Midterm I Practice Problems

Transcription

1 Midterm I Practice Problems Name: Section: andrewid: This PRACTICE midterm is not meant to be a perfect representation of the upcoming midterm! You are responsible for knowing all material covered in homework and lectures. As on the exam, read instructions carefully, and show all work. We will not entertain any question, except for questions pertaining to English vocabulary. Short answer questions should be answered briefly, but completely. Show your work. For solutions, attend a CA-led review session, or contact your CA. Good luck! Time: 80 minutes Question Max Grade Bonus 5 Total 105

2 1. [10 pts; 1 pt each] True or False (circle one): a. TRUE or FALSE: Nested loops always run in O(N**2). b. TRUE or FALSE: Destructive list methods like a.sort create new lists, but nondestructive functions like sorted(a) do not. c. TRUE or FALSE: Mergesort is O(NlogN), and selectionsort is O(N**2), but this alone does not guarantee that mergesort will be faster than selectionsort in all cases. d. TRUE or FALSE: FasterIsPrime runs in O(N**0.5) which is faster than O(N) but slower than O(logN). e. TRUE or FALSE: To work correctly, binary search requires that a list is sorted. f. TRUE or FALSE: For a rectangular 2d list L, len(l[0]) is the number of rows in L. g. TRUE or FALSE: 2d lists in Python are really 1d lists containing 1d lists as elements. h. TRUE or FALSE: For any integers x and y, if ((x/y) == (y%x)) is True, then (y**2 == x) is True. i. TRUE or FALSE: In Tkinter it is generally easy to center text on some location but relatively harder to right- align text to some location. j. TRUE or FALSE: For a 1d List L that only contains int values, copy.copy(l) is effectively the same as copy.deepcopy(l). 2. [15 pts; 3 pts each] Very Short Answers: Answer each of the following with only a few words or numbers. Longer answers will be incorrect. a. Consider the following code, which is meant to return True, if the dictionaries d1 and d2 are equal (and False otherwise). def equal(d1, d2): for key in d1: if (key not in d2) or (d1[key]!= d2[key]): return False return True In just a few words of English, describe the bug in the above code. Fix the bug!

3 b. Very briefly give one clear reason why f(s) is not a very good hash function for strings: def f(s): return sum([ord(c) for c in s]) c. When an exception occurs, Python often prints a stack trace that is full of useful information. List 3 different pieces of information available in a stack trace. d. Given the tuple T containing an odd number of int values, write a single expression, not a statement, that computes the median value in T. For half credit, if you do not know the difference between an expression and a statement (or for any other reason), you may write a function instead. e. Briefly explain how you can use timing information to verify whether or not a given function f(n), for positive int values N, runs in O(N**3) time 3. [15 pts; 3 pts each] Indicate what each will print or draw (assume a 400x400 canvas): For graphics output, do not explain the output in words, but simply draw the resulting canvas. Statement(s): import copy def f(a): b = copy.copy(a) c = copy.deepcopy(a) result = [ ] a[1][1] = 42 for i in xrange(len(a)): for j in xrange(len(a[0])): if (b[i][j]!= c[i][j]): result += [(i,j)] return result a = [[1,2],[1,2]]*2 b = f(a) print a[3],b Prints:

4 fmt = "%s %+d %0.1f" for d in [5.0/3.0, -5.0/3.0]: print fmt % (fmt[0:2], int(d), d) z = 0 for x in xrange(10,1,-3): for y in xrange(1, x, 1+x%4): z += y if (z % 2 == 0): print x,y,z def f(s): (r, s) = ("", str(s)) for i in xrange(len(s)): (c, d) = (s[i], s[len(s)-1-i]) if (c < d): r += d elif (c == d): r += str(len(r)) break else: r += s[0] continue r *= 2 return r print f( ) (x1,y1) = (200,0) for x in xrange(50,500,200): for y in xrange(x, 400, 150): canvas.create_line(x,y,x1,y1) canvas.create_text(x,y,text=str((x,y))) (x1,y1) = (x,y)

