CS106X – Programming Abstractions in C++ Cynthia Bailey Lee CS2 in C++ Peer Instruction Materials by Cynthia Bailey Lee is licensed under a Creative Commons Attribution-NonCommercial- ShareAlike 4.0 International License. Permissions beyond the scope of this license may be available at Bailey LeeCreative Commons Attribution-NonCommercial- ShareAlike 4.0 International Licensehttp://peerinstruction4cs.org

Today’s Topics: Heaps! 1. Linked list coding interview questions 2. Priority queues  Binary trees  Binary heaps 2

Coding interview question

Suppose we have a pointer (current) to the node containing the item to be removed What additional information do we need to successfully remove the node? A) Nothing additional. B) A pointer to the node immediately prior to the to-be- deleted node. C) A pointer to the node immediately after the to-be-deleted node. D) Both B and C. NULL head current (we want to remove this one) Remove

Suppose we have a pointer (current) to the node containing the item to be removed. NULL head current (we want to remove this one) NINJA CODER EDITION

Other classic interview questions  How can you remove a node of a linked list given a pointer to the node itself (and not the previous one)?  Write code to reverse a linked list in place.  How can you detect if there is a loop in a linked list (i.e. list is improperly formed), using constant space (O(1) amount of space)?

Priority Queue Emergency Department waiting room operates as a priority queue: patients are sorted according to seriousness, NOT how long they have waited.

Some priority queue implementation options  Unsorted linked list  Insert new element in front  Remove by searching list for highest- priority item  Sorted linked list  Always insert new elements where they go in priority-sorted order  Remove from front

Unsorted linked list  Add is FAST  Just throw it in the list at the front  O(1)  Remove/peek is SLOW  Hard to find item the highest priority item— could be anywhere  O(N) Priority queue implementations This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. Keyah Cheatum CommonsAttribution-Share Alike 3.0 Unported Keyah Cheatumhttp://commons.wikimedia.org/wiki/File:Messy_Room.JPG

Sorted linked list  Add is SLOW  Need to step through the list to find where item goes in priority- sorted order  O(N)  Remove/peek is FAST  Easy to find item you are looking for (first in list)  O(1) Priority queue implementations Released to the public domain:

We want the best of both  Fast add AND fast remove/peek  We will investigate trees as a way to get the best of both worlds Priority queue implementations +

Binary trees

A binary tree  “In computer science, a binary tree is a tree data structure in which each node has at most two child nodes, usually distinguished as "left" and "right".” (Thanks, Wikipedia!)

How many of these are valid binary trees? A. 0-3 B. 4 C. 5 D. 6 E. 7-8

A node object for binary trees  Similar to a linked list node, it contains a pointer to data, and a pointer to the next elements  Whereas a linked list node has just one next pointer, a binary node tree has two child pointers, left and right

A node object for binary trees  Similar to a linked list node, it contains a pointer to data, and a pointer to the next elements  Whereas a linked list node has just one next pointer, a binary node tree has two child pointers, left and right

Heaps! IMPORTANT NOTE: Despite the shared name, Heaps have nothing to do with the Heap part of memory (Binary Heap = a partially-ordered tree data structure; Heap is in contrast to Stack as a part of memory)

Binary Heaps*  Binary heaps are one kind of binary tree  They have a few special restrictions, in addition to the usual binary tree ADT:  Must be complete  Ordering of data must obey heap property  Min-heap version: a parent’s data is always ≤ its children’s data  Max-heap version: a parent’s data is always ≥ its children’s data * There are other kinds of heaps as well. For example, binomial heap is on your assignment.

How many of these could be valid binary heaps? A. 0-1 B. 2 C. 3 D. 4 E. 5-8

How many of these are valid min-binary-heaps? A. 0 B. 1 C. 2 D. 3

In how many places could the smallest number in this min -binary-heap be located ? A. 0-2 B. 3-4 C. 5-6 D. 7-8

Binary heap in an array

 We actually do NOT typically use a node object to implement heaps  Because they must be complete, they fit nicely into an array, so we usually do that

Heap in an array  For tree of height h, array length is 2 h -1  For a node in array index i:  Parent is at array index: A. i – 2 B. i / 2 C. (i – 1)/2 D. 2i

Binary heap in an array  For tree of height h, array length is 2 h -1  For a node in array index i:  Left child is at array index: A. i +1 B. i + 2 C. 2i D. 2i + 1

Binary heap in an array  For tree of height h, array length is 2 h -1  For a node in array index i:  Parent is at array index: (i – 1)/2  Left child is at array index: 2i + 1  Right child is at array index: 2i + 2

Binary heap insert and delete

Binary heap insert + “bubble up”

Binary heap insert

Binary heap delete + “trickle-down”

TRUE OR FALSE  There is only one configuration of a valid min-heap containing the elements {34, 22, 3, 9, 18} A. TRUE B. FALSE

Heap outcomes by insert order Create a MIN heap by inserting the elements, one by one, in the order given below for the second letter of your first name:  A-F: {3, 9, 18, 22, 34}  G-L: {3, 22, 18, 9, 34}  M-R: {9, 22, 18, 3, 34}  S-Z: {18, 22, 3, 9, 34}

Heap outcomes by insert order Create a MIN heap by inserting the elements, one by one, in the order given below for the first letter of your last name:  A-F: {18, 9, 34, 3, 22}  G-L: {3, 18, 22, 9, 34}  M-R: {22, 9, 34, 3, 18}  S-Z: {34, 3, 9, 18, 22}

How many distinct min-heaps are possible for the elements {3, 9, 18, 22, 34}? A. 1-2 B. 3-4 C. 5-8 D. 5! E. Other/none/more

Time cost  What is the worst-case time cost for each heap operation: Add, Remove, Peek? A. O(n), O(1), O(1) B. O(logn), O(logn), O(1) C. O(n), O(logn), O(logn) D. Other/none/more