All Weeks Algorithms on Strings Coursera Quiz Answers
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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(∣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 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
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