# Algorithms on Strings Coursera Quiz Answers

## All Weeks Algorithms on Strings Coursera Quiz Answers

### Algorithms on Strings Week 01 Quiz Answers

#### Tries and Suffix Trees Quiz Answers

Q1. What is the tightest estimate you can prove on the memory consumption of a trie built off nn non-empty patterns p_1, p_2, \dots, p_np1​,p2​,…,pn​ if all the patterns’ lengths are bounded from above by LL, and the sum of lengths of all patterns is no more than SS?

• O(n + L)O(n+L)
• O(n)
• O(S)
• O(nL)O(nL)

Q2. What is the time complexity of searching all occurrences of nn patterns p_1, p_2, \dots, p_np1​,p2​,…,pn​ in text TT of length |T|∣T∣ if all patterns have length at most LL and the sum of their lengths is at most SS?

• O(L)O(L)
• O(|T|S)O(∣TS)
• O(|T|L)O(∣TL)
• O(S)O(S)

Q3. What is the smallest possible number of nodes in a trie built off nn patterns p_1, p_2, \dots, p_np1​,p2​,…,pn​ if all the patterns have the same length L > 0L>0?

• L + 1
• nn
• nLnL
• LL

Q4. If you take all the suffixes of a string SS of length LL and build a regular trie off those suffixes as patterns, what is the maximum possible number of nodes in such trie?

• \frac{L(L+1)}{2} + 12L(L+1)​+1
• L + 1L+1
• L^2 + 1L2+1

Q5. What is the smallest possible number of nodes in a suffix tree of string SS with length LL?

• L + 1
• LL
• \frac{L(L+1)}{2} + 12L(L+1)​+1