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

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.

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

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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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

Step by step solution

Determine the number of comparisons in each case

Calculate the average number of comparisons

Conclusion

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