## All Weeks Algorithms on Strings Coursera Quiz Answers

The world and the internet are full of textual information. We search for information using textual queries, we read websites, books, e-mails. All those are strings from the point of view of computer science. To make sense of all that information and make search efficient, search engines use many string algorithms.

Moreover, the emerging field of personalized medicine uses many search algorithms to find disease-causing mutations in the human genome. In this online course, you will learn key pattern matching concepts: tries, suffix trees, suffix arrays, and even the Burrows-Wheeler transform.

### 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 n*n* non-empty patterns p_1, p_2, \dots, p_n*p*1,*p*2,…,*p**n* if all the patterns’ lengths are bounded from above by L*L*, and the sum of lengths of all patterns is no more than S*S*?

- 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 n*n* patterns p_1, p_2, \dots, p_n*p*1,*p*2,…,*p**n* in text T*T* of length |T|∣*T*∣ if all patterns have length at most L*L* and the sum of their lengths is at most S*S*?

- O(L)
*O*(*L*) - O(|T|S)
*O*(∣*T*∣*S*) **O(|T|L)***O*(∣*T*∣*L*)- O(S)
*O*(*S*)

Q3. What is the smallest possible number of nodes in a trie built off n*n* patterns p_1, p_2, \dots, p_n*p*1,*p*2,…,*p**n* if all the patterns have the same length L > 0*L*>0?

**L + 1**- n
*n* - nL
*nL* - L
*L*

Q4. If you take all the suffixes of a string S*S* of length L*L* 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} + 12***L*(*L*+1)+1- L + 1
*L*+1 - L^2 + 1
*L*2+1

Q5. What is the smallest possible number of nodes in a suffix tree of string S*S* with length L*L*?

**L + 1**- L
*L* - \frac{L(L+1)}{2} + 12
*L*(*L*+1)+1

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