#### Study sets matching "binary trees"

#### Study sets matching "binary trees"

Binary Trees

Implementation Strategies

Node-and-link based

Array based

Order of 2

Node-and-link based; Array based

Implementation matches our conceptual picture of what a tree…

Implementation could use far too much space; store the root a…

Binary Trees

Order of 2

Implementation Strategies

Node-and-link based; Array based

Test a Binary Tree

Heap

Removal of item in Heap

Insert in a Heap

use In order traversal... after several deletions and insertions…

is a complete Binary Tree... it's root holds the Minimum element…

Remove Root node... replace Root with LIH(last in heap)... while(LI…

Insert into last space in heap or bottom... while (Node > paren…

Test a Binary Tree

use In order traversal... after several deletions and insertions…

Heap

is a complete Binary Tree... it's root holds the Minimum element…

LT and RT

Struct of Binary tree node

Height of a binary tree

Copy tree

Subtree names

Template <class elemType>... {... elemType info;... Struct binaryTreeN…

Count the nodes from the root to the lowest child

Shallow Copy of binary tree

LT and RT

Subtree names

Struct of Binary tree node

Template <class elemType>... {... elemType info;... Struct binaryTreeN…

public class BinaryTree<E> {

BinaryTree(){

BinaryTree(E item){

BinaryTree(E item, BinaryTree<E> left,…

protected E data;... protected BinaryTree<E> left,right;

data = null;... left = right = null;... }

data = item;... left = new BinaryTree<E>();... right = new Binary…

data = item;... this.left = left;... this.right = right;... }

public class BinaryTree<E> {

protected E data;... protected BinaryTree<E> left,right;

BinaryTree(){

data = null;... left = right = null;... }

Binary Tree

Root

Left subtree

Right subtree

Finite set of nodes that is either empty and consists of a ro…

The first node in a binary tree which contains two trees link…

A subtree on the left of its parent and has to be less than o…

A subtree that is larger than its parent tree.

Binary Tree

Finite set of nodes that is either empty and consists of a ro…

Root

The first node in a binary tree which contains two trees link…

Binary Search Tree

Root

Smaller

Larger

(what) are linked structures that are designed to address som…

The BST has a (what) node analogous to the head pointer in a…

Data in the BST is ordered such that the data in all children…

Data in the BST is ordered such that the data in all children…

Binary Search Tree

(what) are linked structures that are designed to address som…

Root

The BST has a (what) node analogous to the head pointer in a…

Tree

Binary Tree and it's major operations

preorder

postorder

empty, or it has a node called the root, followed by zero or…

preorder, inorder, postorder, level-order, height, and Size (…

left child, root, right child

children, then root

Tree

empty, or it has a node called the root, followed by zero or…

Binary Tree and it's major operations

preorder, inorder, postorder, level-order, height, and Size (…

root

children

leaf

subtree

The first node in a binary tree is called the _______.

A binary tree node's left and right pointers point to the nod…

A node with no children is called a(n) _____.

A(n) _______ is an entire branch of the tree, from one partic…

root

The first node in a binary tree is called the _______.

children

A binary tree node's left and right pointers point to the nod…

Tree

Nodes

edges

hierarchical structure

structure consist of nodes and edges that organize data in a…

where the data elements are stored

connects the nodes represents the relationship between the no…

resembles an upside down tree complete with branches leaves a…

Tree

structure consist of nodes and edges that organize data in a…

Nodes

where the data elements are stored

The element at the top of the hierarch…

Elements after a root node in the hier…

Elements after a child node in the hie…

Nodes that have no children are ______…

root

children

grandchildren

leaves

The element at the top of the hierarch…

root

Elements after a root node in the hier…

children

False

root pointer

True

nodes in a binary tree have two succes…

True/False: The number of nodes in a binary tree is the numbe…

The ________ in a binary tree is analogous to the head pointe…

True/False: A subtree is the collection of some node, togethe…

The main difference between a binary tree and a linked list i…

False

True/False: The number of nodes in a binary tree is the numbe…

root pointer

The ________ in a binary tree is analogous to the head pointe…

BST Operations:

Preorder Traversal:

Inorder Traversal:

Postorder Traversal:

contains... get... remove... add... reset... getNext... isEmpty... size

Root then Left then Right

Left then Root then Right

Left then Right then Root

BST Operations:

contains... get... remove... add... reset... getNext... isEmpty... size

Preorder Traversal:

Root then Left then Right

What kind of search is swift built-in…

What's the performance of binary search?

What's the downside of binary search?

What is the key property of binary sea…

In Swift, .indexOf() is linear search.

O(logn)

The array needs to be sorted.

Sorted. Left child always smaller than right child.

What kind of search is swift built-in…

In Swift, .indexOf() is linear search.

What's the performance of binary search?

