116 CS Fall 2010
Assignment 8
Due 10:00 AM on Tuesday, November 16
For this and all subsequent assignments, you are expected to use the design recipe when writing functions from scratch. The solutions you submit must be entirely your own work. Do not look up either full or partial solutions on the Internet or in printed sources. Please read the course Web page for more information on assignment policies and how to organize and submit your work. Be sure to download the interface le from the course Web page and to follow all the instructions listed in the style guide (on the Web page). Specically, your solutions should be placed in les a8qY.rkt, where Y is a value from 1 to 4. This assignment mostly tests your understanding of the material in CS 116 Lecture Module 8, on loops, especially for loops. You may not use recursion or abstract list functions on this assignment. As well, a function may not mutate its arguments unless required to do so. A note on online submission: if there is a problem at the deadline for the assignment, please check www.cs.uwaterloo.ca/cs116, which should be available even if Odyssey is not working. Further information may be available there. Language level: Any Python version in the range 2.5.0 to 2.7. 1. Given a list of positive integers, we can compute the jump out number as the number of jumps required to jump out of a list, starting at the rst position. A jump means that if we are at a value x in the list, we can jump ahead x numbers. Here are some examples, with some explanation: jump_out([])
0, since an empty list requires no jumps to get out of.
jump_out([1]) 1, since we start at the rst position (the number 1), and jump out because our jump of distance one is enough to jump out. jump_out([3,1]) 1 because the number 3 indicates we can jump a distance of 3, and there are less than three elements after 3 in the list, and thus, we can jump out of the list. jump_out[(2, 5, 2, 8, 1, 1]) 4 because we start at 2, which means we can jump two positions to the second 2. After this, we can jump two positions to the rst 1. From there, we jump one position to the second 1. Finally, we jump one position out of the list, which was a total of four jumps. See the following picture:
[2, 5, 2, 8, 1, 1]
Write jump_out which should produce the integer number of jumps required to jump out of the list [clarication added November 10]. 1
2.
(a) Write the function extract_elem which consumes two lists: elements, an arbitrary list and a non-empty list of natural numbers positions. The function should produce a list values of from elements as indicated by positions. Suppose that elements is [x0 , x1 , ..., xn1 ]. Then all values in positions are integers in the range 0 to n 1. In particular, a value 4 in the list positions refers to x4 . Note that the values in positions may be repeated, but they will not be outside the range 0 to n 1. For example, extract_elem([a, b, c, d, e], [2, 0, 3, 0, 4]) should produce [c , a, d, a, e]. (b) Write the function shift_produce which consumes a list and an integer. The function should produce the list obtained after shifting the elements of the given list to the left by the indicated amount. For example:
shift_produce([1,2,3],0) [1,2,3] shift_produce([1,2,3,4], 1) [2,3,4,1] shift_produce([1,2,3,4], -1) [4,1,2,3]
(c) Write the function shift_mutate which consumes a list and an integer. The function should mutate the list obtained after shifting the elements of the given list to the left by the indicated amount. For example, if S = [1,2,3], T = [1,2,3,4] and U = [1,2,3,4,5], then
shift_mutate(S,0) shift_mutate(T, 1) shift_mutate(U, -1)
will cause S [1,2,3], T [2,3,4,1] and U [5,1,2,3,4]. 3. Given a matrix (possibly non-square) as a non-empty list of non-empty lists, we can transpose a matrix by reecting the elements across the diagonal that runs from the top-left corner to the bottom-right corner. For example,
transpose([[1, 2, 3], [4, 5, 6], [7, 8, 9]]) [[1, 4, 7], [2, 5, 8], [3,6,9]]
and
transpose([[1,2,3],[4,5,6]]) [[1,4],[2,5],[3,6]].
Note that the algorithm outlined in Assignment 4 will not work here: you will need to think about solving this problem differently in Python. 4. Write the function kth_largest which returns the k th largest element from a non-empty list of distinct numbers, given k and a non-empty list of numbers. Use a variant of quick-sort to solve this problem. For example, kth_largest(1, [1, 10, 2]) 2]) 1. 2
10 and kth_largest(3, [1, 10,
You may assume that k will be no larger than the length of the given list, and that k 1. You should solve the problem using the following logic: partition the list into three parts: a pivot, a list containing those elements less than the pivot, and a list containing those that are greater than the pivot (Note: you may use filter for this part of this question only). there are three possible positions for the k th largest element: in the greater than set; it is the pivot element; in the smaller than set. You will need to gure out how to recognize these three cases, and what to do in each case. Reminder: you may not use recursion.
3