# Hash Tables with Linear Probing Multiple Choice Questions and Answers (MCQs)

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This set of Data Structures & Algorithms Multiple Choice Questions & Answers (MCQs) focuses on “Hash Tables with Linear Probing”.

1. Which of the following problems occur due to linear probing?
a) Primary collision
b) Secondary collision
c) Separate chaining
d) Extendible hashing

Explanation: Primary collision occurs due to linear probing technique. It is overcome using a quadratic probing technique.

2. How many probes are required on average for insertion and successful search?
a) 4 and 10
b) 2 and 6
c) 2.5 and 1.5
d) 3.5 and 1.5

Explanation: Using formula, the average number of probes required for insertion is 2.5 and for a successful search, it is 1.5.

a) 1
b) 0.5
c) 1.5
d) 0

Explanation: The load factor for an open addressing technique should be 0.5. For separate chaining technique, the load factor is 1.
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4. Which of the following is not a collision resolution strategy for open addressing?
a) Linear probing
c) Double hashing
d) Rehashing

Explanation: Linear probing, quadratic probing and double hashing are all collision resolution strategies for open addressing whereas rehashing is a different technique.

5. In linear probing, the cost of an unsuccessful search can be used to compute the average cost of a successful search.
a) True
b) False

Explanation: Using random collision resolution algorithm, the cost of an unsuccessful search can be used to compute the average cost of a successful search.

6. Which of the following is the correct function definition for linear probing?
a) F(i)= 1
b) F(i)=i
c) F(i)=i2
d) F(i)=i+1

Explanation: The function used in linear probing is defined as, F(i)=I where i=0,1,2,3….,n.

7. ___________ is not a theoretical problem but actually occurs in real implementations of probing.
a) Hashing
b) Clustering
c) Rehashing
d) Collision

Explanation: Clustering is not a theoretical problem but it occurs in implementations of hashing. Rehashing is a kind of hashing.

8. What is the hash function used in linear probing?
a) H(x)= key mod table size
b) H(x)= (key+ F(i2)) mod table size
c) H(x)= (key+ F(i)) mod table size
d) H(x)= X mod 17

Explanation: The hash function used in linear probing is defined to be H(x)= (key+ F(i)) mod table size where i=0,1,2,3,…,n.

9. Hashing can be used in online spelling checkers.
a) True
b) False

Explanation: If misspelling detection is important, an entire dictionary can be pre-hashed and words can be checked in constant time.

10. In the following given hash table, use linear probing to find the location of 49.

 0 1 2 3 4 5 6 7 8 18 9 89

a) 7
b) 6
c) 2
d) 0

Explanation: Initially, collision occurs while hashing 49 for the first time.
Hence, after setting f(i)=1, the hashed location is found to be 0.

11. What is the formula to find the expected number of probes for an unsuccessful search in linear probing?
a) $$\frac{1}{2} \frac{1+1}{(1-⅄)}$$
b) $$\frac{1}{2}\frac{1+1}{(1-⅄)^2}$$
c) $$\frac{1}{2}\frac{1+1}{(1+⅄)}$$
d) $$\frac{1}{2}\frac{1+1}{(1+⅄)(1-⅄)}$$

Explanation: The mathematical formula for calculating the number of probes for an unsuccessful search is $$\frac{1}{2}\frac{1+1}{(1-⅄)^2}$$. For insertion, it is $$\frac{1}{2} \frac{1+1}{(1-⅄)}$$.

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