1. Sorting Sorting is a fundamental problem in computer science.
comparison-based sorting: the only operations allowed on the input data are:
<, > operations
assignment
input data must be comparable. 15 2 8 1 17 10 12 5 3 4 6 7
Nov 30, 2001
CSE 373, Autumn 2001

2. Insertion Sort Simple sorting algorithm. N-1 passes over the array
At the end of pass p, the elements that occupied A[0]…A[p] originally are still in those spots and in sorted order. 2 8 15 1 17 10 12 5 3 4 6 7
after
pass 2 1 2 8 15 17 10 12 5 3 4 6 7
after
pass 3
Nov 30, 2001
CSE 373, Autumn 2001

3. Analysis Insertion sort worst case time:
Insertion sort best case time: array is in sorted order. O(N).
comparisons
assignments
insertion
worst: N2/2
best: N
selection
N2/2 N
Nov 30, 2001
CSE 373, Autumn 2001

4. Average case analysis
Given an array A of elements, an inversion is an ordered pair (i, j) such that i < j, but A[i] > A[j].
Assume no duplicate elements.
Theorem: The average number of inversions in an array of N distinct elements is N(N-1)/4.
Corollary: Any algorithm that sorts by exchanging adjacent elements requires (N2) time on average.
Nov 30, 2001
CSE 373, Autumn 2001