What is the Big-O of String.contains() in Java?

Question

I'm working on a project, and need to optimize the running time. Is String.contains() runtime the same as TreeSet.contains(), which is O(logN)?

The reason I'm asking is I'm building a TreeMap<String, TreeSet<Song>>, where Songs contain a String of lyrics. Depending on the efficiency, I am considering including a Set of the lyric words inside the Song and running searches on that rather than the String.

Solution 1

One of the best known algorithms is the Boyer-Moore string searching algorithm which is O(n) although it can give sublinear performance in the best case.

Which algorithm is used in Java depends on which implemetation you download. It seems that for example OpenJDK uses a naive algorithm that runs in O(nm) and linear performance in the best case. See lines 1770-1806 here.

Solution 2

.contains() definitely uses naive approach and equivalent to O(nm) time complexity.

• Boyer-moore takes O(nm) time in the worst case.
• KMP takes O(n) time in the worst case.

In one of the problems related to pattern matching, I used .contains() and it took 70 ms whereas replacing that line with patternSearch() //KMP search reduced the time to 14 ms.

Java source code | KMP search vs .contains()

Comments

[Nicholas White]

the article you linked to said it's O(n) as it makes at most 3n comparisons. "worst case O(n)" is a tautology - by definition O(n) is the worst case :)

[rakslice]

The jdk1.6.0_23 had the same String.indexOf() implementation as a contemporary OpenJDK, according to programmers.stackexchange.com/questions/65558/… . Someone could tell you if that's true for String.contains()

[cellepo]

Trie reference

[John Kugelman]

@NicholasWhite O(n) is an upper bound. It could be an upper bound of the worst case, average case, or best case performance. Upper and lower bound are orthogonal to best/average/worst case. Another orthogonal dimension is loose vs. tight. O(n) is a loose upper bound. Θ(n) is a tight upper and lower bound.

[coderz]

Seems Trie only supports "starts with", not "contains"?

[sjkm]

KMP worst case is O(n + m) since you need to create the lsp table beforehand.

[Nishant Thapliyal]

True but even in worst-case where n==m -> O(n+m) -> O(2n) -> O(n)