Permutation Generator

Take a look at the algorithm Permutation Generator given in the text Mathematical Structures for Computer Science on pages 282-283. The algorithm takes a set of n integers and generates a list of all possible permutations of those integers. Answer the following questions to analyze the algorithm.

1. If the set consists of the integers {1,2,3,4,5}, how many permutations are possible?

2. If the set consists of the integers {1,2,3,4,,10}, how many permutations are possible?

3. Fill in the table below showing the number of permutations possible on a set of n integers for various values of n. Use scientific notation where appropriate.

n	Number of Permutations
5
10
15
20
25
30

4. If the set consists of the integers {1,2,3,4,n}, how many permutations are possible?

5. Classify the algorithm using Big-O notation.

6. If it takes a computer 10-9 seconds to generate one permutation, how long would it take to run the algorithm on the set {1,2,3,4,10} ?

For which values of n is it reasonable to run this algorithm on the set {1,2,3,4,n} ? Explain.

Please answer all

ALGORITHM PERMUTATION GENERATOR PermGenerator(integer n 22) 1/generates in lexicographical order all permutations //of the integers in the set {1,..., n} Local variables: //indices of permutation elements integers i, j integer k //for loop counter integers d,, d,, ..., d., //left to right elements of a permutation ALGORITHM PERMUTATION GENERATOR PermGenerator(integer n 22) 1/generates in lexicographical order all permutations //of the integers in the set {1,..., n} Local variables: //indices of permutation elements integers i, j integer k //for loop counter integers d,, d,, ..., d., //left to right elements of a permutation