1+ /**
2+ *
3+ * Problem: Given a string of "n" characters, find the longest palindromic subsequence
4+ * of the input string. The subsequnce can remove one or more elements from the original
5+ * string retaining the original order of the string. This is a very different problem
6+ * from finding the longest palindromic substring without the constraint of removing any
7+ * elements.
8+ *
9+ * Use the brute force to generate all possible subsequences. While in a subsequence,
10+ * if the string is already a palindrome from the ends, continue proceeding inwards.
11+ * If it is not palindrome from the end, we can continue ignoring one elements from
12+ * the left and right to see if we can achieve a palindromic subsequence.
13+ *
14+ * Complexity....
15+ * Time: O(2^n) since we are making choices for recursion at each step. We choose to
16+ * either ignore an element or to include id.
17+ * Space: O(n) since in the worst case, we would have all the n positions opened to be
18+ * compared.
19+ *
20+ * @param input
21+ */
22+ function findLongestPalSubseq ( input : string ) {
23+ return findLongestPalSubseqHelper ( input , 0 , input . length - 1 ) ;
24+ }
25+
26+ function findLongestPalSubseqHelper ( input : string , beg : number , end : number ) : number {
27+
28+ if ( end < beg ) return 0 ;
29+ else if ( end === beg ) return 1 ;
30+ else if ( input [ beg ] === input [ end ] ) {
31+ // Ends are matching, continue inwards.
32+ return 2 + findLongestPalSubseqHelper ( input , beg + 1 , end - 1 ) ;
33+ }
34+
35+ // If the ends are not matching, we may try to skip an element from the end, to attempt
36+ // to make a palindromic string
37+ const maxWithLeftInclusion = findLongestPalSubseqHelper ( input , beg + 1 , end ) ;
38+ const maxWithRightInclusion = findLongestPalSubseqHelper ( input , beg , end - 1 ) ;
39+ return Math . max ( maxWithLeftInclusion , maxWithRightInclusion ) ;
40+ }
41+
42+ function testLongestPlalindSubseqBF ( input : string ) {
43+ console . log ( `Longest Palindromic Subsequence for input ${ input } ${ findLongestPalSubseq ( input ) } )
44+ }
45+
46+ testLongestPlalindSubseqBF ( "abdbca" )
47+ testLongestPlalindSubseqBF ( "cddpd" )
48+ testLongestPlalindSubseqBF ( "pqr" )
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