Consider a hash function as h(k) =k%7. The Data Values are 17,22,37 and 51. Identify the correct index value of 51 using Linear Probing.a.2b.3c.5d.4

To solve this problem, we first need to understand what the hash function h(k) = k%7 does. This function takes an input k and returns the remainder of k divided by 7. This is also known as the modulus operation.

Step 1: Apply the hash function to the data value 51. So, h(51) = 51 % 7 = 2. This means that the initial index for the value 51 would be 2.

Step 2: However, we are using linear probing to resolve collisions. This means that if an index is already occupied by another value, we move to the next index until we find an empty one.

Step 3: Check the data values 17, 22, and 37 to see if any of them also have an index of 2.

• h(17) = 17 % 7 = 3
• h(22) = 22 % 7 = 1
• h(37) = 37 % 7 = 2

Step 4: We see that the value 37 also has an index of 2. Therefore, when we try to insert 51, we find that index 2 is already occupied.

Step 5: Because we are using linear probing, we move to the next index, which is 3.

So, the correct index value of 51 using Linear Probing is 3. Therefore, the answer is b.3.