The minimum number of comparisons for a particular record among 32 sor...
Explanation:
To find the minimum number of comparisons for a particular record among 32 sorted records through binary search, we need to determine the maximum number of comparisons required.
Binary Search:
Binary search is a divide and conquer algorithm that works by repeatedly dividing the search interval in half. It starts by comparing the target value with the middle element of the sorted array. If the target value matches the middle element, the search is successful. If the target value is less than the middle element, the search continues on the lower half of the array. If the target value is greater than the middle element, the search continues on the upper half of the array. This process continues until the target value is found or the search interval is empty.
Maximum Number of Comparisons:
In binary search, the search interval is halved at each step. The maximum number of comparisons required to find a particular record can be determined by finding the height of the binary search tree.
- In the first comparison, we compare the target value with the middle element of the array.
- If the target value is less than the middle element, we divide the search interval into two halves. The next comparison will be made with the middle element of one of the halves.
- Each subsequent comparison divides the search interval into half until the target value is found or the search interval is empty.
Height of Binary Search Tree:
The height of a binary search tree with n nodes is given by h = log2(n+1) - 1.
For 32 sorted records, the height of the binary search tree would be:
h = log2(32+1) - 1
= log2(33) - 1
= 5 - 1
= 4
Minimum Number of Comparisons:
The minimum number of comparisons required to find a particular record is equal to the height of the binary search tree. In this case, the height is 4.
Therefore, the minimum number of comparisons for a particular record among 32 sorted records through binary search method will be 4, which corresponds to option 'B'.
The minimum number of comparisons for a particular record among 32 sor...
Concept:
Binary search: Binary search follows the divide and conquer approach. To search for an element, first find the middle element, if a match found, then return the location. Otherwise, if the element is less than the middle element search will proceed in the left half, else the search will proceed into the right half.
Explanation:
Recurrence relation for binary search :
T(n) = T(n/2) + 1
Time Complexity of this algorithm: O(log2n)
Here, we have to apply the binary search on 32 elements. So, it will take log232 = 5 comparisons to search for the element.