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首先AI实现了一个SkipList类，最后基于这个SkipList类，又实现了一个SortedSet类。

import random import bisect class SkipListNode: """跳表节点""" def __init__(self, score, level): self.score = score # 分数 self.members = [] # 该分数对应的元素列表 self.next = [None] * level # 各层的后继节点

class SkipList: """跳表实现""" def __init__(self, max_level=32, p=0.25): """ 初始化跳表 max_level: 最大层数 p: 节点晋升概率 """ self.max_level = max_level # 最大层数 self.p = p # 节点晋升概率 self.level = 1 # 当前跳表层数 # 创建头节点，分数为负无穷，层数为max_level self.header = SkipListNode(float('-inf'), max_level) def _random_level(self): """生成随机层数""" level = 1 # 以p的概率晋升层数，最多到max_level while random.random() < self.p and level < self.max_level: level += 1 return level def search(self, score): """ 查找指定分数对应的元素列表 return: 元素列表或None """ current = self.header # 从最高层开始查找 for i in range(self.level - 1, -1, -1): # 在当前层找到第一个分数不小于目标分数的节点 while current.next[i] and current.next[i].score < score: current = current.next[i] # 移动到下一层 current = current.next[0] # 检查是否找到目标分数 if current and current.score == score: return current.members return None def insert(self, score, members): """ 插入分数和对应的元素列表 """ # 创建更新数组，记录每一层需要更新的节点 update = [None] * self.max_level current = self.header # 从最高层开始查找，记录每一层的前驱节点 for i in range(self.level - 1, -1, -1): while current.next[i] and current.next[i].score < score: current = current.next[i] update[i] = current # 移动到第0层，检查分数是否已存在 current = current.next[0] # 如果分数已存在，更新对应的元素列表 if current and current.score == score: current.members = members return # 生成新节点的随机层数 new_level = self._random_level() # 如果新节点的层数超过当前跳表的层数，更新跳表层数 if new_level > self.level: for i in range(self.level, new_level): update[i] = self.header self.level = new_level # 创建新节点 new_node = SkipListNode(score, new_level) new_node.members = members # 更新各层的指针 for i in range(new_level): new_node.next[i] = update[i].next[i] update[i].next[i] = new_node def delete(self, score): """ 删除指定分数对应的节点 return: True if deleted, False otherwise """ # 创建更新数组，记录每一层需要更新的节点 update = [None] * self.max_level current = self.header # 从最高层开始查找 for i in range(self.level - 1, -1, -1): while current.next[i] and current.next[i].score < score: current = current.next[i] update[i] = current # 移动到第0层，检查分数是否存在 current = current.next[0] # 如果分数不存在，返回False if not current or current.score != score: return False # 更新各层的指针，删除节点 for i in range(self.level): if update[i].next[i] != current: break update[i].next[i] = current.next[i] # 更新跳表的层数 while self.level > 1 and self.header.next[self.level - 1] is None: self.level -= 1 return True def traverse(self): """ 遍历跳表，返回所有(score, members)对，按分数升序排列 """ result = [] current = self.header.next[0] while current: result.append((current.score, current.members)) current = current.next[0] return result def range_search(self, min_score, max_score): """ 返回分数在[min_score, max_score]范围内的所有(score, members)对 """ result = [] current = self.header # 从最高层开始查找，找到第一个分数不小于min_score的节点 for i in range(self.level - 1, -1, -1): while current.next[i] and current.next[i].score < min_score: current = current.next[i] # 移动到第0层 current = current.next[0] # 收集分数在范围内的所有节点 while current and current.score <= max_score: result.append((current.score, current.members)) current = current.next[0] return result

