Change project structure to a Maven Java project + Refactor (#2816)

src/main/java/com/thealgorithms/dynamicprogramming/LongestPalindromicSubsequence.java

@@ -0,0 +1,61 @@
+package com.thealgorithms.dynamicprogramming;
+
+/**
+ * Algorithm explanation
+ * https://www.educative.io/edpresso/longest-palindromic-subsequence-algorithm
+ */
+public class LongestPalindromicSubsequence {
+
+    public static void main(String[] args) {
+        String a = "BBABCBCAB";
+        String b = "BABCBAB";
+
+        String aLPS = LPS(a);
+        String bLPS = LPS(b);
+
+        System.out.println(a + " => " + aLPS);
+        System.out.println(b + " => " + bLPS);
+    }
+
+    public static String LPS(String original) throws IllegalArgumentException {
+        StringBuilder reverse = new StringBuilder(original);
+        reverse = reverse.reverse();
+        return recursiveLPS(original, reverse.toString());
+    }
+
+    private static String recursiveLPS(String original, String reverse) {
+        String bestResult = "";
+
+        // no more chars, then return empty
+        if (original.length() == 0 || reverse.length() == 0) {
+            bestResult = "";
+        } else {
+
+            // if the last chars match, then remove it from both strings and recur
+            if (original.charAt(original.length() - 1) == reverse.charAt(reverse.length() - 1)) {
+                String bestSubResult
+                        = recursiveLPS(
+                                original.substring(0, original.length() - 1),
+                                reverse.substring(0, reverse.length() - 1));
+
+                bestResult = reverse.charAt(reverse.length() - 1) + bestSubResult;
+            } else {
+                // otherwise (1) ignore the last character of reverse, and recur on original and updated
+                // reverse again
+                // (2) ignore the last character of original and recur on the updated original and reverse
+                // again
+                // then select the best result from these two subproblems.
+
+                String bestSubResult1 = recursiveLPS(original, reverse.substring(0, reverse.length() - 1));
+                String bestSubResult2 = recursiveLPS(original.substring(0, original.length() - 1), reverse);
+                if (bestSubResult1.length() > bestSubResult2.length()) {
+                    bestResult = bestSubResult1;
+                } else {
+                    bestResult = bestSubResult2;
+                }
+            }
+        }
+
+        return bestResult;
+    }
+}