TRIES STUDY GUIDE

Terminology and Basics

• Length of string keys = L.
• Alphabet size = R.
• You should be able to build either an R-way Trie and TST. You should be able to search in either a R-way Trie and TST. You should be able to delete from an R-way trie. You should appreciate how a TST can become unbalanced with inserts.
• Given a graphical depiction of either an R-way trie or TST, you should be able to tell which keys are in the trie.

• With String keys, we don't want to think about counting compareTo() or hashCode() and equals() calls. Why? What do we think about instead?
• Know (but you do not have to prove) that LLRBs take order of growth lg² N charAt() calls to compare random strings. Based on this, a hit is order L + lg² N.
• Understand why hash tables are L charAt() calls on a hit or miss (assuming no collisions!)

• Special structure such that you only look at each letter one time. Trivially, misses and hits have a maximum run time of L.
• Be aware that for random inputs, search misses only take an average of log_R N.
• Why do R-way tries use such a huge amount of memory? How much memory in terms of L and R?
• What are the two ways of determining that a key does not exist in a trie?

• When looking for a single character, why is it possible to follow as many as R links before you complete the search for that character?
• If the TST is balanced, typical case inserts and hits cost L + lg N character compares, and typical misses cost lg N character compares.
• If the TST is not balanced, worst case hits, misses, and inserts all include H, where H is the height of the tree.

Recommended Problems

C level

1. Spring 2008 Final, #5
2. Spring 2008 Final, #4
3. Fall 2011 Final, #8
4. Fall 2012 Final, #8
5. Textbook 5.2.3, 5.2.4

B level

1. Fall 2009 Final, #5
2. Spring 2012 Final, #9
3. Textbook 5.2.21 (just design the API)
4. When would we want to use an R-way trie instead of a TST?
5. Give a worst case input that causes a TST to be unbalanced (and thus slow).
6. Is the number of character compares in an R-way trie strictly better than for an LLRB? For a hash table? Is a trie guaranteed to be faster in overall run time than an LLRB or a hash table?

A level

1. When might we want to use a hash table instead of a TST?
2. What would happen if we had an R-way trie where we keep our next nodes in a linked list? How would this affect memory performance? Timing? What if we used an LLRB? A hash table?
3. Repeat Spring 2013 midterm problem #8, but assume your keys are Strings instead of Comparables.