# TCS Papers: Sample Questions 372 - 372 of 502

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## Question number: 372

Essay Question▾

### Describe in Detail

Classify the hashing functions based on the various methods by which the key value is found.

### Explanation

There are 7 hashing functions based on how key value is found.

• Direct Method

• Key is the address without algorithmic manipulation

• Data structure contains element for possible key

• Example problems

• To analyze total monthly sales by days of month

• For each sale we need date and amount of sale

• To calculate sales record for month, we need day of month as key for array and add sales amount to accumulator

• Daily Sales [Sale Day] = Daily Sales [Sale Day] + Sale Amount

• Subtraction Method

• Direct and subtraction hash functions guarantee search effort without no collisions

• In one to one hashing method only one key hashes to each address

• Example

• Company has 100 employees, employee number starts from 1001 to 1100

• Hashing function subtracts 1000 from key to determine address

• Modulo-Division Method

• Divides the key by array size and use remainder for address

• Algorithm works with any list size, but a prime number produces fewer collisions

• Address = key MODULO list Size

• Digit-Extraction Method

• Digits are extracted from key and used as address

• Example:

• Six-digit employee number is used to hash three digit address (000 - 999)

• For example, select first, third, and fourth digits as key

• 379452 - 394

• 121267 - 112

• 378845 - 388

• 160252 - 102

• 045128 - 051

• Mid-square Method

• Key is squared and the address is selected from the middle of the squared number

• Example

• Given a key of 9452, midsquare address calculation is shown using four digit address (0000 - 9999)

• Select first three digits and then use midsquare method

• 379452: 3792 = 143641 - 364

• 121267: 1212 = 014641 - 464

• 378845: 3782 = 142884 - 288

• 160252: 1602 = 025600 - 560

• 045128: 0452 = 002025 - 202

• Folding Method

• Two folding methods

• Fold shift

• Fold boundary

• Fold shift key value is divided into parts whose size matches size of required address

• Left and right parts are shifted and added with middle part

• In fold boundary, left and right numbers are folded on a fixed boundary between them and the center number

• Pseudo-random Method

• Key is used as seed in pseudorandom number generator and the random number is scaled into possible address range using modulo-division.

• A common random number generator is y = ax + c

• Example

• Assume a = 17, c = 7, x = 121267, Prime number = 307

• y= ( (17 * 121267) + 7) modulo 307

• y= (2061539 + 7) modulo 307

• y = 2061546 modulo 307

• y = 41