Midterm I Practice Problems

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

Given the string s $=$ 'Columbus', evaluate the following:

S$[0]$

s$[0$:$1]$

s$[1$:$]$

s$[-1]$

s$[3$: :$-1]$

s$[2$: :$2]$

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

myList$[0]$

myList$[0$:$1]$

myList$[-1]$

myList$[3]$

myList$[$:$2]$

myList$[2$: :$2]$

Evaluate the following:

$\text{'}$a$\text{'}$ in 'backache'

$[1,2,3]+[[11,13,12][1]]+[22,33,44,55][1$:$]$

$[3$ for x in range$(6)]$

$[2*$y $+1$ for y in $[1,3,5,7]]$

$[$x for x in range$(3,10)$ if x $\%2==0]$

$[$len$($w$)$ for w in $[\text{'}$Go$\text{'},$ 'Terriers'$]]$

$[$chr$($ord$($c$)+1)$ for c in 'hello'$]$

Write a function count$\_$ones$($s$)$ that takes in a string s of $\text{'}0\text{'}$s and $\text{'}1\text{'}$s and that uses recursion to count and return the number of $\text{'}1\text{'}$s in the input.

Write a function swap$\_$bits$($s$)$ that takes in a string s of $\text{'}0\text{'}$s and $\text{'}1\text{'}$s and returns a string in which each bit in s has been swapped$/$replaced with the other bit. For example, swap$\_$bits$(\text{'}101011\text{'})$ should return $\text{'}010100\text{'}.$

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 $42.$

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 $12.$

Write a function common$\_$chars$($s$1,$ s$2)$ that takes in two arbitrary strings s$1$ and s$2$ and returns a new string containing only the characters that s$1$ and s$2$ have $$in common$$ i$.$e$.,$ characters from positions in which both s$1$ and s$2$ have the same character. The characters in the returned string should be in the same order with respect to each other as they were in the original string. For example, common$\_$chars$(\text{'}$pretty$\text{'},$ 'pleased'$)$ should return $\text{'}$pe$\text{'}$ because the only positions at which the strings have the same character are position $0(\text{'}$p$\text{'})$ and position $2(\text{'}$e$\text{'}).$

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$([\text{'}$short$\text{'},$ 'longer', 'sesquipedalian'$])$ should return 'sesquipedalian'.

Write a function larger$\_$than$($n$,$ vals$)$ that takes in a single integer n and a list of numbers vals and that returns a list containing the numbers from vals that are larger than n$.($We encourage you to implement this function in two different ways: once using recursion, and once using a list comprehension.$)$

What is printed by the following working Python program?

def dog$($x$)$:

$$print$(\text{'}$in dog, x is$\text{'},$ x$)$

$$y $=$ cat$($x $-1)+$ cat$($x $+2)$

$$print$(\text{'}$in dog, y is$\text{'},$ y$)$

$$return y

def cat$($y$)$:

$$print$(\text{'}$in cat, y is$\text{'},$ y$)$

$$x $=$ rat$($y $*2)+3$

$$print$(\text{'}$in cat, x is$\text{'},$ x$)$

$$return x

def rat$($x$)$:

$$print$(\text{'}$in rat, x is$\text{'},$ x$)$

$$return $2*$ x

y $=$ dog$(3)$

print$(\text{'}$at this level, y is$\text{'},$ y$)$

What is printed by the following working Python program?

def mystery$($x$)$:

$$print$(\text{'}$x is$\text{'},$ x$)$

$$if x $<1$:

$$return $2$

$$else:

$$p $=6-$ mystery$($x $-1)$

$$print$(\text{'}$p is$\text{'},$ p$)$

$$return p

y $=$ mystery$(3)$

print$(\text{'}$y is$\text{'},$ y$)$

help me work this out without giving answers