First, Look at the Lab07 starter code #
- ConsSet is naturally an immutable Set.
- ArraySet is naturally a MutableSet.
New Idea: Skip Lists #
Material:
- Binary search on ArrayList
- Skip lists
Core idea:
- Searching through a list takes O(n) time.
- Searching through a sorted list only needs to take O(log n) time, as long as you have some way to quickly jump to the middle of the unsearched part of the list.
Strategy:
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Start with a doubly linked list.
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Some cells have more than one prev / next link.
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Optimal:
- Cell 0 and N each have log2(N) links.
- The 1/2 point cell has log2(N) - 1 links.
- The 1/4 point cells have one less.
- The 1/8 point cells have one less.
- etc.
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Probabilistic:
- When inserting a new cell, it’ll have a 50/50 chance of having two links, a 0.25 chance of 3, etc.
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This is tricky, so we’re not actually going to build it, but it ends up having expected log2(n) behavior for most simple operations.
