Count Operations

Given an integer n and a string pattern describing a loop structure, return the total number of iterations that pattern would execute.

The patterns are:

• "single" — A single for loop from 0 to n-1: n iterations
• "nested" — Two nested for loops, each from 0 to n-1: n² iterations
• "half" — A loop that starts at n and halves each step until reaching 0: the number of times you can halve n before it reaches 0 (i.e., floor(log₂(n)) + 1 for n > 0, or 0 if n = 0)

This problem tests your understanding of how loop structures map to Big O complexity.