Time efficiency of nonrecursive algorithms

1
Time efficiency of nonrecursive algorithms

• Steps in mathematical analysis of nonrecursive
  algorithms
• Decide on parameter n indicating input size
• Identify algorithms basic operation
• Determine worst, average, and best case for input
  of size n
• Set up summation for C(n) reflecting algorithms
  loop structure
• Simplify summation using standard formulas (see
  Appendix A)

2
Max element

• Input size ??
• Basic operation ??
• C(n) ??
• Worst, average, best case ??

3
Max element

• Input size n
• Basic operation comparison
• C(n) n-1 T(n)
• Worst, average, best case .... all are the same

4
Unique elements
t
5
Unique elements
t
6
Matrix multipliacation
7
Matrix multipliacation
Note The number of multiplications, M(n) is
8
Matrix multipliacation
Note The running time of the algorithm on a
particular machine is
9
Selection sort
10
Selection sort
11
Insertion sort
12
Insertion sort