1 Tables & File © Dave Bockus
19

# 1 Tables & File © Dave Bockus. 2 Binary Search Recursive int Bsearch(TableType T, KeyType key, int lt, int rt) { int mid; mid = (lt+rt)/2; if (lt>rt)

Mar 31, 2015

## Documents

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#### search set

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Transcript

1

Tables & File

2

Binary SearchRecursive

int Bsearch(TableType T, KeyType key, int lt, int rt) {

int mid;

mid = (lt+rt)/2;

if (lt>rt) //Search unsuccessful

return 0;

else if (T[mid]==key) //Search successful

return mid;

else if (T[mid]>key) //Search item < mid

return Bsearch(T,key,lt,mid-1);

else //Search item > mid

return Bsearch(T,key,mid+1,rt);

}

3

public static int binarySearch( Comparable [ ] a, Comparable x ) { int low = 0, high = a.length - 1; int mid; while( low <= high ){ mid = ( low + high ) / 2; if( a[ mid ].compareTo( x ) < 0 ) low = mid + 1; // Search lower partition else if( a[ mid ].compareTo( x ) > 0 ) high = mid - 1; // Search upper partition else return mid; // Found } return NOT_FOUND; // NOT_FOUND is defined as -1}

Binary SearchIterative

4

51

Binary Search Example

1 4 6 7 8 9 10 13 16 20

1 2 3 4 5 6 7 8 9 10

lt = rt = mid = 1 10

2 lt = rt = mid = 1 2

3 lt = rt = mid =

(Array[5] = 8) 7 so… continue(Array[2] = 4) 7 so… continue

4

43 3

(Array[3] = 6) 7 so ... continue

4 lt = rt = mid = 4

(Array[4] = 7) = 7 Found!!!!

4 4

5

Hashing - Chaining

88 75

64

28 41

38

62

3

49

93 54

6

88

75

64

28

41

38

62

3

49

93

54

7

Hashing - Double Hashing

88

75

64

28

41

38

62

3

49

93

54

8

Hashing - Internal Chaining

88 -1

75 -1

3

64 -1

28 -1

41 -1

0

38 -1

7

62 -1

4

3 -1

49 -1

5

93 -1

8

54 -1

9

9

Buckets

Hard Disks consist of platters of magnetic media

10

Buckets - Cont..

Tracks are written to the surface of the disk

11

Buckets - Cont..

Tracks are broken into sectors

12

Buckets - Cont..

Each Sector can have 1 or more blocks of data written to it.

When I/O is performed a block of data is transferred.

13

Buckets - Cont..

Each block can contain multiple records. When a block is read multiple records are pulled into memory

1 23 4 5 6

Block of data read into memory

14

Buckets - Cont..

When a bucket becomes full a pointer to an Overflow bucket tells the search algorithm where to look.

15

Extendible Hashing

• Suffix describes the element in the bucket

An index is broken into 2 sections

aaabbbbbb: aaa - bbbbbb

Prefix describes the index table

001000 010 011 100 101 110 111

bbbbbb bbbbbb bbbbbb bbbbbb bbbbbb

16

Extendible Hashing• As a bucket becomes full, the prefix is split.

• Assume key 000bbbbbb or 001bbbbbb is inserted causing the bucket to become full.

001000 010 011 100 101 110 111

bbbbbb bbbbbb bbbbbb bbbbbb bbbbbbbbbbbb

17

Extendible HashingIf the index can’t support another bucket, then the index is expanded to include another bit. aaaa-bbbbb

Assume key 000-bbbbbb is inserted, then index can’t support a split so the index must be expanded to 4 bits.

bbbbb bbbbb bbbbb bbbbb bbbbbbbbbbbbbbb

00100000 0100 0110 1000 1010 1100 1110…0001 0011 …

18

Hashing - Open Addressing & Deletions

88

75

64

28

41

38

62

3

49

93

54

Delete 75

1

Do a Search

Set Delete Flag

Search For 49

Search skips deleted cell

Continues until 49 is found

Adding a new value 16 => f(16)=1

16

Add value, if deleted remove delete flag.

Search for an empty or deleted cell.

19

Hashing - Internal Chaining& Deletions

88 -1

75 -1

3

64 -1

28 -1

41 -1

0

38 -1

7

62 -1

4

3 -1

49 -1

5

93 -1

8

54 -1

9

Assume 88 is deleted

1

Insert f(a) =1Delete flag is removed, a is inserted

10

a

Idx on 2 is updated

2

Internal chains coalesce

Insert f(b) =1

Search for an empty cell

b -1 Insert b into cell

Update Internal Chain

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