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Some Hashing Techniques (used to randomize the relative addresses) Prepared by Perla P. Cosme 1 Some Hashing Techniques 1. Prime Number Division Remainder Method 2. Digit Extraction 3. Folding 4. Radix Conversion 5. Mid-Square Prepared by Perla P. Cosme 2 Some Hashing Techniques 1. Prime Number Division Remainder Method 2. Digit Extraction 3. Folding 4. Radix Conversion 5. Mid-Square Prepared by Perla P. Cosme 3 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 Prepared by Perla P. Cosme 4 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 5 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. Prepared by Perla P. Cosme 6 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 7 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 8 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 9 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 Prepared by Perla P. Cosme 10 Some Hashing Techniques 1. Prime Number Division Remainder Method 2. Digit Extraction 3. Folding 4. Radix Conversion 5. Mid-Square Prepared by Perla P. Cosme 11 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 12 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 13 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 14 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 Prepared by Perla P. Cosme 15 Some Hashing Techniques 1. Prime Number Division Remainder Method 2. Digit Extraction 3. Folding 4. Radix Conversion 5. Mid-Square Prepared by Perla P. Cosme 16 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. Prepared by Perla P. Cosme 17 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 18 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 Prepared by Perla P. Cosme 19 Some Hashing Techniques 1. Prime Number Division Remainder Method 2. Digit Extraction 3. Folding 4. Radix Conversion 5. Mid-Square Prepared by Perla P. Cosme 20 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. Prepared by Perla P. Cosme 21 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 22 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 23 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 Prepared by Perla P. Cosme 24 Some Hashing Techniques 1. Prime Number Division Remainder Method 2. Digit Extraction 3. Folding 4. Radix Conversion 5. Mid-Square Prepared by Perla P. Cosme 25 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 26 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? Prepared by Perla P. Cosme 27 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 28 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 29 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 Prepared by Perla P. Cosme 30 That ends our discussion on the different hashing techniques. Are there questions????? Coming up next … rehashing techniques Prepared by Perla P. Cosme 31