Midterm I Practice Problems

Solutions will be posted under Other Content on Blackboard as we get closer to the exam.

1. Given the string s = 'Columbus', evaluate the following:

   1. s[0]
   2. s[0:1]
   3. s[1:]
   4. s[-1]
   5. s[3: :-1]
   6. s[2: :2]

2. Given the list myList = [3, 2, -1, [4, 7], 5], evaluate the following:

   1. myList[0]
   2. myList[0:1]
   3. myList[-1]
   4. myList[3]
   5. myList[:2]
   6. myList[2: :2]

3. Evaluate the following:

   1. 'a' in 'backache'
   2. [1, 2, 3] + [[11, 13, 12][1]] + [22, 33, 44, 55][1:]
   3. [3 for x in range(6)]
   4. [2*y + 1 for y in [1, 3, 5, 7]]
   5. [x for x in range(3, 10) if x % 2 == 0]
   6. [len(w) for w in ['Go', 'Terriers']]

4. Write a function count_ones(s) that takes in a string s of '0's and '1's and returns the number of '1's in the input.

5. Write a function swap_bits(s) that takes in a string s of '0's and '1's and returns a string in which each bit in s has been swapped/replaced with the other bit. For example, swap_bits('101011') should return '010100'.

6. Write a function num_divisors(n) that returns the number of integers from 1 to n (inclusive) that divide n evenly. For example, num_divisors(42) should return 8, because 1, 2, 3, 6, 7, 14, 21, and 42 are all divisors of 42.

7. Use the above num_divisors(n) function in order to write a function most_divisors(lst) that takes in a list of integers lst and returns the integer from that list with the most divisors. For instance, most_divisors([2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]) should return 12.

8. Write a function count_transitions(s) that takes in a string s of '0's and '1's and returns the number of times there is a transition from a '0' to a '1' or vice-versa in that input string. For example, count_transitions('1110110000') should return 3.

9. Write a function longest_string(lst) that takes in a list of strings lst as input and returns the longest string from that list. For example, longest_string(['short', 'longer', 'sesquipedalian']) should return 'sesquipedalian'.

10. Write a function cycle(s, n) that takes in a string s of '0's and '1's and an integer n and returns the string in which s has shifted its last character to the initial position n times. For example, cycle('1110110000', 2) should return '0011101100'.

11. What is printed by the following working Python program?

    def dog(x):
        print('in dog, x is', x)
        y = cat(x - 1) + cat(x + 2)
        print('in dog, y is', y)
        return y
    
    def cat(y):
        print('in cat, y is', y)
        x = rat(y * 2) + 3
        print('in cat, x is', x)
        return x
    
    def rat(x):
        print('in rat, x is', x)
        return 2 * x
    
    y = dog(3)
    print('at this level, y is', y)
    

12. What is printed by the following working Python program?

    def mystery(x):
        print('x is', x)
        if x < 1:
            return 2
        else:
            p = 6 - mystery(x - 1)
            print('p is', p)
            return p
    
    y = mystery(3)
    print('y is', y)