Due 11:59pm Tuesday March 31

*For this assignment you should work on your own.* No partners this week.

Run `update21`, if you haven't already, to create the
`cs21/labs/09` directory.

Introduction

For this assignment, you will trace a program and write a few small programs. Code you write should still be submitted via handin21, but you can submit the trace of your program electronically or written on paper. If you choose to submit a written solution, it will be due at the start of class on Wednesday. The focus of this assignment is for you to further practice sorting and to become more comfortable with recursion.

Tracing sort

Insertion sort is an iterative comparision based sorting method similar to selection sort. The algorithm loops over all items in a given input list, and repeatedly In the file `traceSort.py`, you will find an implementation of both selection sort and insertion sort, but a high level description of the insertion sort algorithm is included below.

The top level description of insertion sort can be described as follows:

for each position i in the list A: insert A[i] in sorted orderTo insert in sorted order a value

A step by step execution of insertion sort is shown below.

Original List: [14, 11, 13, 18, 19, 12, 16, 10, 17, 15] inserting 14 from position 0 into position 0 [14, 11, 13, 18, 19, 12, 16, 10, 17, 15] inserting 11 from position 1 into position 0 [11, 14, 13, 18, 19, 12, 16, 10, 17, 15] inserting 13 from position 2 into position 1 [11, 13, 14, 18, 19, 12, 16, 10, 17, 15] inserting 18 from position 3 into position 3 [11, 13, 14, 18, 19, 12, 16, 10, 17, 15] inserting 19 from position 4 into position 4 [11, 13, 14, 18, 19, 12, 16, 10, 17, 15] inserting 12 from position 5 into position 1 [11, 12, 13, 14, 18, 19, 16, 10, 17, 15] inserting 16 from position 6 into position 4 [11, 12, 13, 14, 16, 18, 19, 10, 17, 15] inserting 10 from position 7 into position 0 [10, 11, 12, 13, 14, 16, 18, 19, 17, 15] inserting 17 from position 8 into position 6 [10, 11, 12, 13, 14, 16, 17, 18, 19, 15] inserting 15 from position 9 into position 5 [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]Note that after

[14, 11, 13, 18, 19, 12, 16, 10, 17, 15] inserting 11 from position 1 into position 0 [11, 14, 13, 18, 19, 12, 16, 10, 17, 15]Or, when inserting 12, the sorted items 13, 14, 18, 19 all move over one spot to make room for 12.

[11, 13, 14, 18, 19, 12, 16, 10, 17, 15] inserting 12 from position 5 into position 1 [11, 12, 13, 14, 18, 19, 16, 10, 17, 15]

In the file `traceSort.py`, you will find an implementation of both selection sort and insertion sort. Trace through all the function calls (four in total) for the two sorts and count the number of times the **body of the inner loop** in each sort executes. You should produce a table as follows for each sorting call, and also show the total number of times the inner loop executes over the entire algorithm.

i | # times through inner loop |
---|---|

0 | ? |

1 | ? |

... | ? |

Briefly answer the following questions in your writeup.

- Does the performance of selection sort depend on the original unsorted order of the list?
- Does the performance of insertion sort depend on the original unsorted order of the list?
- Does insertion sort take more or fewer steps than selection sort? Briefly explain your answer.

Recursion

Consider the following functions:
def reverse(ls): """ Given a list ls, returns a new list containing the elements of ls in reverse order """ def sumrange(n): """ Return the sum of the first n integers 1+2+3+4+...+n """

Open the file `iterative.py` and implement iterative
solutions to these functions. Extend the small `main` function
to include more tests for your solution. You cannot use the builtin
`reverse` method for lists to implement this solution. (The
reverse method modifies the list in place anyways, and your solution
must create a new list.)

Next, open the file `recursive.py` and implement
*recursive* solutions to these functions. You can use the same
`main` function from `iterative.py` to test your
recursive solution.
Some example output is shown below:

ls= [1, 2, 7, 8, 9, 4, 0, 3, 6, 5] reverse(ls)= [5, 6, 3, 0, 4, 9, 8, 7, 2, 1] sumrange(3) = 6 sumrange(10) = 55

Submit

Once you are satisfied with your programs, hand them in by typing
**handin21** in a terminal window.