Print out your answers hand them in at the EECS Undergraduate Office (38-476) sometime between Dec. 1 and Spring Registration Day. For the programs (part 2 of the test) make sure to turn in your code together with a few test case results to demonstrate that the code runs. Actually print out your answers and hand them in at the undergraduate office. Do not email them to us. Make sure that the pages of your work are stapled together. In addition to this test to be handed in, there will be a short on-line questionnaire for students who will be taking the class. We will send email about this in mid-January.
sicp.csail.mit.edu/6.01/
This will ask you to register for an account. After you register, the
tutor will mail you a password that you can use to log in.
Log in and select "choose a problem set". "Problem set" 1 is a
short survey to fill out. Please do this now.
Note: The tutor for this survey, and for doing 6.01 homework
during the semester, is a different tutor from the one we're
making available for optional Python programming practice during IAP.
That programming practice tutor is at
sicp.csail.mit.edu/6.01/progSp08/. The two tutor
programs are completely separate; if you use both of them, you'll need
to register for each one individually.
(a) Write a procedure that solves quadratic equations using the quadratic formula: It should take as arguments three numbers a, b, and c. It should print error messages if a is zero, or if the roots are complex. Otherwise it should print the two roots. (b) Modify your procedure to handle the case of complex roots.
Write a procedure that evaluates polynomials. It should take two arguments. The first is a number . The second is a list of of coefficients ordered from highest to lowest:
Your procedure should return the value of the polynomial evaluated at :
A clerk works in a store where the cost of each item is a positive integer number of dollars. So, for example, something might cost $21, but nothing costs $9.99. In order to make change a clerk has an unbounded number of bills in each of the following denominations: $1, $2, $5, $10, and $20. Write a procedure that takes two arguments, the cost of an item and the amount paid, and prints how to make change using the smallest possible number of bills.
(a) Write a procedure that takes a string of words separated by spaces (assume no punctuation or capitalization), together with a "target" word, and shows the position of the target word in the string of words. For example, if the string is:
we dont need no education we dont need no thought control no we dontand the target is the word "dont" then your procedure should return the list 1, 6, 13 because "dont" appears at the 1st, 6th, and 13th position in the string. (We start counting positions of words in the string from 0.) Your procedure should return False if the target word doesn't appear in the string.
(b) Suppose you are repeatedly looking up targets in a fixed long list. It might help to build an "inverted index", that shows the positions of all targets, so that this information can be retrieved quickly. For example, an inverted index for the above string of words would be:
we: 0, 5, 12
dont: 1, 6, 13
need: 2, 7
no: 3, 8, 11
education: 4
thought: 9
control: 10
Use an appropriate data structure to represent an inverted index. Write a procedure that, given a string of words, constructs an inverted index, and show how to use the index to look up target words as in part (a).
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