SlideShare a Scribd company logo
Binary Tree Basics
Binary Tree Definition 
• Every node has at most two children a left 
child and a right child. 
• Root - the top most node in a tree.
A Basic Tree Structure
Leaf 
• A node having no child is a leaf.
Depth of a node 
• The length of the path from the root to the 
node. 
• Depth(root)=0
Height of the tree 
• The height of a node is the length of the 
longest downward path between the node 
and a leaf + 1. 
• The height of a node is the length of the 
longest downward path between the root and 
a leaf +1.
Depth and height
Full Binary Tree 
• Every node has 2 children except the leaves.
Complete Binary Tree 
• A complete binary tree is a binary tree in 
which every level, except possibly the last, is 
completely filled, and all nodes are as far left 
as possible.
• A fully complete binary tree has n nodes what 
is the height of the tree?
• A fully complete binary tree has n nodes what 
are the number of leaves in the tree?
Implementation
Search an element in binary tree
Sum of all the nodes of the tree
Inorder traversal 
• Visit the left subtree first 
• Visit the node. 
• Visit the right subtree.
Code
Postorder traversal 
• Visit the left subtree first 
• Visit the right subtree 
• Visit the node.
Preorder traversal 
• Visit the node. 
• Visit the left subtree first 
• Visit the right subtree.
Vector 
vector<int> a; 
a.push_back(value); 
cout<<a[i]<<endl; 
Accessing the pushed back value similar to an 
array.(REST READ FROM NET)
Oj.leetcode.com 
https://oj.leetcode.com/problems/binary-tree-postorder- 
traversal/ 
https://oj.leetcode.com/problems/binary-tree-preorder- 
traversal/ 
https://oj.leetcode.com/problems/balanced-binary- 
tree/ 
https://oj.leetcode.com/problems/balanced-binary- 
tree/
• https://oj.leetcode.com/problems/binary-tree-level- 
order-traversal/ 
• https://oj.leetcode.com/problems/binary-tree-level- 
order-traversal/ 
• https://oj.leetcode.com/problems/binary-tree-inorder- 
traversal/ 
• https://oj.leetcode.com/problems/construct-binary- 
tree-from-inorder-and-postorder-traversal/ 
• https://oj.leetcode.com/problems/construct-binary- 
tree-from-preorder-and-inorder-traversal/

More Related Content

Similar to Lecture 9: Binary tree basics

TREES34.pptx
TREES34.pptxTREES34.pptx
TREES34.pptx
BharathChalla5
 
Tree
TreeTree
Tree
sbkbca
 
Data structures 3
Data structures 3Data structures 3
Data structures 3
Parthipan Parthi
 
Data structure(Part 2)
Data structure(Part 2)Data structure(Part 2)
Data structure(Part 2)
SURBHI SAROHA
 
tree-160731205832.pptx
tree-160731205832.pptxtree-160731205832.pptx
tree-160731205832.pptx
MouDhara1
 
Tree.pptx
Tree.pptxTree.pptx
Tree.pptx
worldchannel
 
Module - 5_Trees.pdf
Module - 5_Trees.pdfModule - 5_Trees.pdf
Module - 5_Trees.pdf
AnuradhaJadiya1
 
358 33 powerpoint-slides_10-trees_chapter-10
358 33 powerpoint-slides_10-trees_chapter-10358 33 powerpoint-slides_10-trees_chapter-10
358 33 powerpoint-slides_10-trees_chapter-10
sumitbardhan
 
Binary tree
Binary treeBinary tree
Binary tree
MKalpanaDevi
 
Tree
TreeTree
DSA-Unit-2.pptx
DSA-Unit-2.pptxDSA-Unit-2.pptx
DSA-Unit-2.pptx
SeethaDinesh
 
Unit 5 Tree.pptx
Unit 5 Tree.pptxUnit 5 Tree.pptx
Unit 5 Tree.pptx
SurajSharma266169
 
