This document discusses lists and their time complexities. It describes unordered and ordered lists, with unordered lists having O(1) complexity for operations like add and search but O(n) for others like remove. Ordered lists have higher complexities of O(n) for all operations. The document provides examples of list implementations and discusses linked lists and arrays.

1. PROBLEM SOLVING WITH ALGORITHMS
AND DATA STRUCTURES — LISTS
Bruce Tsai
http://interactivepython.org/runestone/static/pythonds/BasicDS/
Lists.html

2. LIST
Unordered list
Collection of items where each item holds a relative position
with respect to the others
[54, 26, 93, 17, 77, 31]
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3. UNORDERED LIST COMPLEXITY
add(item) — O(1)
remove(item) — O(n)
search(item) — O(n)
isEmpty() — O(1)
size() — O(n)
append(item) — O(n)
index(item) — O(n)
insert(pos,item) — O(pos)
pop() — O(n)
pop(pos) — O(pos)
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4. ORDERED LIST
Collection of items where each item holds a relative position
that is based upon some underlying characteristic of the item
Ascending or descending
[54, 26, 93, 17, 77, 31] => [17, 26, 31, 54, 77, 93]
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5. ORDERED LIST COMPLEXITY
add(item) — O(n)
remove(item) — O(n)
search(item) — O(n)
isEmpty() — O(1)
size() — O(n)
index(item) — O(n)
pop() — O(n)
pop(pos) — O(pos)
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6. SELF CHECK
1. Implement the append method for UnorderedList.What is the
time complexity of the method you created?
2. In the previous problem, you most likely created an append
method that was O(n). If you add an instance variable to the
UnorderedList class you can create an append method that is
O(1). Modify your append method to be O(1).
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7. PART 1
Append method adds a new item to the end of the list making it
the last item in the collection.
First traverse UnorderedList to original last item and then set
new item as next node of original last item
The time complexity is O(n)
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8. PART 2
Add instance variable tail to represent the last item
https://gist.github.com/wagamama/18a75738f7dd3dcdf817#file-
unorderedlist-py
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9. DISCUSSION QUESTIONS
7. What is the result of carrying out both steps of the linked list
add method in reverse order? What kind of reference results?
What types of problems may result?
8. Explain how the linked list remove methods works when the
item to be removed is in the last node.
9. Explain how the remove method works when the item is in the
only node in the linked list.
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10. NO. 7

11. NO. 8
previous current

12. NO. 9
previous == None
self.head = current.getNext()
self.head = None
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13. ARRAY (SEQUENCE)
Allocate size first
Item with index
assign — O(1)
insert — O(n)
delete — O(n)

14. PYTHON LIST COMPLEXITY
append — O(1)
insert — O(n)
delete — O(n)
search — O(n)
size — O(1)
get — O(1)
set — O(1)
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15. REFERENCE
http://interactivepython.org/runestone/static/pythonds/BasicDS/
Lists.html
https://gist.github.com/wagamama/18a75738f7dd3dcdf817
http://www.csie.ntnu.edu.tw/~u91029/Sequence.html
https://wiki.python.org/moin/TimeComplexity