Some Hashing Techniques
(used to randomize the relative addresses)
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Some Hashing Techniques
1. Prime Number Division
Remainder Method
2. Digit Extraction
3. Folding
4. Radix Conversion
5. Mid-Square
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Some Hashing Techniques
1. Prime Number Division
Remainder Method
2. Digit Extraction
3. Folding
4. Radix Conversion
5. Mid-Square
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Prime Number Division Remainder Method
• Similar with % (modulo or mod) function or the
integer division remainder method
• The key of the record is used to apply the hash
function
h(x) = x % PN
where x = primary key of the record
% = mod function
PN = prime number
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Some notes to ponder
1. Why do we use the modulo function
when we can choose any user-defined
function?
2. Why would we choose a prime number
when we can choose any positive integer
no.?
3. Is the hash function given as h(x) = x %
PN, the only function we can use?
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Prime Number Division Remainder Method
Notes:
1. Choose PN such that it is the largest among
the prime numbers based from the relative
positions. Why?
2. Relative positions are pre-defined by the
operating system (OS). But for purposes of
illustration, we shall adopt in our class that
our relative position could be any of the form
0..(N-1) positions.
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Just a simple mental exercise ...
Question:
If the relative positions are labelled as 1..10,
what would be the best choice for a prime
number? Justify your answer.
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Another simple mental exercise ...
Question:
If the relative positions are labelled as 1..99,
what would be the best choice for a prime
number? Justify your answer.
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Let’s try this ...
Assuming that there are 100 relative positions
labeled as 0..99, and suppose we have the
following key values: 24964, 25936, 32179,
39652, 40851, 53455, 53758, 54603, 63388,
81347
Questions:
1.Find the relative positions of these records
using the hashing strategy called prime
number division remainder method.
2.Determine the number of synonyms, if any.
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Answer
Key Values
Relative Positions
24964
25936
32179
39652
40851
53455
53758
54603
63388
81347
35
37
72
76
14
8
20
89
47
61
No. of Synonyms
0
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Some Hashing Techniques
1. Prime Number Division
Remainder Method
2. Digit Extraction
3. Folding
4. Radix Conversion
5. Mid-Square
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Digit Extraction
This technique is advisable to use if and
only if you have a prior knowledge in the
distribution or placement of digits within the
record’s primary key. Why?
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Digit Extraction
Algorithm:
1. Lay all the primary keys of all records to be
placed within the relative positions.
2. By cross examination, choose the positions or
columns of digits to be extracted.
3. The relative position of the record is the
concatenated digits from the chosen
columns.
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Let’s try this ...
Assuming that there are 100 relative positions
labeled as 0..99, and suppose we have the
following key values: 24964, 25936, 32179,
39652, 40851, 53455, 53758, 54603, 63388,
81347
Questions:
1. Find the relative positions of these records using
the hashing strategy called digit extraction. Let us
choose the positions of the chosen digits as the
5th and 3rd.
2. Determine the number of synonyms, if any.
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Answer
Key Values
Relative Positions
24964
25936
32179
39652
40851
53455
53758
54603
63388
81347
49
69
91
26
18
54
87
36
83
73
No. of Synonyms
0
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Some Hashing Techniques
1. Prime Number Division
Remainder Method
2. Digit Extraction
3. Folding
4. Radix Conversion
5. Mid-Square
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Folding
Algo:
1. Consider the key values as a sequence of
digits.
2. By “folding” the sequence of digits, we end
up as if we divide the digits into 2.
3. Add up the digits such that the first half of
the digits becomes the first addend while the
second half is composed of the digits
belonging to the other half.
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Let’s try this ...
Assuming that there are 100 relative positions
labeled as 0..99, and suppose we have the
following key values: 24964, 25936, 32179,
39652, 40851, 53455, 53758, 54603, 63388,
81347
Questions:
1. Find the relative positions of these records using
the hashing strategies called folding. Let us
assume that the demarcation line (or where the
folding is made) is after the 3rd digit.
2. Determine the number of synonyms, if any.
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Answer
Key Values
Relative Positions
24964
25936
32179
39652
40851
53455
53758
54603
63388
81347
13
95
0
48
59
89
95
49
21
60
No. of Synonyms
1
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Some Hashing Techniques
1. Prime Number Division
Remainder Method
2. Digit Extraction
3. Folding
4. Radix Conversion
5. Mid-Square
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Radix Conversion
Algorithm: (similar with conversion from one
number system to another number system)
1. With each digit in the primary key, multiply
each digit by powers of the chosen base
number (or radix). The exponent must start
from 0, and it increases as the number of
digits increases.
2. Take the sum of all the products.
3. The last 2 digits of the computed sum is the
relative address.
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Example
Assume that our radix is 8. The octal
number 12345, when converted to its base 10
will be computed as follows:
123458 = __________10
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Let’s try this ...
Assuming that there are 100 relative positions
labeled as 0..99, and suppose we have the
following key values: 24964, 25936, 32179,
39652, 40851, 53455, 53758, 54603, 63388,
81347
Questions:
1. Find the relative positions of these records using
the hashing strategies called radix conversion. Let
us assume that the radix is base 12.
2. Determine the number of synonyms, if any.
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Answer
Key Values
Relative Positions
24964
25936
32179
39652
40851
53455
53758
54603
63388
81347
56
50
1
86
57
5
40
59
36
3
No. of Synonyms
0
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Some Hashing Techniques
1. Prime Number Division
Remainder Method
2. Digit Extraction
3. Folding
4. Radix Conversion
5. Mid-Square
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Mid-Square
Algorithm:
As the name implies, the randomization is
done by taking the middle digits, then, square
the middle values. The result is the relative
address of the record.
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Point of Order
If the relative positions ranges from 0..99,
then take the last 2 digits of the result as the
relative address of the record.
Questions:
1. Why do we take the last 2 digits of the result as
the relative address of the record – why not the
first 2 digits or the middle digits, etc.?
2. If the relative positions are labelled as 0..999,
which digits of the result (of mid-square
operation) is considered as the relative address?
Why?
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Notes to Ponder
1. It is not advisable to get only one digit as the
middle number. Why?
2. If the number of digits in the key value is
even, which digit positions are considered as
the middle digits? Why?
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Let’s try this ...
Assuming that there are 100 relative positions
labeled as 0..99, and suppose we have the
following key values: 24964, 25936, 32179,
39652, 40851, 53455, 53758, 54603, 63388,
81347
Questions:
1. Find the relative positions of these records using
the hashing strategies called mid-square. Let us
take the 2nd up to 4th digits as our middle values.
2. Determine the number of synonyms, if any.
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Answer
Key Values
Relative Positions
24964
25936
32179
39652
40851
53455
53758
54603
63388
81347
16
49
89
25
25
25
25
0
44
56
3
No. of Synonyms
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That ends our discussion on the different
hashing techniques.
Are there questions?????
Coming up next … rehashing techniques
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