Definition
Given the sequence S and the index i, let i-th Z value of S be the length of the longest subsequence of S that starts at i and matches the prefix of S.

Example
Here is an example for string "abababaca":

i:	0	1	2	3	4	5	6	7	8
S:	a	b	a	b	a	b	a	c	a
Z:	9	0	5	0	3	0	1	0	1

Summary
The z-algorithm vocabulary implements algorithm for finding all Z values for sequence S in linear time. In contrast to naive approach which takes Θ(n^2) time.