## We will provide a lower bound, then beat it

- How do you suppose we’ll beat it?

## First, an observation: all of the sorting algorithms so far are comparison sorts

- The only operation used to gain ordering information about a sequence is the pairwise comparison of two elements
- Theorem: all comparison sorts are ?(n lg n)
- A comparison sort must do O(n) comparisons (why?)
- What about the gap between O(n) and O(n lg n)

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