Quiz 5 Study Guide
Quiz Study Guides are provided as a courtesy. You may work with other students on the questions, and ask questions about the guide during evening ninja help sessions, on piazza, or during meetings with faculty and staff. We do not provide full solutions to the quiz guides.
You are responsible for all material covered through the end of Week 11 (recursion).
In addition to all concepts from Quiz 4, you should understand the following:
Python concepts

Searching: linear search and binary search

Analysis of algorithms/bigO notation:

\$O(1)\$ — constant time

\$O(\log N)\$ — logarithmic (ex: binary search)

\$O(N)\$ — linear (ex: linear search)

\$O(N^2)\$ — quadratic (ex: bubble sort)


Sorting: bubble vs selection sort

Swapping two values in a list

Recursion

base case

recursive call

recursion on numbers, strings, and lists

You should be able to

compare different runtime analyses for algorithms

design a recursive function

draw the call stack for a recursive function
Practice problems

What would the output of the following code be?
for i in range(2): for j in range (3): print("i:%d j:%d" % (i,j))

True/False questions:

Linear search requires a number of steps proportional to the size of the list being searched (T/F)

The python
in
operator performs a binary search (T/F) 
Binary search is an \$N^2\$ algorithm (T/F)

The number of times N can be divided by 2 (before reaching 1) is \$\log_2 N\$ (T/F)


How many steps would it take to do binary search on a list of size 1 million, when the item you are searching for is NOT in the list?

How many steps would it take to do linear search on a list of size 1 million, when the item you are searching for is NOT in the list?

Binary search is much faster than linear search, so why don’t we use it for every search problem?

For each iteration of the loop in
binarySearch(x, L)
, show the index values forlow
,high
, andmid
, and the value stored at locationmid
. What will be returned by this function call?x = 67 L = [10, 12, 14, 21, 37, 44, 45, 46, 58, 67, 99] 0 1 2 3 4 5 6 7 8 9 10 low  high  mid  L[mid]                         

For each iteration of the loop in
binarySearch(y, L)
, show the index values for low, high, and mid, and the value stored at location mid. What will be returned by this function call?y = 4 L = [10, 12, 14, 21, 37, 44, 45, 46, 58, 67, 99] 0 1 2 3 4 5 6 7 8 9 10 low  high  mid  L[mid]                         

Write a function to return the index of the smallest item in a given list.
def indexOfSmallest(ls): """ Inputs: A list of values Returns: The index of the smallest item in the list, 1 if the list is empty Purpose: To find the location of the smallest item in the given list """ # complete this function

How many steps are required for each of the following?
for i in range(N): for j in range(N): print(i, j)
while N > 1: print(N) N = N//2
for i in range(N): for j in range(10): print(i*j)

Which algorithm requires time directly proportional to the size of the input list?

linear search

binary search

bubble sort

selection sort


Consider the following function,
oneLoop(L)
, which is similar to the inner loop from bubble sort:def oneLoop(L): for j in range(len(L)1): if L[j] > L[j+1]: tmp = L[j+1] L[j+1] = L[j] L[j] = tmp
Write an expression for the asymptotic runtime of
oneLoop
, in terms of the length \$N\$ of the listL
. 
Show how the following list
L=[17,4,19,3,11,8]
would be changed after selection sort does its first 3 swaps:For concreteness, here is some Python code for selection sort:
def selectionSort(L): for j in range(len(L)): ios = j # index of smallest item so far for i in range(j+1,len(L)): if L[i] < L[ios]: ios = i # swap them L[j],L[ios] = L[ios],L[j]

Write a recursive function
longestWord(words)
that returns the longest word inwords
, a list of strings. You can assume thatwords
contains at least one word.Then, draw the stack as it would look at its largest (i.e, the deepest part of the recursion when it hits a base case), when the function is called on the list
['awesome', 'recursive', 'code']
.