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# of index increment/decrement operations: a(n)
• Hoare: n + 1 a(n) n + 2 (a(n) ce(n))
• Lomuto: n a(n) 2n 1 (a(n) e(n) + (n 1))
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CS473-Algorithms I - Bilkent University Computer Engineering
• For Insertion-Sort, what is its worst-case time
– Depends on speed of primitive operations
• Relative speed (on same machine)
• Absolute speed (on different machines)
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Bilkent University Computer Engineering Department
Inductive hypothesis: T(k) c1k2 – c2k for k < n
T(n) = 4T(n/2) + n
4 (c1 (n/2)2- c2 (n/2)) + n
= c1 n2- 2 c2 n + n
= c1 n2- c2 n –(c2 n - n)
c1 n2- c2 n if c2 > 1
Pick c1 big enough to handle...