5 4. [20 pts; 4 pts each] Reasoning about code In these exercises, you should provide the arguments that cause the function to return the specified value. In most cases, there are many valid answers. You only need to provide one of them. def f(a): count = 0 (oldx, oldy, oldz) = (1,1,1) for (x,y,z) in a: if ((x!= oldy) or (y!= oldz)): return 42 elif (x+y!= z): return -42 else: (oldx, oldy, oldz) = (x,y,z) count += 1 return count # provide a value of a # where f(a) returns 3 def f(a): s = set() d = dict() for i in range(len(a)): if (i%2 == 0): if (a[i] in d): s.add(a[i+1]) else: d[a[i]] = a[i+1] return (sorted(s), d[42]) # provide a value of a # where f(a) returns ([4,5],6)

6 def g(x): while (x >= 10): (y,x) = (x,0) while (y > 0): x += y%10 y /= 10 return x def f(x): (best, result) = (0,0) for n in xrange(500,600): if (g(n) >= best): (best, result) = (g(n), n) return (result == x) # provide a value of x # where f(x) returns True def f(l): (rows,cols) = (len(l), len(l[0])) assert((rows == 2) and (cols == 4)) i = 0 for col in xrange(cols): for row in xrange(rows): assert(l[row][cols-1-col] == i) i += 1 return True # provide a value of L # where f(l) returns True def f(x): assert(10**4 > x > 10**3) (y,z) = (0,1) while (x > 0): d = (x%10) if (d%z!= 0): return False y = 10*y + (d/z) z += 1 x /= 10 return (y == 7431) # provide a value of x # where f(x) returns True

7 5. [15 pts] Free Response: bestquiz Write the function bestquiz(a), which takes a rectangular 2d list of numbers that represents a gradebook, where each column represents a quiz, and each row represents a student, and each value represents that student s score on that quiz (except - 1 indicates the student did not take the quiz). For example: a = [ [ 88, 80, 91 ], [ 68, 100, -1 ] ] This list indicates that student0 scored 88 on quiz0, 80 on quiz1, and 91 on quiz2. Also, student1 scored 68 on quiz0, 100 on quiz1, and did not take quiz2. The function returns the quiz with the highest average. In this case, quiz0 average is 78, quiz1 average is 90, and quiz2 average is 91 (since we ignore the - 1). Thus, quiz2 is the best, and so the function returns 2 in this case. You are not responsible for malformed input, except you should return None if there are no quizzes. Also, resolve ties in favor of the lower quiz number.

8 6. [25 pts] Free Response: iskingstour Background: in Chess, a King can move from any square to any adjacent square. A King s Tour is a series of legal King moves so that every square is visited exactly once. We can represent a Kings Tour in a 2d list where the numbers represent the order the squares are visited, going from 1 to N 2. For example, consider these 2d lists: [ [ 3, 2, 1 ], [ [ 1, 2, 3 ], [ [ 3, 2, 1 ], [ 6, 4, 9 ], [ 7, 4, 8 ], [ 6, 4, 0 ], [ 5, 7, 8 ] ] [ 6, 5, 9 ] ] [ 5, 7, 8 ] ] The first is a legal Kings Tour but the second is not, because there is no way to legally move from the 7 to the 8, and the third is not, because it contains a 0 which is out of range. With this in mind, write the function iskingstour(board) that takes a 2d list of integers, which you may assume is NxN for some N>0, and returns True if it represents a legal Kings Tour and False otherwise.

9 7. [5 pts] Bonus / Optional [2.5 pts] In just a few words of plain English, for what values of n does f(n) return True? def f(n): assert(isinstance(n,int) and (n>1)) product = 1 for i in xrange(2,n): j = 1 while (j < n): j *= i product *= (n % j) return (product == 0) [2.5 pts] What will this print? def g(n): (r,s) = (False,str(n)) for i in xrange(1,len(s)-1): for j in xrange(i+1, len(s)): r = r or (int(s[:i])-int(s[j:])==-int(s[i:j])) return r n = 9000 while (not g(n)): n -= 1 print n