Algorithms / Suffix Ordering
Least You Need to Know: Suffix Ordering, Lexicographic Structure, and LCP Intuition
Suffix-based reasoning sorts all suffixes of a string lexicographically. Even without implementing a full suffix array from scratch, it helps to know how lexicographic suffix order exposes repeated-substring structure and longest-common-prefix reasoning.
Least you need to know
- A suffix is a substring that starts at some position and runs to the end.
- Sorting suffixes lexicographically defines suffix-array order.
- Adjacent suffixes in sorted order are where repeated prefixes show up most locally.
- LCP means longest common prefix.
- Suffix ordering is useful for repeated-substring and pattern-location reasoning.
Key notation
- suffix i — substring
s[i:] - SA — suffix array: starting indices in sorted suffix order
- LCP — longest common prefix of two suffixes
Worked example
- For string
banana, suffixes includebanana,anana,nana,ana,na,a. - Sorting them lexicographically places similar prefixes near each other, such as
a,ana,anana. - The longest repeated substring can then be found by checking large LCP values among adjacent sorted suffixes.
- This is the high-level reason suffix arrays are powerful.
Common mistakes
- Students sometimes compare whole suffix sets conceptually but forget that a suffix must run to the end of the string.
- The longest repeated substring is captured by adjacent suffixes in sorted order, not arbitrary distant pairs.
- Suffix-array order is lexicographic on suffix strings, not on original indices.
How to recognize it
- You care about repeated substrings or lexicographic order of all suffixes.
- Longest common prefix between nearby suffixes is relevant.
- The problem wants a global view of substring repetition structure.
Next recommended lesson
Continue through this topic with Least You Need to Know: Topological Sort, DAG Dependencies, and Prerequisite Order.
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