LPS Algorithm is Added Fixed Issues keon#746 (keon#788)

* Longest Palindromic Subsequence Algorithm is Added

* test case added

* Renamed

README.md

@@ -194,6 +194,7 @@ If you want to uninstall algorithms, it is as simple as:
     - [hashtable](algorithms/map/hashtable.py)
     - [separate_chaining_hashtable](algorithms/map/separate_chaining_hashtable.py)
     - [longest_common_subsequence](algorithms/map/longest_common_subsequence.py)
+    - [longest_palindromic_subsequence](algorithms/map/longest_palindromic_subsequence.py)
     - [randomized_set](algorithms/map/randomized_set.py)
     - [valid_sudoku](algorithms/map/valid_sudoku.py)
     - [word_pattern](algorithms/map/word_pattern.py)

algorithms/map/longest_palindromic_subsequence.py

@@ -0,0 +1,22 @@
+def longest_palindromic_subsequence(str):
+    n = len(str)
+
+    # Create a table to store results of subproblems
+    L = [[0 for x in range(n)] for x in range(n)]
+
+    for i in range(n):
+        L[i][i] = 1
+
+
+    for sub_string_length in range(2, n + 1):
+        for i in range(n-sub_string_length + 1):
+            j = i + sub_string_length-1
+            if str[i] == str[j] and sub_string_length == 2:
+                L[i][j] = 2
+            elif str[i] == str[j]:
+                L[i][j] = L[i + 1][j-1] + 2
+            else:
+                L[i][j] = max(L[i][j-1], L[i + 1][j]);
+
+    return L[0][n-1]
+

tests/test_map.py

@@ -3,7 +3,8 @@
     Node, SeparateChainingHashTable,
     word_pattern,
     is_isomorphic,
-    is_anagram
+    is_anagram,
+    longest_palindromic_subsequence,
 )
 
 import unittest
@@ -164,6 +165,18 @@ def test_is_isomorphic(self):
         self.assertFalse(is_isomorphic("foo", "bar"))
         self.assertTrue(is_isomorphic("paper", "title"))
 
+class TestLongestPalindromicSubsequence(unittest.TestCase):
+    def test_longest_palindromic_subsequence_is_correct(self):
+        self.assertEqual(7,longest_palindromic_subsequence('BBABCBCAB'))
+        self.assertEqual(4,longest_palindromic_subsequence('abbaeae'))
+        self.assertEqual(8,longest_palindromic_subsequence('babbbababaa'))
+        self.assertEqual(6,longest_palindromic_subsequence('daccandeeja'))
+
+    def test_longest_palindromic_subsequence_is_incorrect(self):
+        self.assertEqual(4,longest_palindromic_subsequence('BBABCBCAB'))
+        self.assertEqual(5,longest_palindromic_subsequence('abbaeae'))
+        self.assertEqual(2,longest_palindromic_subsequence('babbbababaa'))
+        self.assertEqual(1,longest_palindromic_subsequence('daccandeeja'))
 
 class TestIsAnagram(unittest.TestCase):
     def test_is_anagram(self):