Rec_9
For the worst case : what is the run time complexity of the find_min function below

Question

BlackTom AI · Accepted Answer

Understanding the question: we are evaluating the worst-case time complexity of a function find_min, with the provided options.
Option 1: O(2n). In big-O notation, constant factors are ignored, so O(2n) simplifies to O(n). While technically equivalent in growth rate to O(n), it is still a linear-time bound and not a distinct complexity class from O(n). This option can be considered correct in terms of describing linear time, but many instructors expect the simplest canonical form, O(n).
Option 2: O(n). This expresses linear time, meaning the running time grows proportionally with the size of the input. For a simple find_min that scans each element once, this is the standard and accurate worst-case bound.
Option 3: O(n2). This denotes quadratic time, where the running time grows with the square of the input size. This would only be the case if the algorithm performed nested loops over the data, which is not characteristic of a straightforward linear scan.
Option 4: O(log n). This indicates logarithmic time, typical of divide-and-conquer strategies or balanced search structures. A simple find_min does not reduce the problem size by a constant factor in a way that yields logarithmic growth, so this is incorrect.
Option 5: O(1). This is constant time, implying the algorithm does not depend on n at all. A find_min that checks every element cannot be constant-time in the worst case, so this is incorrect.
Putting it together, the commonly accepted worst-case bound for a linear scan-based find_min is linear time, which corresponds to O(n). The presence of O(2n) is functionally the same growth rate as O(n) after simplification, but canonical answers typically use the simplified form O(n).

Rec_9 For the worst case : what is the run time complexity of the find_min function below

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