ITECH 3109 Data Structures and Algorithms- Element Comparisons

1.Listing all permutations of n numbers.In this section you are required to write a Java (or C) implementation of the recursive algorithm described below. Using this algorithm, you will be able to generate, one by one, all permutations of n elements.

2. Recursive algorithm nextPermutation.[5 marks]

The algorithm should be implemented as a recursive function (method) named nextPermutation. The function receives an argument, which is an array of integers that represents a permutation. The function may change the received array (to the “next permutation”) and return true (or 1 in C) or it can leave the array unchanged and return false (0 in C).

You are required to modify C/Java code for Quicksort, Mergesort and Insertionsort algorithms to be able to count the number of element comparisons performed by each of them.

The original Quicksort, Mergesort and Insertionsort algorithms and their C implementations are discussed in Lecture 3.1.

Recommendation. Check that your modified sorting algorithms count element comparisons correctly by running them on small arrays of size 3 or 4, where the results can be computed by hand.

In this task you are required to compute and print out the average number of element comparisons for each of the Quicksort, Mergesort and Insertionsort algorithms to sort 10-element integer arrays containing the elements 1,2,3,4,5,6,7,8,9,10.

Note. Use the recursive nextPermutation when generating the permutations.

Recommendation. In your main function, use a variable, n, for the array size instead of a hard-coded number 10.  This will allow you to verify the correctness of your program on small instances, e.g., n = 3 or n = 4, where the average number of comparisons can be computed by hand. 

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