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TREESUSING DATA STRUCTURES

GROUP MEMBERS

AILANI SAGAR

RAMRAKHIANI ASHISH

PARMAR JATIN

GUWALANI JAIKUMAR

KUKREJA YASH

WANI PURSHOTTAM

MORE ABHISHEK

DEFINITIONA tree is a non-linear data structure that consists of a root node and many levels of additional nodes that form a hierarchy. A tree can be empty with no nodes called the null or empty tree or a tree is a structure consisting of one node called the root and one or more sub trees.

TreeNODESVERTICES

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FOR EG.

OPERATING SYSTEM OF A COMPUTER ORGANIZES FILES INTO DIRECTORIES AND SUB-DIRECTORIES.

DIRECTORIES ARE ALSO REFERED AS FOLDERS.OPERATING SYSTEM ORGANIZES FOLDERS AND FILES USING A TREE STRUCTURE.

A FOLDER CONTAINS OTHER FOLDERS(SUB-DIRECTORIES AND FILES)THIS CAN BE VIEWED AS TREE DRAWN BELOW..THE ROOT IS DESKTOP.

TERMINOLOGIES ROOT NODE :

ROOT NODEROOT NODE IS THE MOTHER NODE OF A TREE STRUCTURE. THIS NODE DOES NOT HAVE ANY PARENT. LEAF NODE : LEAF NODE IS A TERMINAL NODE OF A TREE. IT DOES NOT HAVE ANY NODES CONNECTED TO IT

LEAF NODES

A B C H E F G DTree DEGREE OF A NODE : THE NUMBER OF SUB TREES OF A NODE IS CALLED ITS DEGREE. DEGREE OF A TREE : THE DEGREE OF A TREE IS THE MAXIMUM DEGREE OF THE NODES IN THE TREE.DEGREE OF NODE IS 1DEGREE OF NODE IS 2 DEGREE OF NODE IS 3 DEGREE OF TREE IS 3

LEVEL : LEVEL IS A RANK OF TREE HIERARCHY. THE WHOLE TREE STRUCTURE IS LEVELED.LEVEL OF ROOT NODE IS 0.

G F C D B A ELEVEL OF NODE IS 0LEVEL OF NODE IS 1LEVEL OF NODE IS 2

PARENT NODE : IT IS A NODE HAVING OTHER NODES CONNECTED TO IT. THESE NODES ARE CALLED THE CHILDREN OF PARENT NODE. G F C D B A EA IS PARENT OF ALL NODES

B IS PARENT OF D AND E

HEIGHT OF A TREE : THE HIGHEST NO OF NODES THAT IS POSSIBLE IN A WAY STARTING FROM THE FIRST NODE TO A LEAF NODE IS CALLED THE HEIGHT OF A TREE. G F C D B A ELEVEL 0LEVEL 1LEVEL 2LEVEL 3HEIGHT OF TREE IS 4

PATH : A SEQUENCE OF CONSECUTIVE EDGES IS CALLED A PATH. G F C D B A EPATH FROM A TO EPATH FROM A TO G

FOREST : FOREST IS A SET OF SEVERAL TREES THAT ARE NOT LINKED TO EACH OTHER. SIBLINGS : CHILDREN OF THE SAME PARENT ARE CALLED SIBLINGS. G F C D B A E

B AND C ARE SIBLINGS.

D AND E ARE SIBLINGS.F AND G ARE SIBLINGS.

DESCENDENTS : THE CHILD, GRAND CHILD OR ANY CHILD DOWN TO HIERARCHY IS CALLED DESCENDENTS. G F C D B A EE, F AND G ARE GRAND CHILDS OF AB, C AND D ARE CHILDS OF ATHEREFORE B, C, D, E, F, G ARE DESCENDENTS

ANCESTORS : THE PARENT, GRAND FATHER, THE GREAT GRAND FATHER OF A NODE ARE CALLED ANCESTORS. G F C D B A EA IS GRAND PARENT OF D, E, F,GA IS PARENT OF B AND CA IS ANCESTORS OF ALL THE NODES.

TYPES OF TREES GENERAL TREE.

BINARY TREE.

STRICTLY BINARY TREE.

COMPLETE BINARY TREE.

EXTENDED BINARY TREE.

EXPRESSION TREE.

SKEWED TREE.

BINARY SEARCH TREE.

GENERAL TREE : A GENERAL TREE IS A TYPE OF TREE THAT DOESNOT HAVE ANY RESTRICTION ON IT. IT CAN HAVE ANY NO. OF CHILD NODES. G F C D B A E

A HAS THREE CHILDS B, C AND DTHEREFORE, THERE ARE NO RESTRICTIONS ON ITS NO. OF CHILD NODES.

BINARY TREE : THE TREE WHICH HAS A RESTRICTION OF HAVING ONLY 0, 1 OR 2 CHILD NODES IS CALLED A BINARY TREE. G F C D B A EA HAS RESTRICTION OF HAVING NOT MORE THAN TWO CHILD NODES.THEREFORE, IT IS A BINARY TREE.

STRICTLY BINARY TREE : THE BINARY TREE IN WHICH THE SUBTREE STARTS FROM WHERE THE NODE IS ENDED. F E C H B A G IT IS A STRICTLYBINARY TREE.

COMPLETE BINARY TREE : A BINARY TREE IN WHICH ALL THE LEAF NODES END AT THE SAME LEVEL IS CALLED COMPLETE BINARY TREE. G F C D B A EIT IS A COMPLETE BINARY TREEAS ALL THE NODES ARE COMPLETED ON SAME LEVEL

EXTENDED BINARY TREE : THE BINARY TREE IN WHICH ALL THE LEAF NODES ARE EXTENDED BY PUTTING A BOX. G F C D B A E

IT IS A EXTENDED BINARY TREE

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EXPRESSION TREE : WHEN ANY EXPRESSION IS REPRESENTED IS IN THE FORM OF THE TREE IS CALLED EXPRESSION TREE.

FOR EG: (A+B)*(C+D) D C + B + * AIT IS A EXPRESSION TREE

SKEWED TREE : THE BINARY TREE WHICH IS INCLINED ON ANY ONE SLIDE EITHER ON THE LEFT SIDE OR RIGHT SIDE IS CALLED SKEWED TREE F C H A F C H AIT IS LEFT SKEWED TREEIT IS RIGHT SKEWED TREE

BINARY SEARCH TREE : THE BINARY TREE IN WHICH CERTAIN RULES AND REGULATION ARE FOLLOWED IS KNOWN IS BINARY SEARCH TREE.

IN THIS TREE THE FIRST CHARACTER IS TAKEN AS ROOT NODE, THE CHARACTER SMALLER THAN ROOT NODE IS GIVEN THE LEFT POSITION FROM THE ROOT AND THE CHARACTER WHICH IS GREATER THAN ROOT NODE IS GIVEN THE RIGHT POSITION FROM THE NODE.

FOR EG. 10, 20, 05, 15, 25, 07, 03

051020

15250703SO, LETS SEE HOW IT WORKS.10, 20, 05, 15, 25, 07, 03

ARRAY REPRESENTATION OF BINARY TREE G F C E B A D

0

1

2

3

4

5

6ABCDEFG 0 1 2 3 4 5 6

LINK LIST REPRESENTATION OF BINARY TREE

A

C

B

D

E