python实现小顶堆MinHeap和哈夫曼树HaffumanTree

小顶堆

堆是一种非线性结构，可以被视作数组，也可以被视作完全二叉树
堆就是利用完全二叉树的结构来维护的一维数组
大顶堆：每个结点的值都大于或等于其左右孩子结点的值
小顶堆：每个结点的值都小于或等于其左右孩子结点的值

class MinHeap:
    def __init__(self):
        self.__values: list = []

    def __swap(self, i, j):
        self.__values[int(i)], self.__values[int(j)] = self.__values[int(j)], self.__values[int(i)]

    def push(self, data):
        self.__values.append(data)
        i = len(self.__values) - 1
        while i != 0 and self.__values[int(i)] < self.__values[int((i - 1) / 2)]:
            self.__swap(i, (i - 1) / 2)
            i -= 1
            i /= 2

    def top(self):
        if len(self.__values) == 0: return None
        return self.__values[0]

    def pop(self):
        top = self.__values[0]
        self.__swap(0, len(self.__values) - 1)
        self.__values.pop()
        i = 0
        while True:
            left = 2 * i + 1
            right = 2 * i + 2
            max_ = i
            if left < len(self.__values) and self.__values[left] < self.__values[max_]: max_ = left
            if right < len(self.__values) and self.__values[right] < self.__values[max_]: max_ = right
            if max_ == i: break
            self.__swap(i, max_)
            i = max_
        return top

    def isEmpty(self):
        return len(self.__values) == 0

    def __len__(self):
        return len(self.__values)

    @staticmethod
    def fromList(dataList: list):
        heap = MinHeap()
        for i in dataList:
            heap.push(i)
        return heap

哈夫曼树

现在让我使用小顶堆来构造一颗哈夫曼树,并输出它的WPL(带权路径长度), 首先我们需要一个哈夫曼树类

class HaffumanTree:
    class Node:
        def __init__(self, value, left=None, right=None):
            self.value = value
            self.left: HaffumanTree.Node = left
            self.right: HaffumanTree.Node = left

        def __lt__(self, other) -> bool:
            return self.value < other.value

        def __gt__(self, other):
            return self.value > other.value

    def __init__(self, datas: list):
        self.__root: HaffumanTree.Node = None
        self.__WPL: int = 0
        minHeap = MinHeap()
        for item in datas:
            minHeap.push(HaffumanTree.Node(item))
        while len(minHeap) != 1:
        	# 贪婪
        	# 每次把最小的两个结点取出来然后合并成一个大结点并加入小顶堆,当堆中只剩一个结点时,这个结点就是哈夫曼树的根节点
            left = minHeap.pop()
            right = minHeap.pop()
            minHeap.push(HaffumanTree.Node(left.value + right.value, left, right))
            # 计算带权路径长度
            self.__WPL += left.value + right.value
        self.__root = minHeap.top()

    def WPL(self):
        return self.__WPL

测试

def main():
    print(HaffumanTree([2, 1, 4, 5, 7, 3, 4, 9]).WPL()) 

最后输出98，这是正确的。