Why checking for a trillion in a quintillion-sized range is lightning fast in Python 3!

Understanding range(a, b):

• The range(a, b) function in Python generates a sequence of numbers starting from a (inclusive) and ending just before b (exclusive).
• In your example, range(1000000000000001) creates a sequence from 0 to 999999999999999 (10 quintillion numbers).

Why is checking for 10^12 in this range fast?

• Lazy generation: Unlike previous versions, Python 3's range doesn't pre-create the entire sequence in memory. It generates numbers one by one, on demand.
• Smart containment check: When you use in like 10^12 in range(1000000000000001), the range object doesn't actually iterate through all numbers! It uses a clever mathematical check:
  • It verifies if 10^12 lies between the minimum (0) and maximum (999999999999999) of the range.
  • It also ensures the "step" (always 1 in this case) doesn't skip over 10^12.
• Fast check, quick answer: Since 10^12 is clearly larger than the maximum in the range, the check instantly determines it's not present. That's why the operation is incredibly fast despite dealing with such a massive range.

Examples for clarity:

Here are some comparisons to illustrate the performance difference:

• Direct list creation:

range_list = list(range(1000000000000001))
10**12 in range_list  # This is much slower as the entire list is created first.

• Checking within a smaller range:

10**12 in range(10**12, 10**12 + 1)  # This is also fast as the check is within a small range.

Important to remember:

• This optimization for in checks applies only to integers in Python 3. Floats have different behavior.
• While checking for very large numbers in these huge ranges is fast, remember that creating and working with such ranges themselves can still be resource-intensive.

Learning takeaway:

This seemingly simple question unveils hidden layers of efficiency in Python's range function. Understanding these optimizations can help you write cleaner and more performant code.

By exploring code examples and comparing different approaches, you can become a better programmer yourself. Keep learning and happy coding!