CMU 15-112: Fundamentals of Programming and Computer Science
- These exercises will help you prepare for writing-session1, which is on Fri 30-Aug, and which will contain a randomly-chosen subset of exercises from among these.
- Unlike the hw, you may work collaboratively on these practice exercises.
- That said, during the actual writing session on Friday you must work alone, and without any notes or access to the web or other resources.
- To start:
- Do not use strings, loops, lists, or recursion this week.
- Do not hardcode the test cases in your solutions.
- distance(x1, y1, x2, y2)
Write the function distance(x1, y1, x2, y2) that takes four int or float values x1, y1, x2, y2 that represent the two points (x1, y1) and (x2, y2), and returns the distance between those points as a float.
- circlesIntersect(x1, y1, r1, x2, y2, r2)
Write the function circlesIntersect(x1, y1, r1, x2, y2, r2) that takes 6 numbers (ints or floats) -- x1, y1, r1, x2, y2, r2 -- that describe the circle centered at (x1,y1) with radius r1, and the circle centered at (x2,y2) with radius r2, and returns True if the two circles intersect and False otherwise.
- getInRange(x, bound1, bound2)
Write the function getInRange(x, bound1, bound2) which takes 3 int or float values -- x, bound1, and bound2, where bound1 is not necessarily less than bound2. If x is between the two bounds, just return it unmodified. Otherwise, if x is less than the lower bound, return the lower bound, or if x is greater than the upper bound, return the upper bound. For example:
- getInRange(1, 3, 5) returns 3 (the lower bound, since 1 lies to the left of the range [3,5])
- getInRange(4, 3, 5) returns 4 (the original value, since 4 is in the range [3,5])
- getInRange(6, 3, 5) returns 5 (the upper bound, since 6 lies to the right of the range [3,5])
- getInRange(6, 5, 3) also returns 5 (the upper bound, since 6 lies to the right of the range [3,5])
Write the function eggCartons(eggs) that takes a non-negative integer number of eggs, and returns the smallest integer number of cartons required to hold that many eggs, where a carton may hold up to 12 eggs.
- pascalsTriangleValue(row, col)
Write the function pascalsTriangleValue(row, col) that takes int values row and col, and returns the value in the given row and column of Pascal's Triangle where the triangle starts at row 0, and each row starts at column 0. If either row or col are not legal values, return None, instead of crashing. Hint: math.factorial may be helpful!
- isFactor(f, n)
Write the function isFactor(f, n) that takes two int values f and n, and returns True if f is a factor of n, and False otherwise. Note that every integer is a factor of 0.
Write the function isMultiple that takes two int values m and n and returns True if m is a multiple of n and False otherwise. Note that 0 is a multiple of every integer including itself. Also, you should make constructive use of the isFactor function you just wrote above.
Write the function nearestBusStop(street) that takes a non-negative int street number, and returns the nearest bus stop to the given street, where buses stop every 8th street, including street 0, and ties go to the lower street, so the nearest bus stop to 12th street is 8th street, and the nearest bus stop to 13 street is 16th street.
- getKthDigit(n, k)
Write the function getKthDigit(n, k) that takes a possibly-negative int n and a non-negative int k, and returns the kth digit of n, starting from 0, counting from the right. So:
getKthDigit(789, 0) == 9 getKthDigit(789, 1) == 8 getKthDigit(789, 2) == 7 getKthDigit(789, 3) == 0 getKthDigit(-789, 0) == 9
- setKthDigit(n, k, d)
Write the function setKthDigit(n, k, d) that takes three integers -- n, k, and d -- where n is a possibly-negative int, k is a non-negative int, and d is a non-negative single digit (between 0 and 9 inclusive). This function returns the number n with the kth digit replaced with d. Counting starts at 0 and goes right-to-left, so the 0th digit is the rightmost digit. For example:
setKthDigit(468, 0, 1) == 461 setKthDigit(468, 1, 1) == 418 setKthDigit(468, 2, 1) == 168 setKthDigit(468, 3, 1) == 1468