Question

Hashing can best be compared to the index of a book. You look up a key word or phrase, and the index gives you what page to look at. But when you get to the page, you may have to do a little more scanning until you actually find the word. A little work, but better than scanning from the start of the book to the end.

So, for this discussion, in your own words, explain how hashing works when used to find an item in a list. Make sure to include how the hash key is created and what happens if something is already in that hash location. Please write at least 200 words.

Answer 1

Hashing is a data structure which has a hash function to map the values to the hash table. As mentioned hashing is quite similar to a book index. Using hash function we will be calculating index for each value and can be stored in that particular index of hash table.

Hash function is basically denoted with H(x) where x is the value to be stored in hash table and the function can be user defined also.

For example, H(x)=x%10 and (21,22,23,24,25,26,27,28,29,30) are the list of values. To store these values into the hash table we should know at what positions to insert. So for calculating use the hash function, H(x)=H(21)=21%10=1

22%10=2

23%10=3

24%10=4

25%10=5

26%10=6

27%10=7

28%10=8

29%10=9

30%10=0

So {1,2,3,4,5,6,7,8,9,0} are the respective positions to store the list of values.

If the two or more values get the same index then collision occurs because the first value will be stored in the index and the second value which is having same index cannot be stored in that position since it is already occupied.

So to avoid these type of collisions we have some collision resolution methods :

• Linear probing
• Quadratic probing
• Double hashing
• Chaining method

And few more methods to avoid the collision for keys in the hash table. Here I'm putting it in a simplified way for better understanding.

Linear probing is a division hash method as mentioned above with adding a integer to the key value as h(x)=(h(x)+t) %k where t=1,2,3,.... and k is size of the hash table.

For quadratic probing the hash function is h(x)= (h(x)+t²)%k where t²=1²,2²,3³,..... and k is the size of hash table.