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

2. Stacks and Queues

3. Stack-based Recursion
Computers use stacks to manage function calls/function returns.
When a function is called, data is pushed onto the stack
When a function finishes, data is popped off the stack
Rather than using the computer’s stack, we can use our own to implement recursion!
Binary tree traversal

4. Stacks and Recursion
Any recursive algorithm can be implemented non-recursively.
Do you have to use a function that calls itself?
No. You can use a stack to implement recursion
Do you have to use a recursive algorithm?
Yes. How do you traverse a binary tree without a recursive algorithm?

5. Queues A queue is a “First-In, First-Out” = “FIFO” buffer.
e.g. line-ups
people enter from the back of the line
people are served (exit) from the front of the line
When elements are added, they are enqueued to the back.
When elements are removed, they are dequeued from the front.
enqueue() and dequeue() are the two defining functions of a queue.
Example
Link-based Queue

6. Priority Queues
Previous queues were based on entry order (e.g. LIFO, FIFO).
Priority queues are based on item value.
Stacks and queues aren’t designed for searches.
BST could work, but there is more overhead than we need.
don’t need completely sorted queue – only need first element

7. Heaps and Heapsort

8. Key Points
Heaps
Make a heap
Heapsort

9. Heaps Complete binary tree Partially ordered
max heap – the value of every node is greater than its children
min heap – the value of every node is smaller than its children
No relationship between siblings, only ancestors (up-down)
BST has left-right relationships.

10. Removing the Minimum Value
Minimum value is at root, so we should remove this element.
How do we maintain a complete binary tree?
Put last value at the root and sift down
Switch the value with the smallest of its children – continue
Heap property is maintained.

11. Inserting a new value How do we maintain a complete binary tree?
Put value at the bottom and sift up
Heap property is maintained.

12. Complexity Analysis Remove minimum Insert
Best  value stays at depth 1  O(1)
Worst  value goes back to bottom  O(logn)
Average  value goes half way O(logn)
Insert
Best  value stays at bottom  O(1)
Worst  value goes to top  O(logn)

13. Making a Heap Array representation Make a heap
Analysis of building a heap
Heapsort