(self._items)):
            self._items[i] = value

    def __iter__(self):
        for item in self._items:
            yield item


"""heap 实现"""
class Maxheap(object):
    def __init__(self, maxsize=None):
        self.maxsize = maxsize
        self._elements = Array(maxsize)
        self._count = 0

    def __len__(self):
        return self._count

    def add(self, value):
        if self._count >= self.maxsize:
            raise Exception('full')
        # 开始加入，先把值放在最后一位，最后一位就是_count
        self._elements[self._count] = value
        self._count += 1
        self._siftup(self._count - 1)  # 定义_siftup函数，传入的值是添加元素的位置

    def _siftup(self, ndx):  # 递归交换，直到满足最大堆的特性。
        if ndx > 0:
            parent = int((ndx - 1 / 2))
            if self._elements[ndx] > self._elements[parent]:  # 如果他的值大于父亲就交换
                self._elements[ndx], self._elements[parent] = self._elements[parent], self._elements[ndx]
                self._siftup(parent)  # 递归

    def extract(self):
        if self._count <= 0:
            raise Exception('empty')
        value = self._elements[0]
        self._count -= 1
        self._elements[0] = self._elements[self._count]
        self._siftdown(0)
        return value

    def _siftdown(self, ndx):
        left = 2 * ndx + 1
        right = 2 * ndx + 2
        largest = ndx
        if (left < self._count and self._elements[left] >= self._elements[largest] and self._elements[left] >=
                self._elements[right]):
            largest = left
        elif right < self._count and self._elements[right] >= self._elements[largest]:
            largest = right
        if largest != ndx:
            self._elements[ndx], self._elements[largest] = self._elements[largest], self._elements[ndx]
            self._siftdown(largest)


def test_max_heap():
    import random
    n = 5
    h = Maxheap(n)
    for i in range(n):
        h.add(i)
    for i in reversed(range(n)):
        assert i == h.extract()