Simple question but, I see exclusive and inclusive when referring to number ranges.
For example, this is a line from an algorithms book:
The following function prints the powers of 2 from 1 through n (inclusive).
What is meant by this? What makes a number range inclusive or exclusive?
The following function prints the powers of 2 from 1 through n (inclusive).
This means that the function will compute 2^i where i = 1, 2, ..., n, in other words, i can have values from 1 up to and including the value n. i.e n is Included in Inclusive
If, on the other hand, your book had said:
The following function prints the powers of 2 from 1 through n (exclusive).
This would mean that i = 1, 2, ..., n-1, i.e. i can take values up to n-1, but not including, n, which means i = n-1 is the highest value it could have.i.e n is excluded in exclusive.
In Computer Science, inclusive/exclusive doesn't apply to algorithms, but to a number range (more specifically, to the endpoint of the range):
1 through 10 (inclusive)
1 2 3 4 5 6 7 8 9 10
1 through 10 (exclusive)
1 2 3 4 5 6 7 8 9
In mathematics, the 2 ranges above would be:
[1, 10]
[1, 10)
You can remember it easily:
- Inclusive - Including the last number
- Exclusive - Excluding the last number
来源：https://stackoverflow.com/questions/39010041/what-is-the-meaning-of-exclusive-and-inclusive-when-describing-number-ranges