# 基于SkipList实现的有序集合（SortedSet） class SortedSet: """基于SkipList实现的有序集合（SortedSet）""" def __init__(self, max_level=32, p=0.25): """ 初始化有序集合 max_level: 跳表的最大层数 p: 节点晋升概率 """ # SkipList，键为分数(score)，值为具有该分数的元素列表(保持有序) self.skiplist = SkipList(max_level=max_level, p=p) # 反向映射，元素到分数的映射，用于快速查找元素的分数 self.member_to_score = {} # 元素总数 self.size = 0 def zadd(self, score, member): """ 添加元素到有序集合 score: 元素的分数 member: 元素 return: 1 if member是新添加的，0 if member已存在并更新了分数 """ is_new_member = member not in self.member_to_score old_score = self.member_to_score.get(member) # 如果元素已存在且分数相同，无需操作 if old_score is not None and old_score == score: return 0 # 如果元素已存在但分数不同，先删除旧的分数关联 if old_score is not None: # 从旧分数对应的元素列表中移除该元素 members = self.skiplist.search(old_score) if members: idx = bisect.bisect_left(members, member) if idx < len(members) and members[idx] == member: del members[idx] # 如果列表为空，删除该分数 if not members: self.skiplist.delete(old_score) else: # 更新分数对应的元素列表 self.skiplist.insert(old_score, members) # 添加或更新元素的分数映射 self.member_to_score[member] = score # 获取或创建新分数对应的元素列表 members = self.skiplist.search(score) if members is None: members = [] # 二分查找插入位置，保持列表有序 idx = bisect.bisect_left(members, member) if idx >= len(members) or members[idx] != member: bisect.insort_left(members, member) # 插入或更新分数对应的元素列表 self.skiplist.insert(score, members) # 如果是新元素，增加大小 if is_new_member: self.size += 1 return 1 return 0 def zadd_multi(self, *args): """ 批量添加元素，格式：zadd_multi(score1, member1, score2, member2, ...) return: 添加的新元素数量 """ if len(args) % 2 != 0: raise ValueError("参数数量必须为偶数") added = 0 for i in range(0, len(args), 2): score = args[i] member = args[i+1] added += self.zadd(score, member) return added def zscore(self, member): """ 获取元素的分数 return: 元素的分数，如果元素不存在返回None """ return self.member_to_score.get(member) def zcard(self): """ 获取有序集合的成员数量 return: 成员数量 """ return self.size def zrem(self, member): """ 从有序集合中删除元素 return: 1 if member存在并被删除，0 if member不存在 """ score = self.member_to_score.pop(member, None) if score is None: return 0 # 从分数对应的元素列表中移除该元素 members = self.skiplist.search(score) if members: idx = bisect.bisect_left(members, member) if idx < len(members) and members[idx] == member: del members[idx] self.size -= 1 # 如果列表为空，删除该分数 if not members: self.skiplist.delete(score) else: # 更新分数对应的元素列表 self.skiplist.insert(score, members) return 1 return 0 def zrange(self, start, end, withscores=False): """ 按分数从小到大返回指定范围的元素 start: 起始索引 end: 结束索引 withscores: 是否返回分数 return: 元素列表或(元素, 分数)元组列表 """ if self.size == 0: return [] # 处理索引 if start < 0: start = max(0, self.size + start) if end < 0: end = self.size + end else: end = min(end, self.size - 1) if start > end: return [] # 计算需要返回的元素数量 count = end - start + 1 result = [] current_idx = 0 # 直接遍历跳表，不需要先收集所有元素 current = self.skiplist.header.next[0] while current: members = current.members score = current.score # 如果当前分数段的所有元素都在start之前，跳过 if current_idx + len(members) <= start: current_idx += len(members) current = current.next[0] continue # 遍历当前分数段的元素 for member in members: if current_idx < start: current_idx += 1 continue if current_idx > end: break if withscores: result.append((member, score)) else: result.append(member) current_idx += 1 if len(result) == count: return result if current_idx > end: break current = current.next[0] return result def zrevrange(self, start, end, withscores=False): """ 按分数从大到小返回指定范围的元素 start: 起始索引 end: 结束索引 withscores: 是否返回分数 return: 元素列表或(元素, 分数)元组列表 """ if self.size == 0: return [] # 处理索引 if start < 0: start = max(0, self.size + start) if end < 0: end = self.size + end else: end = min(end, self.size - 1) if start > end: return [] # 计算需要返回的元素数量 count = end - start + 1 # 收集所有元素到列表 all_elements = [] current = self.skiplist.header.next[0] while current: score = current.score for member in current.members: all_elements.append((member, score)) current = current.next[0] # 直接从列表末尾开始取元素，不需要反转 result = [] total = len(all_elements) start_pos = total - 1 - end end_pos = total - 1 - start # 确保范围有效 if start_pos > end_pos: return [] # 提取需要的元素 for i in range(end_pos, start_pos - 1, -1): member, score = all_elements[i] if withscores: result.append((member, score)) else: result.append(member) if len(result) == count: break return