CPSC 241                           Name: ___________________________           
Homework #1                        Due July 12, 2000

For each of the following, determine the order of complexity.  Explain fully
how you arrived at your answer.  Your answer should be one of the following:

    O(1)   O(log n)  O(n)   O(n^2)   O(n log n)   O(n^3)   O(n!)   O(2^n)

followed by your explanation.


 O(?)

______  1. Finding the sum of a sorted list of n integers, counting additions.


______  2. Finding the maximum value in a sorted list of n integers, 
           counting comparisons.

______  3. Bubble sort on a list of n values, counting comparisons


______  4. Binary search on a list of n sorted values, counting comparisons


______  5. Matrix multiplication on two (n x n) matrices, counting arithmetic 
           operations


______  6. Printing all of the values that can be represented by in an n-bit
           register, counting print statements.


______  7. Printing all of the permutations of n values,  counting print statements.


______  8. What is the complexity of the following loop, counting print statements?

           for(int i=0; i<n; i++)
              for (int j=0; j<=i; j++)
                 System.out.print((i*j) + " ");


______  9. Computing the average of a list of n numeric values, counting arithmetic 
           operations.


______  10. Computing the standard deviation of a list of n numeric values, counting
           arithmetic operations.  (Research the formula for standard deviation)


______  Bonus Question: QuickSort, counting comparisons