How to express interval in C language

In C language, square brackets are used to express intervals, with the left side representing the left endpoint and the right side representing the right endpoint. Interval types include closed intervals that include endpoints, open intervals that do not include endpoints, and half-open and half-closed intervals. C language provides operators such as interval merging, subtraction, intersection, and remainder. The use of interval representation and operators can be clearly understood through examples.

Interval representation in C language

In C language, the interval can be expressed using a pair of square brackets, where the left The side square bracket represents the left endpoint of the interval, and the right square bracket represents the right endpoint of the interval.

Interval type

C language provides the following interval types:

• [a, b] : Closed interval including endpoints
• (a, b): Open interval not including endpoints
• [a, b): Including left end A half-open and half-closed interval that does not include the right endpoint
• (a, b]: A half-open and half-closed interval that does not include the left endpoint but includes the right endpoint

Operators

C language provides the following interval operators:

• : Interval merge, merge two intervals It is an interval that contains all elements of the two intervals.
• -: Interval subtraction, subtracts the second interval from the first interval, and returns the first interval that is not included in the first interval. Elements in two intervals.
• *: The intersection of intervals, returns the overlapping part of the two intervals.
• ##%: The remainder of the intervals. , returns the elements in the first range that are not included in the second range

Example

The following are some examples of range representations and operators. :

##[1, 5]
• represents the closed interval from 1 to 5 (including 1 and 5)
(2, 7).
• represents an open interval that does not include 2 to 7 (excluding 2 and 7)
[3, 6)
• represents an open interval that contains 3 to 6 (including 3 but excluding 6). The half-open and half-closed interval.
(1, 4] (5, 8]
• represents a closed interval from 1 to 8 (including 1 and 8).
[2, 6 ] - (3, 5)
• represents two open intervals from 2 to 3 (including 2 but not including 3) and from 5 to 6 (including 5 but not including 6) .

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