In the decrease by a constant approach, the problem size is reduced by a constant amount in each step. What is the time complexity of this approach?

The correct answer is O(n).

Key Points

• In the decrease by a constant approach, the size of the problem is reduced by a fixed constant amount (e.g., reducing a problem size of n to n - k, where k is a constant).
• For each step of the algorithm, the size of the problem decreases linearly, and the process repeats until the problem size becomes zero or some base case is reached.
• This means the number of steps required is proportional to the size of the input n.
• As the algorithm involves a linear number of steps, the time complexity is O(n).

Additional Information

• Examples of algorithms that use the decrease by a constant approach include linear search or algorithms that iterate through an array with a fixed step size.
• It contrasts with the divide-and-conquer approach, where the problem size is reduced by a fraction (e.g., halving the size).
• This approach is simple and effective for many problems but may not be optimal for larger inputs compared to logarithmic or sub-linear approaches.