代码随想录算法训练营第五十七天丨647. 回文子串、516. 最长回文子序列

原创已于 2024-03-11 14:56:43 修改 · 230 阅读

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#算法 #leetcode #动态规划

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本文介绍了使用动态规划和双指针技巧求解回文子串的数量问题，以及如何找到最长回文子序列的算法。通过实例代码展示了如何在Python中实现这两种方法。

647. 回文子串

没接触过有点难想，题解思路比较直观。

动态规划写法：

class Solution:
    def countSubstrings(self, s: str) -> int:
        n = len(s)
        dp = [[False] * n for _ in range(n)]
        count = 0
        
        for i in range(n):
            dp[i][i] = True
            count += 1
        
        for i in range(n - 1):
            if s[i] == s[i + 1]:
                dp[i][i + 1] = True
                count += 1

        for length in range(3, n + 1):
            for start in range(n - length + 1):
                end = start + length - 1
                if s[start] == s[end] and dp[start + 1][end - 1]:
                    dp[start][end] = True
                    count += 1
        
        return count

双指针：

class Solution:
    def countSubstrings(self, s: str) -> int:
        def count_palindromes_around_center(left: int, right: int) -> int:
            count = 0
            while left >= 0 and right < len(s) and s[left] == s[right]:
                left -= 1
                right += 1
                count += 1
            return count
    
        total_palindromes = 0
        for i in range(len(s)):
            total_palindromes += count_palindromes_around_center(i, i)
            total_palindromes += count_palindromes_around_center(i, i + 1)
        
        return total_palindromes

516. 最长回文子序列

class Solution:
    def longestPalindromeSubseq(self, s: str) -> int:
        n = len(s)
        dp = [[0] * n for _ in range(n)]
        
        for i in range(n):
            dp[i][i] = 1

        for length in range(2, n + 1):
            for start in range(n - length + 1):
                end = start + length - 1
                if s[start] == s[end]:
                    dp[start][end] = dp[start + 1][end - 1] + 2
                else:
                    dp[start][end] = max(dp[start + 1][end], dp[start][end - 1])
        
        return dp[0][n-1]

总结：

动规还是需要大量经验的...看新题只能说有概率做出来。