Suffix arrays in Data Structures Theory - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the basic structure of suffix arrays

What does a suffix array represent for a given string?

A An array of all suffixes of the string sorted in lexicographical order, represented by their starting indices.

B An array containing the frequency of each character in the string.

C An array of all prefixes of the string sorted by length.

D An array of the string's characters sorted alphabetically.

💡 Hint

Think about how suffixes are organized to help with substring searches.

A suffix array stores the starting positions of all suffixes of a string sorted lexicographically. This helps in efficient substring search and pattern matching.

📋 Factual

intermediate

Suffix array construction time complexity

What is the best known time complexity for constructing a suffix array for a string of length n?

A O(n log n)

B O(n)

C O(n^2)

D O(log n)

💡 Hint

Modern algorithms can build suffix arrays very efficiently.

There exist algorithms like SA-IS that can construct suffix arrays in linear time O(n), which is optimal for this problem.

🚀 Application

advanced

Using suffix arrays for substring search

Given a suffix array for a string, how can you efficiently check if a substring exists in the string?

A Perform a binary search on the suffix array comparing the substring with suffixes starting at indices stored in the array.

B Scan the entire string from start to end to find the substring.

C Sort the characters of the substring and compare with sorted characters of the string.

D Use the suffix array to count character frequencies and infer substring presence.

💡 Hint

Think about how the suffix array is sorted and how binary search works.

Since suffixes are sorted lexicographically in the suffix array, binary search can quickly find if the substring matches the prefix of any suffix.

🔍 Analysis

advanced

Comparing suffix arrays and suffix trees

Which of the following is a key advantage of suffix arrays over suffix trees?

A Suffix arrays allow faster substring search than suffix trees.

B Suffix arrays are always faster to build than suffix trees.

C Suffix arrays can represent all substrings explicitly, unlike suffix trees.

D Suffix arrays use less memory and are simpler to implement than suffix trees.

💡 Hint

Consider memory usage and implementation complexity.

Suffix arrays are more space-efficient and simpler to implement compared to suffix trees, though suffix trees can offer faster queries in some cases.

❓ Reasoning

expert

Determining the number of distinct substrings using suffix arrays

Given a string of length n and its suffix array along with the longest common prefix (LCP) array, how can you compute the number of distinct substrings of the string?

A Number of suffixes minus the maximum LCP value.

B Sum of all LCP values only.

C Sum of lengths of all suffixes minus the sum of all LCP values.

D Length of the string multiplied by the number of suffixes.

💡 Hint

Think about how suffixes overlap and how LCP helps avoid counting duplicates.

The total number of substrings is the sum of lengths of all suffixes. Subtracting the sum of LCP values removes duplicates counted due to common prefixes.