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The average number of key comparisons required for a successful search for sequential search on items is
- a)n/2
- b)(n-1)/2
- c)(n+1)/2
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The average number of key comparisons required for a successful search...
If element is at i-th position where 1 <= i <= n, then we need i comparisons. So average number of comparisons is (1 + 2 + 3 + ..... n)/n = (n * (n + 1)/ 2) / n = (n + 1)/2
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Community Answer
The average number of key comparisons required for a successful search...
Understanding Sequential Search
Sequential search, also known as linear search, involves checking each element in a list one by one until the desired item is found. The average number of key comparisons for a successful search can be derived from basic principles of probability and counting.
Calculating Average Comparisons
- In a list of 'n' items, when searching for an item, there are 'n' possible positions where the item could be located.
- For a successful search, the item could be at any position in the list (1st, 2nd, ... nth).
- The average position of the item can be computed by considering the contributions from all positions:
Average Position Formula
- The average position (where the item is found) is given by the sum of all positions divided by the number of items:
(1 + 2 + 3 + ... + n) / n
- The sum of the first 'n' integers is n(n + 1)/2. Thus, the average position becomes:
n(n + 1)/(2n) = (n + 1)/2.
Conclusion
- Therefore, the average number of key comparisons required for a successful search in a sequential search is indeed (n + 1)/2.
- This result leads us to select option 'C' as the correct answer.
Key Takeaway
- Average comparisons for a successful search in sequential search: (n + 1)/2.
- This understanding helps in estimating the efficiency of search algorithms in data structures.
Sequential search, also known as linear search, involves checking each element in a list one by one until the desired item is found. The average number of key comparisons for a successful search can be derived from basic principles of probability and counting.
Calculating Average Comparisons
- In a list of 'n' items, when searching for an item, there are 'n' possible positions where the item could be located.
- For a successful search, the item could be at any position in the list (1st, 2nd, ... nth).
- The average position of the item can be computed by considering the contributions from all positions:
Average Position Formula
- The average position (where the item is found) is given by the sum of all positions divided by the number of items:
(1 + 2 + 3 + ... + n) / n
- The sum of the first 'n' integers is n(n + 1)/2. Thus, the average position becomes:
n(n + 1)/(2n) = (n + 1)/2.
Conclusion
- Therefore, the average number of key comparisons required for a successful search in a sequential search is indeed (n + 1)/2.
- This result leads us to select option 'C' as the correct answer.
Key Takeaway
- Average comparisons for a successful search in sequential search: (n + 1)/2.
- This understanding helps in estimating the efficiency of search algorithms in data structures.
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