Huffman哈夫曼树（霍夫曼树，赫夫曼树）在通信领域最主要的应用是数据编码。假设现在有A、B、C、D、E五个字符，它们出现的概率或者权值不同，从A到E，权值依次降低，那么就可以用哈夫曼最优二叉树对其进行编码。左边为0，右边为1，通信网络电气链路的传输数据是0或者1。

from binarytree import Node, get_parent
def app():
    data = [(1, 'E'), (3, 'D'), (7, 'C'), (9, 'B'), (11, 'A')]
    huffman_tree = build_huffman_tree(data)
    print('-----')
    print('最终的Huffman树')
    root = huffman_tree.pop()
    print(root)
    print('---')
    print(data)
    travle(root, data)
def travle(root, data):
    for leave in root.leaves:
        print('==')
        path = find_path(root, leave, data)
        d = find_data(data, leave.value)
        print('节点', d, '路径 ->', path)
def find_data(data, v):
    for d in data:
        if d[0] == v:
            return d
def build_huffman_tree(data):
    nodes = []
    for i in data:
        nodes.append(Node(i[0]))
    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
def find_path(root, node, data):
    root_value = root.value
    path = [node]
    temp = node.value
    codes = []
    while True:
        p = get_parent(root, node)
        path.append(p)
        if p.left.value == node.value:
            codes.append(0)
        elif p.right.value == node.value:
            codes.append(1)
        if p.value == root_value:
            break
        else:
            node = p
    list.reverse(codes)
    s = ''.join(str(item) for item in codes)
    print(find_data(data, temp), '字符', find_data(data, temp)[1], '编码:', s)
    list.reverse(path)
    return path
if __name__ == '__main__':
    app()

输出：

nodes [Node(1), Node(3), Node(7), Node(9), Node(11)]
开始构建Huffman树
-----
最终的Huffman树
        ___31__
       /       \
    __11        20
   /    \      /  \
  4      7    9    11
 / \
1   3
---
[(1, 'E'), (3, 'D'), (7, 'C'), (9, 'B'), (11, 'A')]
==
(7, 'C') 字符 C 编码: 01
节点 (7, 'C') 路径 -> [Node(31), Node(11), Node(7)]
==
(9, 'B') 字符 B 编码: 10
节点 (9, 'B') 路径 -> [Node(31), Node(20), Node(9)]
==
(11, 'A') 字符 A 编码: 11
节点 (11, 'A') 路径 -> [Node(31), Node(20), Node(11)]
==
(1, 'E') 字符 E 编码: 000
节点 (1, 'E') 路径 -> [Node(31), Node(11), Node(4), Node(1)]
==
(3, 'D') 字符 D 编码: 001
节点 (3, 'D') 路径 -> [Node(31), Node(11), Node(4), Node(3)]