Question

The following algorithm returns the boolean value true if the array has more than z elements equal to x and false otherwise. What is the time complexity of this algorithm?

a) O(z)
b) O(x)
c) O(n²)
d) O(n)

Answer 1

The algorithm's time complexity to check if there are more than z elements equal to x in an array is O(n), where n is the number of elements in the array.

Step-by-step explanation:

The time complexity of an algorithm that checks if an array has more than z elements equal to x is dependent on the number of elements in the array, and not on the values of x or z. The algorithm must potentially check each element in the array to see whether it is equal to x. Therefore, if the array has n elements, the algorithm has a time complexity of O(n), which corresponds to option d. This is because in the worst-case scenario, where x is not found or is found after checking all other elements, the algorithm will make n comparisons.