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Chapter 8: Problem 3

In an average case involving an array of N elements, how many times will a linear search function have to read the array to locate a specific value?

Short Answer

Expert verified
Answer: On average, a linear search function will have to read the array (N + 1) / 2 times to locate a specific value in an array of N elements.

Step by step solution

01

Determine the number of comparisons in each case

For each element in the array, the number of comparisons required to find that element using a linear search will vary. In the best case, the first element is the target, and only 1 comparison is required. In the worst case, the last element is the target and N comparisons are required.
02

Calculate the average number of comparisons

To find the average number of comparisons, we need to add the number of comparisons for all cases and divide the total by the number of cases. The total number of comparisons in all cases is (1 + 2 + 3 + ... + N). Formula to calculate the sum of first N natural numbers is: SUM(N) = N * (N + 1) / 2 So, the total number of comparisons in all cases is: SUM(N) = N * (N + 1) / 2 Since there are N elements, the average number of comparisons needed to find a specific element using linear search is: Average Comparisons = SUM(N) / N = (N * (N + 1) / 2) / N By simplifying the expression, we get: Average Comparisons = (N + 1) / 2
03

Conclusion

On average, a linear search function will have to read the array (N + 1) / 2 times to locate a specific value in an array of N elements.

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Most popular questions from this chapter

What is the maximum number of comparisons that a binary search function will make when searching for a value in a 1,000-element array?

Why is the selection sort more efficient than the bubble sort on large arrays?

T F The average number of comparisons performed by the linear search on an array of N elements is N/2 (assuming the search values are consistently found).

The _________ search algorithm steps sequentially through an array, comparing each item with the search value.

If a linear search function is searching for a value that is stored in the last element of a 10,000-element array, how many elements will the search code have to read to locate the value?
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