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Prepared by Perla P. Cosme 2
Some Hashing Techniques
1. Prime Number Division Remainder Method
2. Digit Extraction3. Folding4. Radix Conversion5. Mid-Square
Prepared by Perla P. Cosme 3
Some Hashing Techniques
1. Prime Number Division Remainder Method
2. Digit Extraction3. Folding4. Radix Conversion5. Mid-Square
Prepared by Perla P. Cosme 4
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
where x = primary key of the record % = mod function
PN = prime number
h(x) = x % PN
Prepared by Perla P. Cosme 5
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?
Prepared by Perla P. Cosme 6
Prime Number Division Remainder MethodNotes: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.
Prepared by Perla P. Cosme 7
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.
Prepared by Perla P. Cosme 8
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.
Prepared by Perla P. Cosme 9
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.
Prepared by Perla P. Cosme 10
AnswerKey Values Relative Positions
24964 3525936 3732179 7239652 7640851 1453455 853758 2054603 8963388 4781347 61
No. of Synonyms 0
Prepared by Perla P. Cosme 11
Some Hashing Techniques
1. Prime Number Division Remainder Method
2. Digit Extraction3. Folding4. Radix Conversion5. Mid-Square
Prepared by Perla P. Cosme 12
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?
Prepared by Perla P. Cosme 13
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.
Prepared by Perla P. Cosme 14
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.
Prepared by Perla P. Cosme 15
Answer
Key Values Relative Positions
24964 4925936 6932179 9139652 2640851 1853455 5453758 8754603 3663388 8381347 73
No. of Synonyms 0
Prepared by Perla P. Cosme 16
Some Hashing Techniques
1. Prime Number Division Remainder Method
2. Digit Extraction3. Folding4. Radix Conversion5. Mid-Square
Prepared by Perla P. Cosme 17
FoldingAlgo: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.
Prepared by Perla P. Cosme 18
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.
Prepared by Perla P. Cosme 19
Answer
Key Values Relative Positions
24964 1325936 9532179 039652 4840851 5953455 8953758 9554603 4963388 2181347 60
No. of Synonyms 1
Prepared by Perla P. Cosme 20
Some Hashing Techniques
1. Prime Number Division Remainder Method
2. Digit Extraction3. Folding4. Radix Conversion5. Mid-Square
Prepared by Perla P. Cosme 21
Radix ConversionAlgorithm: (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.
Prepared by Perla P. Cosme 22
Example
Assume that our radix is 8. The octal number 12345, when converted to its base 10 will be computed as follows:
123458 = __________10
Prepared by Perla P. Cosme 23
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.
Prepared by Perla P. Cosme 24
Answer
Key Values Relative Positions
24964 5625936 5032179 139652 8640851 5753455 553758 4054603 5963388 3681347 3
No. of Synonyms 0
Prepared by Perla P. Cosme 25
Some Hashing Techniques
1. Prime Number Division Remainder Method
2. Digit Extraction3. Folding4. Radix Conversion5. Mid-Square
Prepared by Perla P. Cosme 26
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.
Prepared by Perla P. Cosme 27
Point of OrderIf 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?
Prepared by Perla P. Cosme 28
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?
Prepared by Perla P. Cosme 29
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.
Prepared by Perla P. Cosme 30
Answer
Key Values Relative Positions
24964 1625936 4932179 8939652 2540851 2553455 2553758 2554603 063388 4481347 56
No. of Synonyms 3