O(logn)

binary trees

binary search trees

binary search trees time complexity

binary tree node

a nonlinear linked data structure in which each node may poin…

binary tree whose data is ordered to simplify searches... searc…

worst: O(n)... average: O(log2(n))... time slows down- searching f…

holds:... 1. the data (value field)... 2. a pointer to its left chi…

binary trees

a nonlinear linked data structure in which each node may poin…

binary search trees

binary tree whose data is ordered to simplify searches... searc…

Binary Tree

Children

Complete Tree

Full Tree

A data structure that consists of nodes, with one root node a…

The term used in binary trees to indicate a node that extends…

A binary tree in which there are no missing nodes when lookin…

A binary tree in which every level of the tree is completely…

Binary Tree

A data structure that consists of nodes, with one root node a…

Children

The term used in binary trees to indicate a node that extends…

B. binary search tree

A. length

B. depth

C. height

A __________ (with no duplicate elements) has the property th…

The ________ of a path is the number of the edges in the path.

The _______ of a node is the length of the path from the root…

The _______ of a nonempty tree is the length of the path from…

B. binary search tree

A __________ (with no duplicate elements) has the property th…

A. length

The ________ of a path is the number of the edges in the path.

There are n nodes in a tree. How many…

Run time for in order tree walk

Describe in order tree walk

Run time for tree search

n-1

theta(n). Every node is traversed once.

Print left subtree, node, and right subtree

order(h), where log(n) <= h <= n

There are n nodes in a tree. How many…

n-1

Run time for in order tree walk

theta(n). Every node is traversed once.

Advantage over Hash tables

How to represent an ordered map

Ordered map: Advantages = access

Ordered map: Disadvantages = insertion…

Hash tables are fast (on average) and quite useful, but they…

Two obvious choices are a sorted array (or arraylist) and a s…

Either representation will implement the operations (firstEnt…

Unfortunately, put and remove are O(n) time, because you need…

Advantage over Hash tables

Hash tables are fast (on average) and quite useful, but they…

How to represent an ordered map

Two obvious choices are a sorted array (or arraylist) and a s…

A collection of tree is called a _____…

A node with no children is called a __…

A node with no parent is called the __…

Is number 1 binary tree... FULL?... Complete?

Forest

Leaf

Root

Full = no... Complete = no

A collection of tree is called a _____…

Forest

A node with no children is called a __…

Leaf

Is number 8 a binary tree ?

How many BST can you make with the val…

Is number 7 a binary tree ?

Is number 9 a binary tree ?

- Yes... - With a height of 3

...

- Yes... - With a height of 0

- No... -With a height of 2

Is number 8 a binary tree ?

- Yes... - With a height of 3

How many BST can you make with the val…

...

True

False

False

False

In selection sort, the first step we locate the smallest item…

Insertion sort cannot be applied to linked lists

Mergesort and quicksort are similar in how they partition the…

In heapsort, only the elements at position 2k+1 are accessed…

True

In selection sort, the first step we locate the smallest item…

False

Insertion sort cannot be applied to linked lists

What is the primary characteristic of…

what are the values of interior nodes…

What are the values of the descendants…

What is the height of 7... -------(1)... ---…

The value, (or key depending on the implementation) of any no…

1 4 4 7 8 9

2 4 4 4 8 8 9

3 (the height of a node is the length of the longest downward…

What is the primary characteristic of…

The value, (or key depending on the implementation) of any no…

what are the values of interior nodes…

1 4 4 7 8 9

tree

parent node

child node

root

a set of one or more nodes, partitioned into root... node and su…

the node directly above node n in... the tree.

a node directly below node n in the tree.

the only node in the tree without a parent.

tree

a set of one or more nodes, partitioned into root... node and su…

parent node

the node directly above node n in... the tree.

sublinear

Search

Insertion

Deletion

Binary trees can be used for _______________ searching, inser…

_____________ algorithm:... if lower, go left... if higher, go righ…

_______________ algorithm... if lower, go left... if higher, go rig…

___________ algorithm... 1) search for n... case 0: n has 0 childre…

sublinear

Binary trees can be used for _______________ searching, inser…

Search

_____________ algorithm:... if lower, go left... if higher, go righ…

Number of children of each node

Leaf node

Strict/proper binary tree

Complete binary tree

Each node can have at most two children

A node with 0 child

Each node can have either 2 or 0 children

All levels except possible the last are completely filled and…

Number of children of each node

Each node can have at most two children

Leaf node

A node with 0 child

Binary search tree

Total order

Where can values go?

Searching for values

Binary tree in which the

**search property**holds on**every**n…order imposed on all elements (ex. inorder?)

Items can only go at bottom of tree

Begin at root; use search property of nodes to guide the sear…

Binary search tree

Binary tree in which the

**search property**holds on**every**n…Total order

order imposed on all elements (ex. inorder?)

Tree

Children

Level of a node

BST access time (avg case)

A nonlinear structure in which each node is capable of having…

Successor nodes to another node in a tree.

Distance from the root

O(logN)

Tree

A nonlinear structure in which each node is capable of having…

Children

Successor nodes to another node in a tree.

