which of the following algorithims has the smallest time complexity
merge sort
binary search
insertion sort
linear search
The algorithm with the smallest time complexity among the options given is binary search. Its time complexity is O(log n), where n is the number of elements in the sorted array being searched. This time complexity is faster than the others: merge sort has a time complexity of O(n log n), insertion sort has a time complexity of O(n^2), and linear search has a time complexity of O(n).
The algorithm with the smallest time complexity from the given options is binary search.
To determine which algorithm has the smallest time complexity among merge sort, binary search, insertion sort, and linear search, we need to analyze the time complexity of each algorithm.
1. Merge Sort:
Time Complexity: O(n log n)
2. Binary Search:
Time Complexity: O(log n)
3. Insertion Sort:
Time Complexity: O(n^2)
4. Linear Search:
Time Complexity: O(n)
Comparing the time complexities, we can see that the smallest time complexity is O(log n), which belongs to the Binary Search algorithm. Therefore, Binary Search has the smallest time complexity among the given algorithms.