Tree 11.ppt
Tree 11.pptTree 11.ppt
Tree 11.ppt
DEEPAK948083
 
Tree
TreeTree
Search tree,Tree and binary tree and heap tree
Search tree,Tree  and binary tree and heap treeSearch tree,Tree  and binary tree and heap tree
Search tree,Tree and binary tree and heap tree
zia eagle
 
Final tree.ppt tells about tree presentation
Final tree.ppt tells about tree presentationFinal tree.ppt tells about tree presentation
Final tree.ppt tells about tree presentation
nakulvarshney371
 
Trees
TreesTrees
BINARY SEARCH TREE
BINARY SEARCH TREEBINARY SEARCH TREE
BINARY SEARCH TREE
ER Punit Jain
 
trees in data structure
trees in data structure trees in data structure
trees in data structure
shameen khan
 
Tree
TreeTree

Similar to Lecture 9: Binary tree basics (20)

TREES34.pptx
TREES34.pptxTREES34.pptx
TREES34.pptx
 
Tree
TreeTree
Tree
 
Data structures 3
Data structures 3Data structures 3
Data structures 3
 
Data structure(Part 2)
Data structure(Part 2)Data structure(Part 2)
Data structure(Part 2)
 
tree-160731205832.pptx
tree-160731205832.pptxtree-160731205832.pptx
tree-160731205832.pptx
 
Tree.pptx
Tree.pptxTree.pptx
Tree.pptx
 
Module - 5_Trees.pdf
Module - 5_Trees.pdfModule - 5_Trees.pdf
Module - 5_Trees.pdf
 
358 33 powerpoint-slides_10-trees_chapter-10
358 33 powerpoint-slides_10-trees_chapter-10358 33 powerpoint-slides_10-trees_chapter-10
358 33 powerpoint-slides_10-trees_chapter-10
 
Binary tree
Binary treeBinary tree
Binary tree
 
Tree
TreeTree
Tree
 
DSA-Unit-2.pptx
DSA-Unit-2.pptxDSA-Unit-2.pptx
DSA-Unit-2.pptx
 
Unit 5 Tree.pptx
Unit 5 Tree.pptxUnit 5 Tree.pptx
Unit 5 Tree.pptx
 
Tree 11.ppt
Tree 11.pptTree 11.ppt
Tree 11.ppt
 
Tree
TreeTree
Tree
 
Search tree,Tree and binary tree and heap tree
Search tree,Tree  and binary tree and heap treeSearch tree,Tree  and binary tree and heap tree
Search tree,Tree and binary tree and heap tree
 
Final tree.ppt tells about tree presentation
Final tree.ppt tells about tree presentationFinal tree.ppt tells about tree presentation
Final tree.ppt tells about tree presentation
 
Trees
TreesTrees
Trees
 
BINARY SEARCH TREE
BINARY SEARCH TREEBINARY SEARCH TREE
BINARY SEARCH TREE
 
trees in data structure
trees in data structure trees in data structure
trees in data structure
 
Tree
TreeTree
Tree
 

More from Vivek Bhargav

Lecture 11.2 : sorting
Lecture 11.2 :  sortingLecture 11.2 :  sorting
Lecture 11.2 : sorting
Vivek Bhargav
 
Lecture 11.1 : heaps
Lecture 11.1 :  heapsLecture 11.1 :  heaps
Lecture 11.1 : heaps
Vivek Bhargav
 
Lecture 10 : trees - 2
Lecture 10 : trees - 2Lecture 10 : trees - 2
Lecture 10 : trees - 2
Vivek Bhargav
 
Lecture 7 & 8: Stack & queue
Lecture 7 & 8: Stack  & queueLecture 7 & 8: Stack  & queue
Lecture 7 & 8: Stack & queue
Vivek Bhargav
 
Lecture 6: linked list
Lecture 6:  linked listLecture 6:  linked list
Lecture 6: linked list
Vivek Bhargav
 
