which of the following Determine the time and space complexities of a linear search.
Time complexity :O(log(n)) Space complexity O(n)
Time complexity :O(n) Space complexity O(log(n))
Time complexity :O(n) Space complexity O(n)
Time complexity O(log(n)) Space complexity O(log(n))
The correct answer is:
Time complexity :O(n) Space complexity O(1)
To determine the time and space complexities of a linear search, we need to analyze the characteristics of the algorithm.
A linear search is a simple algorithm that sequentially checks each element in a list or array until it finds the desired value or reaches the end of the list. The time complexity measures how the algorithm's runtime increases as the input size (n) grows. The space complexity measures how much additional memory the algorithm needs as the input size grows.
From the given options:
Option 1: Time complexity: O(log(n)), Space complexity: O(n)
Option 2: Time complexity: O(n), Space complexity: O(log(n))
Option 3: Time complexity: O(n), Space complexity: O(n)
Option 4: Time complexity: O(log(n)), Space complexity: O(log(n))
To determine the time complexity of a linear search, we can observe that in the worst-case scenario, the algorithm may need to traverse the entire list or array, giving us a time complexity of O(n). Therefore, options 1 and 4 can be eliminated since they have a time complexity of O(log(n)).
Regarding the space complexity, a linear search does not require any additional memory proportional to the input size. It only needs a few variables to store intermediate values, resulting in a space complexity of O(1) or constant.
None of the given options match the correct time and space complexities for a linear search. The correct answer for a linear search would be:
Time complexity: O(n)
Space complexity: O(1)
The correct answer is:
Time complexity: O(n)
Space complexity: O(1)
Explanation:
In a linear search, the algorithm iterates through each element in the given list/array until it finds the target value or reaches the end. Therefore, the time complexity of a linear search is proportional to the number of elements in the list, denoted as O(n).
The space complexity of a linear search is constant, denoted as O(1), because it does not require any additional space that grows based on the input size. Only a few variables are needed to keep track of the current position and compare the elements in the list.