#tree traversal

Topics

Abstract Data Types - the abstract set of data types

Agnostic to programming language

ADTs can be made using several specific data structures, as long as they retain the same functionality/have the same public API

Set - collection of objects such that each object either exists or does not exist in the set (all are unique, no duplicates)

include - add to set

query - check if in set

remove - from set

Map

set - value from key (must check whether key already exists)

get - value from key

delete - by key

HashMap - most common way of implementing a Map

Stack

LIFO - Last In, First Out (considered unfair)

Similar to cafeteria trays

push/pop || shift/unshift - push/pop most common

Queue

FILO - First In, First Out (considered fair)

dequeueing - take object away from front of queue

enqueue -- add object ot end of queue

Similar to line at the register

push/shift || pop/unshift

Trees

Parent-child relationships where each child has at most 1 parent

Trees have directionality

Root/Base - single node with no children

Empty tree is still a tree!

Binary - max 2 children per node

Ternary - max 3 children per node

Unary - max 1 child per node (also called a Linked List)

Polytree / N-ary Tree - a tree with no guarantee of its number of children

Subtrees often named/referenced by root

Tree Traversal & Tree Searching Algorithms

Depth First Search (BFS) - use a Stack, recursion

Breadth First Search (DFS) - use a Queue, iterative

Very useful for predicting the outcome of a game/set of steps

Projects

PolyTreeNode class - a class for defining an uncapped number of children for a given node

@parent, @children, @value

@parent= - set new parent and update new & old parent as well as child's instance variables

add_child(child_node)

remove_child(child)

dfs(target_value) - Depth First tree searching algorithm to find a given child node

bfs(target_value) - Breadth First tree searching algorithm to find a given child node

Knight's Travails - find all the possible positions a knight can get to from a given starting position on a chess board. Find the shortest path to get from one tile to another.

Tic-Tac-Toe AI - Build an AI that can predict all possible winning/losing moves in a polytree, so that it always to chooses a move that will not allow it to lose. It's unbeatable!

Learnings

Traversing Trees is cool!!

Although technically Depth First Search visits & checks all of the leaves before the upper branches, it is more efficient to check a given node when you first reach it. So developers generally check a parent before all its children, even on its way down to the roots.

attr_accessor / attr_reader - make a setter & getter method for instance variables that have the same name as the instance variable.

public vs private

public methods are available to all objects of all classes

private methods - available only to objects of the same class

private instance variable methods -- vailable only to the object itself (cannot be called by different objects of the same class

class methods

defined as self.method_name

called as ClassName.method_name

Ampersand & in &prc is used to convert in both directions:

Block --> Proc

Proc --> Block

Generally used as method_name(&prc)

Exception Handling

begin

regular body of code

rescue OneTypeOfException

What to do for this exception

rescue AnotherTypeOfException

What to do for this type of exception

else

What to do for all all other exceptions

ensure

Will always be executed

end

Introduction

A very interesting problem is to find the diameter of a tree. The challenge is not in coding the algorithm but in understanding the meaning of the problem. We will try to define the problem so that visualizing the solution becomes easy.

Defining the problem – Tree Diameter

Few confusions about the diameter must be avoided before we start.

The tree diameter is always the distance…

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