Huffman Tree哈夫曼树（霍夫曼树、赫夫曼树）权值路径长度WPL计算

计算定义：把构建成功的哈夫曼树的每一个边缘节点（叶子）值乘以该节点到根的路径长度，最后求合。

import random

from binarytree import Node, get_parent

def app():
    data = []
    # 生成随机测试数据。
    for i in range(5):
        d = random.randint(1, 50)
        data.append(d)
    random.shuffle(data)
    print(data)
    huffman_tree = build_huffman_tree(data)
    print('-----')
    print('最终的Huffman树')
    root = huffman_tree.pop()
    print(root)
    print('---')
    print(data)
    print('计算WPL')
    wpl(root)

def build_huffman_tree(data):
    nodes = []
    for i in data:
        nodes.append(Node(i))
    print('nodes', nodes)
    print('开始构建Huffman树')

    while True:
        nodes = sorted(nodes, key=lambda x: x.value)
        # print('nodes', nodes)

        if len(nodes) == 1:
            # print('仅剩一个节点，建树结束')
            break

        left = nodes.pop(0)
        right = nodes.pop(0)
        # print('选取节点', left.value, right.value)

        root = Node(left.value + right.value)
        root.left = left
        root.right = right
        nodes.append(root)

    return nodes

# 计算带权值路径长度WPL
def wpl(root):
    leaves = root.leaves
    sum = 0
    for l in leaves:
        path = count_path(root, l)
        print(l.value, '->', root.value, '长度 = ', path)
        sum = sum + path * l.value

    print('带权值路径长度WPL =', sum)

def count_path(root, node):
    root_value = root.value
    count = 0
    while True:
        p = get_parent(root, node)
        count = count + 1
        if p.value == root_value:
            break
        else:
            node = p
    return count

if __name__ == '__main__':
    app()

输出：

[18, 35, 40, 3, 9]
nodes [Node(18), Node(35), Node(40), Node(3), Node(9)]
开始构建Huffman树
-----
最终的Huffman树

  _105_____________
 /                 \
40              ____65
               /      \
           ___30       35
          /     \
         12      18
        /  \
       3    9

---
[18, 35, 40, 3, 9]
计算WPL
40 -> 105 长度 =  1
35 -> 105 长度 =  2
18 -> 105 长度 =  3
3 -> 105 长度 =  4
9 -> 105 长度 =  4
带权值路径长度WPL = 212