result def zrangebyscore(self, min_score, max_score, withscores=False, limit=None): """ 按分数范围返回元素（从小到大） min_score: 最小分数 max_score: 最大分数 withscores: 是否返回分数 limit: (offset, count) 用于分页 return: 元素列表或(元素, 分数)元组列表 """ # 应用limit的默认值 offset = 0 count = None if limit: offset, count = limit # 使用跳表的range_search获取分数范围内的所有项 items = self.skiplist.range_search(min_score, max_score) # 转换为扁平化的元素列表，提前应用limit flat_list = [] current_offset = 0 for score, members in items: for member in members: # 跳过offset个元素 if current_offset < offset: current_offset += 1 continue # 添加元素 flat_list.append((member, score)) # 如果count不为None且已收集足够元素，提前返回 if count is not None and len(flat_list) >= count: break # 如果count不为None且已收集足够元素，提前返回 if count is not None and len(flat_list) >= count: break # 根据withscores参数返回不同格式 if withscores: return flat_list else: return [item[0] for item in flat_list] def zrevrangebyscore(self, max_score, min_score, withscores=False, limit=None): """ 按分数范围返回元素（从大到小） max_score: 最大分数 min_score: 最小分数 withscores: 是否返回分数 limit: (offset, count) 用于分页 return: 元素列表或(元素, 分数)元组列表 """ # 应用limit的默认值 offset = 0 count = None if limit: offset, count = limit # 使用跳表的range_search获取分数范围内的所有项 items = self.skiplist.range_search(min_score, max_score) # 先收集所有元素，然后反转 all_elements = [] for score, members in items: for member in members: all_elements.append((member, score)) # 反转列表 all_elements.reverse() # 应用limit，提前终止 flat_list = [] current_offset = 0 for element in all_elements: # 跳过offset个元素 if current_offset < offset: current_offset += 1 continue # 添加元素 flat_list.append(element) # 如果count不为None且已收集足够元素，提前返回 if count is not None and len(flat_list) >= count: break # 根据withscores参数返回不同格式 if withscores: return flat_list else: return [item[0] for item in flat_list] def zrank(self, member): """ 获取元素的排名（升序，从0开始） return: 排名，如果元素不存在返回None """ score = self.member_to_score.get(member) if score is None: return None # 获取所有分数和对应的元素 all_items = self.skiplist.traverse() # 计算排名 rank = 0 for s, members in all_items: if s < score: # 累加之前所有分数的元素数量 rank += len(members) elif s == score: # 找到目标分数，计算该分数内的排名 # 由于members已经是有序的，可以使用二分查找 idx = bisect.bisect_left(members, member) if idx < len(members) and members[idx] == member: return rank + idx break else: # 已经超过目标分数，无需继续遍历 break return None def zrevrank(self, member): """ 获取元素的排名（降序，从0开始） return: 排名，如果元素不存在返回None """ # 获取升序排名 asc_rank = self.zrank(member) if asc_rank is None: return None # 降序排名 = 总元素数 - 升序排名 - 1 return self.size - asc_rank - 1 def zincrby(self, increment, member): """ 增加元素的分数 increment: 增加的分数 member: 元素 return: 新的分数 """ current_score = self.member_to_score.get(member, 0) new_score = current_score + increment self.zadd(new_score, member) return new_score def zremrangebyrank(self, start, end): """ 删除指定排名范围的元素（升序） start: 起始排名 end: 结束排名 return: 删除的元素数量 """ if self.size == 0: return 0 # 处理索引 if start < 0: start = max(0, self.size + start) if end < 0: end = self.size + end else: end = min(end, self.size - 1) if start > end: return 0 # 计算需要删除的元素数量 count = end - start + 1 # 获取要删除的元素 to_delete = self.zrange(start, end) # 删除元素 deleted = 0 for member in to_delete: if self.zrem(member): deleted += 1 return deleted def zremrangebyscore(self, min_score, max_score): """ 删除指定分数范围的元素 min_score: 最小分数 max_score: 最大分数 return: 删除的元素数量 """ if self.size == 0: return 0 # 获取分数范围内的所有元素 to_delete = self.zrangebyscore(min_score, max_score) # 删除元素 deleted = 0 for member in to_delete: if self.zrem(member): deleted += 1 return deleted def zcount(self, min_score, max_score): """ 统计指定分数范围内的元素数量 min_score: 最小分数 max_score: 最大分数 return: 元素数量 """ # 获取分数范围内的所有元素 items = self.skiplist.range_search(min_score, max_score) # 计算元素总数 count = 0 for _, members in items: count += len(members) return count