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Unformatted text preview: remaining elements. (a) Write down the recursive version of Bubble Sort in psuedocode. (b) Derive a recurrence for the exact number of comparisons the algorithm uses. (c) Solve the recurrence (any way you like). Simplify as much as possible. “Master Theorem”: T ( n ) = b aT ( n/b ) + cn d n > 1 f n = 1 implies T ( n ) = p f + c ab-d-1 P n log b a-cn d ab-d-1 = b Θ( n log b a ) a > b d Θ( n d ) a < b d n d ( f + c log b n ) = Θ( n d log b n ) a = b d . Summing solutions: If T ( n ) = b aT ( n/b ) + ∑ c i n d i n > 1 f n = 1 then we can just sum the solutions of each recurrence: T i ( n ) = b aT i ( n/b ) + c i n d i n > 1 n = 1 and add in fn log b a for the contribution from the leaves. 2...
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- Fall '11
- Recursion, Natural number, Recurrence relation, following recurrence, ci ndi