This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.

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When a queue is implemented using arrays, the run time complexity of its operations depends on how the array is managed.
Enqueue operation (adding an element to the rear):
rear pointer) takes constant time, , assuming there is space available or that array resizing is handled efficiently (e.g., amortized ).Dequeue operation (removing an element from the front):
front and rear pointers move around the array. Removing an element from the front simply involves incrementing the front pointer, which takes time.The question asks for the worst run time complexity. While a circular array can achieve for both, a common array implementation (especially if not explicitly stated as circular) can have a dequeue operation due to the need to shift elements. Therefore, considering the worst-case scenario for a general array implementation, dequeue can be .
Thus, the enqueue operation is , and the dequeue operation is .
The final answer is
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When a queue is implemented using arrays, the run time complexity of its operations depends on how the array is managed.
This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.