Substring Search Patterns in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal of substring search in strings?

To find if a smaller string (pattern) exists inside a larger string (text) and locate its position(s).

beginner

Explain the naive substring search approach.

Check every possible position in the text where the pattern could start and compare characters one by one until a match is found or all positions are checked.

intermediate

What is the key idea behind the Knuth-Morris-Pratt (KMP) algorithm?

Use information from previous character matches to avoid rechecking characters, by precomputing a longest prefix suffix (LPS) array.

intermediate

What does the LPS (Longest Prefix Suffix) array represent in KMP?

For each position in the pattern, it stores the length of the longest proper prefix which is also a suffix up to that position.

intermediate

Why is KMP more efficient than the naive approach?

Because it avoids re-examining characters that have already been matched, leading to a time complexity of O(n + m) instead of O(n*m), where n is text length and m is pattern length.

What is the worst-case time complexity of the naive substring search?

A O(n*m)

B O(n + m)

C O(n)

D O(m)

The naive approach checks each position in the text and compares up to m characters, leading to O(n*m) in the worst case.

In KMP, what does the LPS array help to avoid?

A Rechecking characters that matched before

B Searching the entire text again

C Comparing characters in the pattern

D Building the pattern string

The LPS array helps KMP skip rechecking characters that have already matched, improving efficiency.

Which substring search algorithm uses a precomputed table to skip characters?

A Naive Search

B Bubble Sort

C KMP Algorithm

D Binary Search

KMP uses the LPS table to skip unnecessary comparisons.

If the pattern is 'ABABC', what is the LPS value at index 4 (0-based)?

A 3

B 1

C 2

D 0

The LPS array for 'ABABC' is [0, 0, 1, 2, 0]. At index 4, it is 0, as no proper prefix matches the suffix.

Which of these is NOT a substring search algorithm?

A Rabin-Karp

B Merge Sort

C KMP

D Naive Search

Merge Sort is a sorting algorithm, not used for substring search.

Describe how the naive substring search algorithm works step-by-step.

Think about sliding the pattern over the text and comparing characters.

Explain the purpose and construction of the LPS array in the KMP algorithm.

Focus on how pattern prefixes relate to suffixes.