Final answer:
The worst-case runtime complexity refers to the growth of an algorithm's execution time with increasing input size and can vary from linear (O(n)) to quadratic (O(n^2)). Option O(n^2) typically represents the worst-case among the choices given, especially in scenarios involving nested iterations or comparison-based algorithms.
Step-by-step explanation:
The student has queried about the worst-case runtime complexity of a certain algorithm (represented as (x)). Runtime complexity is a concept from computer science that describes the amount of time an algorithm takes to complete as a function of the size of its input, which is usually denoted by n. In analyzing the complexities, we see the following:
- O(n) denotes a linear time complexity. Here, the time taken grows linearly with the input size. For example, a for-loop that goes through each element of an array once would have O(n) complexity.
- O(log n) indicates logarithmic time complexity, which is particularly efficient, as operations grow slower than linearly with the input size. Binary search is a common example of this.
- O(n log n) represents a time complexity that is a combination of linear and logarithmic behaviors. It is commonly seen in efficient sorting algorithms like quicksort or mergesort.
- O(n^2) denotes quadratic time complexity, which means that the time taken grows quadratically with the size of the input. Nested for-loops that iterate through an array are a classic example of this.
Without additional context about the nature of the algorithm (x), we cannot determine the exact worst-case runtime complexity. However, when considering the options provided, O(n^2) often represents the worst case among them, especially in terms of comparison-based algorithms where each element is compared to each other element.