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What is the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n?
- a)Θ(√n)
- b)Θ(log2(n))
- c)Θ(n2)
- d)Θ(n)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
What is the worst-case number of arithmetic operations performed by re...
Worst-case number of arithmetic operations in recursive binary search:
Binary search is a divide and conquer algorithm that searches for a target value within a sorted array. In the worst-case scenario, the target value is not present in the array, leading to the maximum number of comparisons.
Reasoning:
- In each recursive call of binary search, the array is divided into two halves.
- This process continues until the target value is found or the subarray size becomes 0.
- In the worst-case scenario, the target value is not present in the array, and the recursion reaches the base case with a single element or an empty subarray.
Analysis:
- At each step of the recursion, the algorithm performs a constant number of arithmetic operations to calculate the mid-point and compare the target value.
- The number of recursive calls required to reduce the array size to 1 in the worst-case scenario is logarithmic with respect to the size of the array (log2(n)).
- Hence, the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n is Theta(n) due to Theta(n) comparisons in the worst case.
Therefore, the correct answer is option 'C' - Theta(n^2).
Binary search is a divide and conquer algorithm that searches for a target value within a sorted array. In the worst-case scenario, the target value is not present in the array, leading to the maximum number of comparisons.
Reasoning:
- In each recursive call of binary search, the array is divided into two halves.
- This process continues until the target value is found or the subarray size becomes 0.
- In the worst-case scenario, the target value is not present in the array, and the recursion reaches the base case with a single element or an empty subarray.
Analysis:
- At each step of the recursion, the algorithm performs a constant number of arithmetic operations to calculate the mid-point and compare the target value.
- The number of recursive calls required to reduce the array size to 1 in the worst-case scenario is logarithmic with respect to the size of the array (log2(n)).
- Hence, the worst-case number of arithmetic operations performed by recursive binary search on a sorted array of size n is Theta(n) due to Theta(n) comparisons in the worst case.
Therefore, the correct answer is option 'C' - Theta(n^2).
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Community Answer
What is the worst-case number of arithmetic operations performed by re...
Arithmetic operations performed by binary search on sorted data items means computation of mid element required arithmetic operation. So it will be computed log(n) time and Hence option (C) will be correct.
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