权威分析揭示：行业趋势深度解读与未来展望

进行n-1次插入和删除操作，所以总的时间复杂度为O((n-1)logn)。空间复杂度：优先队列的大小为n，所以空间复杂度为O(n)。 以下是哈夫曼编码的实验代码： ```python import heapq from collections import defaultdict def huffman_encoding(s): # 统计字符频率 freq = defaultdict(int) for c in s: freq[c] += 1 # 初始化优先队列（最小堆） min_heap = [[weight, [char, ""]] for char, weight in freq.items()] heapq.heapify(min_heap) # 构建哈夫曼树 while len(min_heap) > 1: lo = heapq.heappop(min_heap) hi = heapq.heappop(min_heap) for pair in lo[1:]: pair[1] = '0' + pair[1] for pair in hi[1:]: pair[1] = '1' + pair[1] heapq.heappush(min_heap, [lo[0] + hi[0]] + lo[1:] + hi[1:]) # 提取哈夫曼编码 huff_dict = dict(heapq.heappop(min_heap)[1:]) encoded_str = "".join(huff_dict[c] for c in s) return huff_dict, encoded_str # 测试 s = "this is an example for huffman encoding" huff_dict, encoded_str = huffman_encoding(s) print("哈夫曼编码字典：", huff_dict) print("编码后的字符串：", encoded_str) ``` 注意：这个代码示例仅适用于给定的输入字符串，如果需要处理其他字符串，请将`s`替换为相应的输入。