Data Structures and Algorithm Analysis in C - SVS

Structures, Algorithm Analysis: CHAPTER 7: SORTING
Figure 7.15 A small change to quicksort, which breaks the algorithm
Worst-Case Analysis
Best-Case Analysis
Average-Case Analysis
Worst-Case Analysis
The pivot is the smallest element, all the time. Then i = 0 and if we ignore T(0)
= 1, which is insignificant, the recurrence is
T(n) = T(n - 1) + cn, n > 1
(7.2)
We telescope, using Equation (7.2) repeatedly. Thus
T(n -1) = T(n - 2) + c(n - 1)
(7.3)
T(n - 2) = T(n - 3) + c(n - 2)
(7.4)
...
T(2) = T(1) + c(2)
(7.5)
Adding up all these equations yields
(7.6)
as claimed earlier.
Best-Case Analysis
In the best case, the pivot is in the middle. To simplify the math, we assume
that the two subfiles are each exactly half the size of the original, and
although this gives a slight overestimate, this is acceptable because we are only
interested in a Big-Oh answer.
T(n) = 2T(n/2) + cn
mk:@MSITStore:K:\Data.Structures.and.Algorithm.Analysis.in.C.chm::/...
页码,27/49
2006-1-27