Description
In mathematics, the notion of permutation relates to the act of rearranging, or permuting, all
the members of a list into some sequence or order. For example, there are six permutations of the
list [1,2,3], namely: [1,2,3], [1,3,2], [2,1,3], [2,3,1], [3,1,2], and [3,2,1]. The number
of permutations of n distinct objects is n factorial (n!).
What to do
Implement the recursive method named permutation (marked TO DO) which can be found in
Permutation.java. This method takes an ArrayList as an argument and returns
ArrayList<ArrayList> as a result. For example, suppose you have a list of class wrapper Integer named list which contains [1,2,3] (from the first index to the last index). By
calling the method permutation using the following statement (Permutation is a static class):
ArrayList<ArrayList> result = Permutation.permutation(list);
The result should be [[1,2,3],[1,3,2],[2,1,3],[2,3,1],[3,1,2],[3,2,1]] (not necessary in
that order). To generate this, you can perform the following steps:
1. Remove the first index of the list and store it in a variable (let’s named this variable firstEntry)
2. Permute the rest of the list which should give you a list of list (let’s call this result)
3. For every list inside result, insert firstEntry into every valid index. Every time you insert,
you get a new list which will be a member of your final result.
For example, start with the list [1,2,3], at step 1, you store 1 in firstEntry and the rest of
the list is [2,3]. After you permute the list [2,3], you should get the list of list [[2,3],[3,2]]
(let’s call this result. The first index of result is the list [2,3]. In that list, there are three
valid indexes, 0, 1, and 2, that we can insert an item. By inserting firstEntry into [2,3] at all
possible valid indexes, you will get three new lists, [1,2,3], [2,1,3], and [2,3,1]. The second
index of the result is the list [3,2]. Again, by inserting firstEntry into [3,2] at all possible
valid indexes, you will get three new lists, [1,3,2], [3,1,2], and [3,2,1]. Note that all new
lists are permutation of the list [1,2,3]. You can see that the step 2 above is where recursive call
happens. Do not forget about the base case. Think about the base case by yourselves.
Note that it may be a good idea to create your own test class before running the given test class.
To see the content of an ArrayList named aList, you can simply use the statement
System.out.println(aList).
CS/COE 0445 — Data Structure Page 1
Lab 5: Permutation using Recursion
Test Class
A test class (PermutationTester.java) is provided. Simply compile and run this test class. This
program will test your Permutation.java and show your total points (out of 10). If you do not get
the full 10 points, you should keep trying to fix your code until you get 10 points. Note that this
test class is not perfect. It cannot tell you why your program is incorrect. You may have to look
at the source code of PermutationTester.java and see why it says FAIL and trace your code.
Due Date and Submission
For the due date, please check the lab in the CourseWeb. Submit your Permutation.java to the
CourseWeb under this lab by the due date. No late submission will be accepted.
CS/COE 0445 — Data Structure Page 2
