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Leetcode131题解 -Python-回溯+cache缓存

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Leetcode131题解 -Python-回溯+cache缓存

回溯算法与缓存优化思路

LeetCode 131题要求将字符串分割为所有可能的回文子串组合。回溯算法能系统地探索所有可能的分割方式,而缓存可以避免重复计算回文判断。

核心代码实现

def partition(s: str) -> List[List[str]]: n = len(s) res = [] # 使用缓存存储已判断过的回文子串 @lru_cache def is_palindrome(l, r): while l < r: if s[l] != s[r]: return False l += 1 r -= 1 return True def backtrack(start, path): if start == n: res.append(path.copy()) return for end in range(start, n): if is_palindrome(start, end): path.append(s[start:end+1]) backtrack(end+1, path) path.pop() backtrack(0, []) return res

关键步骤解析

回文判断优化
通过lru_cache装饰器缓存回文判断结果,避免对相同子串重复计算。双指针法验证子串s[l...r]是否为回文。

回溯过程
从字符串起始位置开始,逐步扩展子串范围。当发现回文子串时,将其加入当前路径,并递归处理剩余部分。完成搜索后回溯到上一步状态。

终止条件
当遍历指针到达字符串末尾时,将当前有效分割方案加入结果集。

复杂度分析

  • 时间复杂度:O(N*2^N),最坏情况下需要检查所有可能的分割方式
  • 空间复杂度:O(N^2),缓存存储所有可能的子串判断结果

优化对比

相比朴素回溯(每次重新判断回文),缓存版本可减少时间复杂度常数项。实际测试中,对于长字符串效率提升显著。例如输入"aabaa"时,缓存能避免重复判断重叠子串。

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