avl tree deletion

8/12/2019 AVL Tree Deletion

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Hash,

AVL Tree/ Binary Tree deletion and

Graph Creation


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What is a Hash Table ?

The simplest kind of hash

table is an array of records.

This example has 701records.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]

An array of records

. . .

[ 700]


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Each record has a special

field, called its key.

In this example, the key is a

long integer field called

Number.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]

. . .

[ 700]

Number 506643548


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The number might be a

person's identification

number, and the rest of the

record has informationabout the person.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ]

. . .

[ 700]

Number 506643548


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When a hash table is in use,

some spots contain valid

records, and other spots are

"empty".

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]

Number 506643548Number 233667136Number 281942902

Number 155778322

. . .


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Inserting a New Record

In order to insert a new

record, the keymust

somehow be converted to

an array index.

The index is called the hash

value of the key.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .

Number 580625685


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Typical way create a hash

value:

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .

Number 580625685

(Number mod 701)

What is (580625685 mod 701) ?


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Typical way to create a hash

value:

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .

Number 580625685

(Number mod 701)

What is (580625685 mod 701) ?3


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The hash value is used for

the location of the new

record.

Number 580625685

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .

[3]


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The hash value is used for

the location of the new

record.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685


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Collisions

Here is another new record

to insert, with a hash value

of 2.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685

Number 701466868

My hash

value is [2].


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Collisions

This is called a collision,

because there is already

another valid record at [2].

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685

Number 701466868

When a collision occurs,

move forward until you

find an empty spot.


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Collisions




[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685

Number 701466868



find an empty spot.


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Collisions




[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685

Number 701466868



find an empty spot.


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Collisions




[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

The new record goes

in the empty spot.


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Searching for a Key

The data that's attached to

a key can be found fairly

quickly.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

Number 701466868


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Searching for a Key

Calculate the hash value.

Check that location of the array

for the key.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

Number 701466868

My hash

value is [2].

Not me.


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Searching for a Key

Keep moving forward until you

find the key, or you reach an

empty spot.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

Number 701466868

My hash

value is [2].

Not me.


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Searching for a Key



empty spot.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

Number 701466868

My hash

value is [2].

Not me.


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Searching for a Key



empty spot.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

Number 701466868

My hash

value is [2].

Yes!


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Searching for a Key

When the item is found, the

information can be copied to

the necessary location.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

Number 701466868

My hash

value is [2].

Yes!


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Deleting a Record

Records may also be deleted from a hash table.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]


Number 155778322

. . .Number 580625685 Number 701466868

Please

delete me.


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Deleting a Record


But the location must not be left as an ordinary

"empty spot" since that could interfere with

searches.

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]Number 233667136Number 281942902

Number 155778322

. . .Number 580625685 Number 701466868


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Deleting a Record

[ 0 ] [ 1 ] [ 2 ] [ 3 ] [ 4 ] [ 5 ] [ 700]Number 233667136Number 281942902

Number 155778322

. . .Number 580625685 Number 701466868


But the location must not be left as an ordinary

"empty spot" since that could interfere with

searches.

The location must be marked in some special way so

that a search can tell that the spot used to have

something in it.


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Binary Tree Deletion


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DELETING IN AVL TREES:


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-2, -1, 0, +1, +2

-- , - , 0, +, ++


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Adjacency Matrix

1

2

3

04

0 1 2 3 4

0 false false true false false

1 false false false true false

2 false true false false true

3 false false false false false

4 false false false true false


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Adjacency Matrix

Can be implemented with a two-dimensional

array, e.g.:

boolean[][] adjMatrix;adjMatrix = new boolean[5][5];


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Edge Lists

Graphs can also be represented by creating

a linked list for each vertex

1

2

3

04

2

null

0

3

null

1

1

2

4

null

For each entry J in listnumber I, there is an edgefrom I to J.


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Thank You

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