Create 0516-longest-palindromic-subsequence.py

python/0516-longest-palindromic-subsequence.py

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+# Time: O(n^2) Space: O(n^2) - For all three solutions
+class Solution:
+ def longestPalindromeSubseq(self, s: str) -> int: 
+ # Dynamic Programming
+ dp = [ [0] * (len(s) + 1) for i in range(len(s) + 1)]
+ res = 0
+
+ for i in range(len(s)):
+ for j in range(len(s) - 1, i - 1, -1):
+ if s[i] == s[j]:
+ dp[i][j] = 1 if i == j else 2
+ if i - 1 >= 0:
+ dp[i][j] += dp[i - 1][j + 1]
+ else:
+ dp[i][j] = dp[i][j + 1]
+ if i - 1 >= 0:
+ dp[i][j] = max(dp[i][j], dp[i - 1][j])
+ res = max(res, dp[i][j])
+ return res
+
+
+ # Memoization
+ cache = {}
+
+ def dfs(i, j):
+ if i < 0 or j == len(s):
+ return 0
+ if (i, j) in cache:
+ return cache[(i, j)]
+
+ if s[i] == s[j]:
+ length = 1 if i == j else 2
+ cache[(i, j)] = length + dfs(i - 1, j + 1)
+ else:
+ cache[(i, j)] = max(dfs(i - 1, j), dfs(i, j + 1))
+ return cache[(i, j)]
+
+ for i in range(len(s)):
+ dfs(i, i) # odd length
+ dfs(i, i + 1) # even length
+
+ return max(cache.values())
+
+# LCS Solution
+class Solution:
+ def longestPalindromeSubseq(self, s: str) -> int:
+ return self.longestCommonSubsequence(s, s[::-1])
+
+
+ def longestCommonSubsequence(self, s1: str, s2: str) -> int:
+ N, M = len(s1), len(s2)
+ dp = [[0] * (M+1) for _ in range(N+1)]
+
+ for i in range(N):
+ for j in range(M):
+ if s1[i] == s2[j]:
+ dp[i+1][j+1] = 1 + dp[i][j]
+ else:
+ dp[i+1][j+1] = max(dp[i][j+1], dp[i+1][j])
+ return dp[N][M]