1. Algoritma Analizi 1 QuickSort Divide: A[p…r] bos olmayan iki alt diziye bolunur, A[p…q] ve A[q+1…r] s.t. oyleki A[p…q] nin her bir elemani A[q+1…r]. Nin herbir elemanindan kucuk veya kucuk esit. Conquer: iki alt dizi quicksort e recursive cagrimla siralanir Combine: herhangi bir islem yapilmaz cunku alt diziler kendi aralarinda zaten sirali

2. Algoritma Analizi 2 Quicksort (A, p, r) 1. if p < r 2. then q  Partition ( A, p, r ) 3. Quicksort ( A, p, q ) 4. Quicksort ( A, q+1, r ) * In place, not stable

3. Algoritma Analizi 3 Partition(A, p, r) 1. x  A[p] 2. i  p - 1 3. j  r + 1 4. while TRUE do 5. repeat j  j - 1 6. until A[j]  x 7. repeat i  i + 1 8. until A[i]  x 9. if i < j 10. then exchange A[i]  A[j] 11. else return j

4. Algoritma Analizi 4 Example: Partitioning Array

5. Algoritma Analizi 5 Algorithm Analysis Quicksort un calisma zamani partition (bolumleme) nin balanced (dengeli) olup olmadigina baglidir Worst-Case Performance (unbalanced): T(n) = T(1) + T(n-1) +  (n)  partitioning takes  (n) =  k = 1 to n  (k)  T(1) takes  (1) time & reiterate =  (  k = 1 to n k ) =  (n 2 ) * This occurs when the input is completely sorted.

6. Algoritma Analizi 6 Worst Case Partitioning

7. Algoritma Analizi 7 Best Case Partitioning

8. Algoritma Analizi 8 Analysis for Best Case Partition Eger her tefasinda balanced partition elde edersek (alt diziler n/2 boyunda), en iyi performansi elde etmis oluruz. T(n) = 2T(n/2) +  (n) T(n) =  (n log n)