Create 0516-longest-palindromic-subsequence.py

Author: neetcode-gh

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]