Question

The average successful search time for sequential search on ‘n’ items is
1. \(\frac{{\left( {n + 1} \right)}}{2}\)
2. \(\frac{n}{2}\)
3. \(\frac{{\left( {n - 1} \right)}}{2}\)
4. log(n) + 1

Answer 1

Correct Answer - Option 1 : \(\frac{{\left( {n + 1} \right)}}{2}\)

Consider items in an array

1

2

3

4

5

……

n

 

Assume 1 unit time is needed for 1 item comparison

Best case:

search 1 in a sequential manner:

Element is found for a single comparison

time take = 1

Worst case: 

search n+1 in a sequential manner:

Element is not found for n comparison

time take = n

Average time = \(\frac{best\;case\; time + worst \;case \;time}{2} = \frac{n+1}{2}\)

Therefore option 1 is correct