Final answer:
To find the value 86 in the given list using a binary search, it would take approximately 7 comparisons.
To determine the number of comparisons needed to find the value 86 with binary search, the formula to use is log₂(n) + 1, assuming the list is sorted. The exact number of comparisons cannot be determined without the list size, but for a given size, the calculations could be performed.
Step-by-step explanation:
To find the value 86 in a list using a binary search, the number of comparisons necessary depends on the size of the list. In a binary search, the list is divided into two halves and the middle element is compared to the target value. If the middle element is greater than the target value, the search continues in the left half of the list. If the middle element is smaller, the search continues in the right half.
Since a binary search divides the list in half at each step, each comparison eliminates half of the remaining elements. If the list has N elements, it would take log2(N) comparisons to find the value using a binary search. In this case, if the list has 100 elements, it would take log2(100) = 6.64, which can be rounded up to 7 comparisons to find the value 86.
To determine the number of comparisons needed to find the value 86 with binary search, the formula to use is log₂(n) + 1, assuming the list is sorted. The exact number of comparisons cannot be determined without the list size, but for a given size, the calculations could be performed.
To find the value 86 in a list using binary search, the list must first be sorted. Binary search compares the target value to the middle element of the list. If the target value is higher or lower, it halves the list and continues the search on the relevant half. This process repeats until the value is found or the list cannot be halved further.
The number of comparisons needed in a binary search can be determined by the formula =log₂(n) + 1, where n is the number of items in the list. Without knowing the exact size of the list in the question, we can't give a precise number of comparisons needed to find the value 86; however, if we assume a specific list size, we can calculate an example.