Time Complexity of an Algorithm

The time complexity of an algorithm is a measure of the amount of time it takes to run based on the input size. It helps in determining how the algorithm's performance scales with increasing input size. The worst-case time complexity represents the maximum amount of time the algorithm takes to run for any input of size 'n'.

Options for Worst-Case Time Complexity
The given options are:
a) O(1)
b) O(n)
c) O(n^2)
d) O(log n)

a) O(1)
An algorithm with a time complexity of O(1) means that its running time is constant, regardless of the input size. It implies that the algorithm takes the same amount of time to execute, regardless of the size of the input. This is the best-case scenario for time complexity.

b) O(n)
An algorithm with a time complexity of O(n) means that its running time is directly proportional to the input size 'n'. It implies that the algorithm's execution time increases linearly with the increase in input size. Although it is not the best-case scenario, it is still considered efficient.

c) O(n^2)
An algorithm with a time complexity of O(n^2) means that its running time is directly proportional to the square of the input size 'n'. It implies that the algorithm's execution time increases exponentially with the increase in input size. This is considered an inefficient scenario as the execution time grows rapidly as the input size increases.

d) O(log n)
An algorithm with a time complexity of O(log n) means that its running time increases logarithmically with the increase in input size 'n'. It implies that the execution time grows slowly even when the input size increases significantly. This is considered an efficient scenario.

Conclusion
The worst-case time complexity represents the maximum execution time an algorithm can have for any given input size. Among the provided options, O(n^2) has the highest growth rate and is considered the worst-case time complexity. As the input size increases, the execution time of an algorithm with O(n^2) complexity increases rapidly, making it inefficient for large input sizes.