Lecture 5: Asymptotic analysis of algorithms
Lecture 5: Asymptotic analysis of algorithmsLecture 5: Asymptotic analysis of algorithms
Lecture 5: Asymptotic analysis of algorithms
Vivek Bhargav
 
Lecture 4: Functions
Lecture 4: FunctionsLecture 4: Functions
Lecture 4: Functions
Vivek Bhargav
 
Lecture 3: Strings and Dynamic Memory Allocation
Lecture 3: Strings and Dynamic Memory AllocationLecture 3: Strings and Dynamic Memory Allocation
Lecture 3: Strings and Dynamic Memory Allocation
Vivek Bhargav
 
Lecture 2: arrays and pointers
Lecture 2: arrays and pointersLecture 2: arrays and pointers
Lecture 2: arrays and pointers
Vivek Bhargav
 
Lecture 1: basic syntax
Lecture 1: basic syntaxLecture 1: basic syntax
Lecture 1: basic syntax
Vivek Bhargav
 

More from Vivek Bhargav (10)

Lecture 11.2 : sorting
Lecture 11.2 :  sortingLecture 11.2 :  sorting
Lecture 11.2 : sorting
 
Lecture 11.1 : heaps
Lecture 11.1 :  heapsLecture 11.1 :  heaps
Lecture 11.1 : heaps
 
Lecture 10 : trees - 2
Lecture 10 : trees - 2Lecture 10 : trees - 2
Lecture 10 : trees - 2
 
Lecture 7 & 8: Stack & queue
Lecture 7 & 8: Stack  & queueLecture 7 & 8: Stack  & queue
Lecture 7 & 8: Stack & queue
 
Lecture 6: linked list
Lecture 6:  linked listLecture 6:  linked list
Lecture 6: linked list
 
Lecture 5: Asymptotic analysis of algorithms
Lecture 5: Asymptotic analysis of algorithmsLecture 5: Asymptotic analysis of algorithms
Lecture 5: Asymptotic analysis of algorithms
 
Lecture 4: Functions
Lecture 4: FunctionsLecture 4: Functions
Lecture 4: Functions
 
Lecture 3: Strings and Dynamic Memory Allocation
Lecture 3: Strings and Dynamic Memory AllocationLecture 3: Strings and Dynamic Memory Allocation
Lecture 3: Strings and Dynamic Memory Allocation
 
Lecture 2: arrays and pointers
Lecture 2: arrays and pointersLecture 2: arrays and pointers
Lecture 2: arrays and pointers
 
Lecture 1: basic syntax
Lecture 1: basic syntaxLecture 1: basic syntax
Lecture 1: basic syntax
 

Recently uploaded

integral complex analysis chapter 06 .pdf
integral complex analysis chapter 06 .pdfintegral complex analysis chapter 06 .pdf
integral complex analysis chapter 06 .pdf
gaafergoudaay7aga
 
Data Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason WebinarData Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason Webinar
UReason
 
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURSCompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
RamonNovais6
 
Mechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdfMechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdf
21UME003TUSHARDEB
 
Curve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods RegressionCurve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods Regression
Nada Hikmah
 
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
Yasser Mahgoub
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
171ticu
 
Rainfall intensity duration frequency curve statistical analysis and modeling...
Rainfall intensity duration frequency curve statistical analysis and modeling...Rainfall intensity duration frequency curve statistical analysis and modeling...
Rainfall intensity duration frequency curve statistical analysis and modeling...
bijceesjournal
 
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
shadow0702a
 
An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...
IJECEIAES
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
KrishnaveniKrishnara1
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
kandramariana6
 
Welding Metallurgy Ferrous Materials.pdf
Welding Metallurgy Ferrous Materials.pdfWelding Metallurgy Ferrous Materials.pdf
Welding Metallurgy Ferrous Materials.pdf
AjmalKhan50578
 
Data Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptxData Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptx
ramrag33
 
ITSM Integration with MuleSoft.pptx
ITSM  Integration with MuleSoft.pptxITSM  Integration with MuleSoft.pptx
ITSM Integration with MuleSoft.pptx
VANDANAMOHANGOUDA
 
