1. Sorting Algorithms
Department of Computer Science
Islamia College University Peshawar
Fall 2012 Semester
BCS course: CS 00 Analysis of Algorithms
Course Instructor: Mr. Zahid

2. MergeSort - Illustration
2
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009

3. MergeSort – Illustration (contd…)
3
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009

4. MergeSort – Illustration (contd…)
4
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009

5. Pseudo code
5
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009

6. Pseudo code
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Lecture #5
Wednesday, March 4, 2009

7. Recurrence Relation
 Recall for Divide and Conquer algorithms
T(n) = aT(n/b) + D(n) + C(n)
 Here a=2, and if we assume n is a power of 2, then each divide
step leads to sub-arrays of size n/2
 D(n)=θ(1)
 C(n)= θ(n)
 T(n)=2T(n/2)+θ(n)
7
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009

8. Worst-case scenario
8
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009

9. Worst and Average-case Scenario
 Worst case running time of merge sort is θ(nlgn)
 Average case running time of merge sort is also θ(nlgn)
 Best case?
9
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009

10. Worst and Average-case Scenario
 Worst case running time of merge sort is θ(nlgn)
 Average case running time of merge sort is also θ(nlgn)
 Best case?
9
Lecture #5
Adapted from slides by Dr A. Sattar
Wednesday, March 4, 2009