Advantage of binary search tree over b…

In java, what interface should you ext…

How to insert into BST?

How to delete from BST when two child…

Arrays have bad insertion and deletion but good search. With…

Extend Comparable interface to use compareTo method.

Compare element and traverse appropriate tree - left or right…

Travel down right subtree of node you want to delete until yo…

Advantage of binary search tree over b…

Arrays have bad insertion and deletion but good search. With…

In java, what interface should you ext…

Extend Comparable interface to use compareTo method.

What are the differences between a ful…

All nodes to the descendant left are _…

How is a pre-order traversal implement…

How is an in-order traversal implement…

Full - The last level is full... Complete - The next-to-last lev…

Left - Smaller... Right - Bigger

Root -> Left -> Right... !) Recurses whenever a new root node wi…

Left -> Root -> Right... !) Recurses whenever a new root node wi…

What are the differences between a ful…

Full - The last level is full... Complete - The next-to-last lev…

All nodes to the descendant left are _…

Left - Smaller... Right - Bigger

How does one enter a smaller node in a…

How does one enter a larger node in a…

What happens when you add a value to a…

What happens when you remove a value t…

to the left of the sub-tree

to the right of the sub-tree

every addition adds a new leaf to the tree on the right

It is just removed

How does one enter a smaller node in a…

to the left of the sub-tree

How does one enter a larger node in a…

to the right of the sub-tree

Definition

INSERT (x,k)

SEARCH

DELETION - x has no children

A binary rooted tree with, for y in left subtree and z in rig…

If x=NIL, then key[x]=k... Else, if k>key[x], then INSERT(right(…

If x=NIL, then return NOT-FOUND;... Else, if key[x]=k, then retu…

If it is left child of its parent p, then make left(p)=NIL... If…

Definition

A binary rooted tree with, for y in left subtree and z in rig…

INSERT (x,k)

If x=NIL, then key[x]=k... Else, if k>key[x], then INSERT(right(…

Balance Factor Equation

When is a tree unbalanced?

Describe a tree

The root is the only node at level __,…

bF = h ( Left subtree) - h (Right subtree)

BF > absvalue(1)

Set of nodes which is either ... A) empty ... B) consists of a node…

The root is the only node at level 0, and its depth is 0

Balance Factor Equation

bF = h ( Left subtree) - h (Right subtree)

When is a tree unbalanced?

BF > absvalue(1)

Tree

Nodes

Edges

Path

A data structure that uses nodes to hold data and edges to co…

The data field(s) in a tree.

The references to a node's child(ren).

The sequence of nodes that must be traveled to get from one n…

Tree

A data structure that uses nodes to hold data and edges to co…

Nodes

The data field(s) in a tree.

Preorder Traversal

Inorder Traversal

Postorder Traversal

Recursive Preorder

(i) Visit the root ... (ii) Traverse the left subtree... (iii) Trav…

(i) Traverse left subtree starting at the left external node…

(i) Traverse all left external nodes starting with the left m…

template <class ItemType>... void BST <ItemType>::preOrder(TreeN…

Preorder Traversal

(i) Visit the root ... (ii) Traverse the left subtree... (iii) Trav…

Inorder Traversal

(i) Traverse left subtree starting at the left external node…

Binary Search Tree Property

Representing Binary Search Trees

BST Search - Recursion

BST Search - While Loop

- nodes in left subtree have values <= current node's value... -…

class BST... int key... BST parent... BST left... BST right... public B…

Search (node, int k)... if (node == null)... return null // base…

Search (node, int k)... while (node != null && node.key != k)…

Binary Search Tree Property

- nodes in left subtree have values <= current node's value... -…

Representing Binary Search Trees

class BST... int key... BST parent... BST left... BST right... public B…

A __________ (with no duplicate elemen…

A _____ of a path is the number of the…

The _______ of a node is the length of…

the ______ of a nonempty tree is the l…

binary search tree

length

depth

height

A __________ (with no duplicate elemen…

binary search tree

A _____ of a path is the number of the…

length

Left subtree

Right subtree

No

Find operation

In a BST the smaller keyed node is in the...

In a BST the larger keyed node is in the...

Are duplicates allowed?

This operation is performed by repeatedly branching either le…

Left subtree

In a BST the smaller keyed node is in the...

Right subtree

In a BST the larger keyed node is in the...

in-order pseudo code

pre-order pseudo code

post-order pseudo code

pre-order diagram

sub TraverseRoutine(TreeNode)... If LeftPointer(TreeNode) != NU…

sub TraverseRoutine(TreeNode)... Output(TreeNode.value)... If Lef…

sub TraverseRoutine(TreeNode)... If LeftPointer(TreeNode) != NU…

in-order pseudo code

sub TraverseRoutine(TreeNode)... If LeftPointer(TreeNode) != NU…

pre-order pseudo code

sub TraverseRoutine(TreeNode)... Output(TreeNode.value)... If Lef…