GXTXAYB

GXTXAYB is a seven-character string frequently used as an input example in discussions of the Longest Common Subsequence (LCS) problem. It is typically paired with the string AGGTAB in educational materials to illustrate a dynamic programming solution to LCS.

The two strings have lengths seven and six, respectively. In this canonical example, the longest common subsequence of GXTXAYB and AGGTAB is GTAB, of length four. This subsequence preserves the relative order of characters in both strings but does not require contiguity.

The example serves to demonstrate the construction of a two-dimensional dynamic programming table, where the entry at position (i, j) stores the length of the LCS of the prefixes GXTXAYB[1..i] and AGGTAB[1..j]. The recurrence compares the current characters and propagates the maximum length from neighboring cells, illustrating core DP ideas such as overlapping subproblems and optimal substructure.

In broader terms, GXTXAYB is used to teach the standard LCS algorithm, which runs in O(mn) time and O(mn) space for strings of lengths m and n. Variations may employ space optimization or alternative formulations, but the GXTXAYB–AGGTAB example remains a common reference point for explaining the concept.