LongestPalindromicSubsequence

The length of the longest subsequence that reads the same backwards.

✓ checked against that system · ! checked, with disagreements (hover a chip)FindStatSt001417via BinaryWord✓↗

LongestPalindromicSubsequence(word)The length of the longest subsequence that reads the same backwards.

Typed signatures

Type	Package	Applies
(binary_word) -> number	combinatorics	always

Domain: Binary word statistics

Details

• Defined over BinaryWord as an expression in _x, evaluated by compute-engine — the definition IS the implementation.
• Takes a BinaryWord and nothing else — it reads values against their positions, or walks the orbits, so it needs the bijection. Applying it to a bare list is a type error, not a wrong answer.
• FindStat's St001417: the longest common subsequence of the word and its reverse. After the first i letters, entry j + 1 holds that for the first j letters of the reverse.

Definition

Epsil, as the implementation runs it.

on BinaryWord, over _x

0 if Length(_x) < 1 else Apply(
                                (a_init: list<integer>) => Fold((
                                                                  a: list<integer>,
                                                                  b,
                                                                ) => Apply(
                                                                           (a_next: list<integer>) => a_next,
                                                                           Join(
                                                                                 [0],
                                                                                 Map(Function(Max(
                                                                                                   a[j + 1],
                                                                                                   Max(Join(
                                                                                                             [0],
                                                                                                             Map(
                                                                                                                  Function(a[jp] + 1 if _x[b] ==
                                                                                                                                        _x[Length(_x) + 1 -
                                                                                                                                           jp] else 0, jp),
                                                                                                                  Range(1, j, 1),
                                                                                                                ),
                                                                                                           )),
                                                                                                 ), j), Range(1, Length(_x))),
                                                                               ),
                                                                         ), a_init, Range(1, Length(_x))),
                                Map(Function(0, z), Range(0, Length(_x), 1)),
                              )[Length(_x) + 1]

Examples

Basic #

the word $110100111$

live ↗

In$\mathrm{LongestPalindromicSubsequence}({\operatorname{BinaryWord}}([1, 1, 0, 1, 0, 0, 1, 1, 1]))$Out$8$

Properties #

FindStat's value for 0

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0]), \text{LongestPalindromicSubsequence})$Out$1$

Known value · FindStat St001417

FindStat's value for 1

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([1]), \text{LongestPalindromicSubsequence})$Out$1$

Known value · FindStat St001417

FindStat's value for 00

live ↗

In$\mathrm{CombinatorialStat}({\operatorname{BinaryWord}}([0, 0]), \text{LongestPalindromicSubsequence})$Out$2$

Known value · FindStat St001417

About

Examples	4
Crosswalk	FindStat