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# Merge sort

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### Merge sort

1. 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. 2. MergeSort - Illustration 2 Lecture #5 Adapted from slides by Dr A. Sattar Wednesday, March 4, 2009
3. 3. MergeSort – Illustration (contd…) 3 Lecture #5 Adapted from slides by Dr A. Sattar Wednesday, March 4, 2009
4. 4. MergeSort – Illustration (contd…) 4 Lecture #5 Adapted from slides by Dr A. Sattar Wednesday, March 4, 2009
5. 5. Pseudo code 5 Lecture #5 Adapted from slides by Dr A. Sattar Wednesday, March 4, 2009
6. 6. Pseudo code 6 Lecture #5 Wednesday, March 4, 2009
7. 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. 8. Worst-case scenario 8 Lecture #5 Adapted from slides by Dr A. Sattar Wednesday, March 4, 2009
9. 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. 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