Properties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptxProperties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptx
MDSABBIROJJAMANPAYEL
 
Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...
IJECEIAES
 
CEC 352 - SATELLITE COMMUNICATION UNIT 1
CEC 352 - SATELLITE COMMUNICATION UNIT 1CEC 352 - SATELLITE COMMUNICATION UNIT 1
CEC 352 - SATELLITE COMMUNICATION UNIT 1
PKavitha10
 
Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...
Prakhyath Rai
 
Software Quality Assurance-se412-v11.ppt
Software Quality Assurance-se412-v11.pptSoftware Quality Assurance-se412-v11.ppt
Software Quality Assurance-se412-v11.ppt
TaghreedAltamimi
 

Recently uploaded (20)

integral complex analysis chapter 06 .pdf
integral complex analysis chapter 06 .pdfintegral complex analysis chapter 06 .pdf
integral complex analysis chapter 06 .pdf
 
Data Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason WebinarData Driven Maintenance | UReason Webinar
Data Driven Maintenance | UReason Webinar
 
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURSCompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
CompEx~Manual~1210 (2).pdf COMPEX GAS AND VAPOURS
 
Mechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdfMechanical Engineering on AAI Summer Training Report-003.pdf
Mechanical Engineering on AAI Summer Training Report-003.pdf
 
Curve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods RegressionCurve Fitting in Numerical Methods Regression
Curve Fitting in Numerical Methods Regression
 
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
 
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样官方认证美国密歇根州立大学毕业证学位证书原版一模一样
官方认证美国密歇根州立大学毕业证学位证书原版一模一样
 
Rainfall intensity duration frequency curve statistical analysis and modeling...
Rainfall intensity duration frequency curve statistical analysis and modeling...Rainfall intensity duration frequency curve statistical analysis and modeling...
Rainfall intensity duration frequency curve statistical analysis and modeling...
 
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
Use PyCharm for remote debugging of WSL on a Windo cf5c162d672e4e58b4dde5d797...
 
An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...An improved modulation technique suitable for a three level flying capacitor ...
An improved modulation technique suitable for a three level flying capacitor ...
 
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.pptUnit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
Unit-III-ELECTROCHEMICAL STORAGE DEVICES.ppt
 
132/33KV substation case study Presentation
132/33KV substation case study Presentation132/33KV substation case study Presentation
132/33KV substation case study Presentation
 
Welding Metallurgy Ferrous Materials.pdf
Welding Metallurgy Ferrous Materials.pdfWelding Metallurgy Ferrous Materials.pdf
Welding Metallurgy Ferrous Materials.pdf
 
Data Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptxData Control Language.pptx Data Control Language.pptx
Data Control Language.pptx Data Control Language.pptx
 
ITSM Integration with MuleSoft.pptx
ITSM  Integration with MuleSoft.pptxITSM  Integration with MuleSoft.pptx
ITSM Integration with MuleSoft.pptx
 
Properties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptxProperties Railway Sleepers and Test.pptx
Properties Railway Sleepers and Test.pptx
 
Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...Advanced control scheme of doubly fed induction generator for wind turbine us...
Advanced control scheme of doubly fed induction generator for wind turbine us...
 
CEC 352 - SATELLITE COMMUNICATION UNIT 1
CEC 352 - SATELLITE COMMUNICATION UNIT 1CEC 352 - SATELLITE COMMUNICATION UNIT 1
CEC 352 - SATELLITE COMMUNICATION UNIT 1
 
Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...Software Engineering and Project Management - Introduction, Modeling Concepts...
Software Engineering and Project Management - Introduction, Modeling Concepts...
 
Software Quality Assurance-se412-v11.ppt
Software Quality Assurance-se412-v11.pptSoftware Quality Assurance-se412-v11.ppt
Software Quality Assurance-se412-v11.ppt
 

Lecture 9: Binary tree basics