Palindromic (#9288)

* added longest palindromic subsequence

* removed

* added longest palindromic subsequence

* added longest palindromic subsequence link

* added comments

dynamic_programming/longest_palindromic_subsequence.py

@@ -0,0 +1,44 @@
+"""
+author: Sanket Kittad
+Given a string s, find the longest palindromic subsequence's length in s.
+Input: s = "bbbab"
+Output: 4
+Explanation: One possible longest palindromic subsequence is "bbbb".
+Leetcode link: https://leetcode.com/problems/longest-palindromic-subsequence/description/
+"""
+
+
+def longest_palindromic_subsequence(input_string: str) -> int:
+    """
+    This function returns the longest palindromic subsequence in a string
+    >>> longest_palindromic_subsequence("bbbab")
+    4
+    >>> longest_palindromic_subsequence("bbabcbcab")
+    7
+    """
+    n = len(input_string)
+    rev = input_string[::-1]
+    m = len(rev)
+    dp = [[-1] * (m + 1) for i in range(n + 1)]
+    for i in range(n + 1):
+        dp[i][0] = 0
+    for i in range(m + 1):
+        dp[0][i] = 0
+
+    # create and initialise dp array
+    for i in range(1, n + 1):
+        for j in range(1, m + 1):
+            # If characters at i and j are the same
+            # include them in the palindromic subsequence
+            if input_string[i - 1] == rev[j - 1]:
+                dp[i][j] = 1 + dp[i - 1][j - 1]
+            else:
+                dp[i][j] = max(dp[i - 1][j], dp[i][j - 1])
+
+    return dp[n][m]
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()