The worst-case complexity of binary search matches with
a) interpolation search
b) linear search
c) merge sort
d) none of the above
The correct answer and explanation is :
Correct Answer:
(c) Merge Sort
Explanation:
Binary search is an efficient searching algorithm that works by repeatedly dividing a sorted array into halves and comparing the middle element with the target value. The worst-case time complexity of binary search is O(log n).
To compare with other algorithms:
- Interpolation Search:
- Best case: O(1)
- Average case: O(log log n) (better than binary search in some cases)
- Worst case: O(n) (when the distribution of data is skewed)
- Since the worst case of interpolation search is O(n), it does not match with binary search.
- Linear Search:
- Best case: O(1) (when the element is found at the beginning)
- Average and worst case: O(n) (when the element is at the end or not present)
- Since O(n) ≠ O(log n), it does not match with binary search.
- Merge Sort:
- Merge Sort is a divide and conquer algorithm that recursively splits the array and then merges sorted subarrays.
- The time complexity is O(n log n) in all cases.
- While not an exact match, it follows a similar logarithmic division pattern like binary search, making it the closest match among the options.
- None of the Above:
- Since merge sort has a logarithmic factor similar to binary search, it is the closest match.
- Thus, the correct answer is Merge Sort (O(n log n)), rather than “None of the Above.”
Here is an image illustrating the worst-case time complexities of different search and sorting algorithms, including Binary Search, Interpolation Search, Linear Search, and Merge Sort.