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1 Tables & File © Dave Bockus

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2 Binary Search Recursive 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); }

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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 Search Iterative

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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 2lt =rt =mid = 1 2 3lt =rt =mid = (Array[5] = 8) 7 so… continue (Array[2] = 4) 7 so… continue 4 4 3 3 (Array[3] = 6) 7 so... continue 4lt =rt =mid = 4 (Array[4] = 7) = 7 Found!!!! 4 4

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5 Hashing - Chaining 887564284138623 49 9354

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6 Hashing - Open Addressing 88 75 64 28 41 38 62 3 49 93 54

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7 Hashing - Double Hashing 88 75 64 28 41 38 62 3 49 93 54

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8 Hashing - Internal Chaining 88 75 3 64 28 41 0 38 7 62 4 3 49 5 93 8 54 9

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9 Buckets Hard Disks consist of platters of magnetic media

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10 Buckets - Cont.. Tracks are written to the surface of the disk

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11 Buckets - Cont.. Tracks are broken into sectors

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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.

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13 Buckets - Cont.. Each block can contain multiple records. When a block is read multiple records are pulled into memory 1 2 3 4 5 6 Block of data read into memory

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

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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 001000010011100101110111 bbbbbb

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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. 001000010011100101110111 bbbbbb

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17 Extendible Hashing If the index cant support another bucket, then the index is expanded to include another bit. aaaa-bbbbb Assume key 000-bbbbbb is inserted, then index cant support a split so the index must be expanded to 4 bits. bbbbb 00100000010001101000101011001110 … 00010011 …

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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.

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19 Hashing - Internal Chaining & Deletions 88 75 3 64 28 41 0 38 7 62 4 3 49 5 93 8 54 9 Assume 88 is deleted 1 Insert f(a) =1 Delete 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 Insert b into cell Update Internal Chain

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