1. ITEC 2620M Introduction to Data Structures
Instructor: Prof. Z. Yang
Course Website:
Office: DB 3049

2. Sorting

3. Key Points Recursive sorting algorithms Achieving leverage Quicksort
Mergesort

4. Review Previous sorting algorithms were O(n2) on average.
What if we could get O(nlogn)
Where have we seen O(logn) before?
Binary search
How did binary search work?
first query explores 1 element
second query explores 2 elements
third query explores 4 elements

5. Recursive Sorting Split the elements into smaller sub-groups
Partially sort each sub-group
Trust recursion to put everything back together

6. Quicksort Algorithm Pick an element
partially sort them
move all larger elements on one side, and smaller elements on the other
have to look at all elements to get one element in position
Pick one element in each sub-division (2)
move all elements as before (twice)
have to look at half of the elements to get each new element into position
Pick one element in each sub-division (4)
move all elements as before (four times)

7. Quicksort Algorithm (Cont’d)
Each sub-division is being sorted by the same algorithm as the overall set
recursion
base case is 0 or 1 elements – already sorted
Work to sort each element is cut in half each level down
Get twice as much done for our effort
How many times can we cut something in half?
O(logn)
Pseudocode

8. Mergesort Algorithm Divide what you have to do into two halves
sort each half
merge the two halves into a fully sorted set
Each half will be sorted by the same algorithm as the overall set
recursion
base case is 0 or 1 elements – already sorted
Each upward merge sorts twice as much
How many times can we cut something in half?
O(logn)
Pseudocode

9. Binary Search Trees

10. Key Points Inserting and Deleting into Linked Structures Linked lists
Basic BST operations
Deleting from BSTs

11. Codes Inserting into a Linked List Deleting from a Linked List
Inserting into a BST
insertion always happens at the bottom of the tree
new node will be a leaf node
Deleting from a BST – target node has less than two children
Deleting from a BST – target node has two children
Deleting from a BST – a better way