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5. C-3.14 and/or 3.15 |
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5. C-3.14 and/or C-3.15. (hint for 3.14: Try to do O(n) work to reduce the problem to size n/2. Then recurse. If you can do this, the total running time will be proportional to n + n/2 + n/4 + ... + 1 = O(n).) (hint for 3.15: have each taster sample more than one bottle. you want to be able to uniquely identify the bottle by seeing which set of tasters dies.) |
Homework 1, due Thursday, Jan 20 at the beginning of class.
If you can't attend class, slide it under my office door before 11am.
1. Problem R-3.6 (from the text). Do the top two rows of functions only.
2. Problem R-3.8, except do only two columns: 1 hour (column 2) and 2 hours (not in the table).
3. R-3.13
4. C-3.8 The input is a sequence a1, a2, ..., an. The output is a sequence A1, A2, ..., An where Ai = a1 + a2 + ... + ai. Explain why your algorithm is correct (this should be easy). Explain what the running time is, and why. Try to find an O(n)-time algorithm.
5. C-3.14 and/or C-3.15. (hint for 3.14: Try to do O(n) work to reduce the problem to size n/2. Then recurse. If you can do this, the total running time will be proportional to n + n/2 + n/4 + ... + 1 = O(n).) (hint for 3.15: have each taster sample more than one bottle. you want to be able to uniquely identify the bottle by seeing which set of tasters dies.)