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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