How many comparisons does binary search make in the worst case for an array of s
Practice Questions
Q1
How many comparisons does binary search make in the worst case for an array of size 16?
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Questions & Step-by-Step Solutions
How many comparisons does binary search make in the worst case for an array of size 16?
Step 1: Understand what binary search is. It is a method to find an item in a sorted array by repeatedly dividing the search interval in half.
Step 2: Know the size of the array. In this case, the array size is 16.
Step 3: Use the formula for the worst-case number of comparisons in binary search, which is log2(n), where n is the size of the array.
Step 4: Calculate log2(16). Since 16 is 2 raised to the power of 4 (2^4 = 16), log2(16) equals 4.
Step 5: Remember that we start counting comparisons from 0. So, if log2(16) is 4, the total number of comparisons made is 4 + 1 = 5.
Binary Search – A search algorithm that finds the position of a target value within a sorted array by repeatedly dividing the search interval in half.
Logarithmic Complexity – The time complexity of binary search is O(log n), which indicates that the number of comparisons grows logarithmically with the size of the array.
Worst-Case Scenario – The maximum number of comparisons needed to find an element or determine its absence in the array.
