bag

(data structure)

Definition: An unordered collection of values that may have duplicates.

Formal Definition: A bag has a single query function, numberIn(v, B), which tells how many copies of an element are in the bag, and two modifier functions, add(v, B) and remove(v, B). These may be defined with axiomatic semantics as follows.

1. new() returns a bag
2. numberIn(v, new()) = 0
3. numberIn(v, add(v, B)) = 1 + numberIn(v, B)
4. numberIn(v, add(u, B)) = numberIn(v, B) if v ≠ u
5. remove(v, new()) = new()
6. remove(v, add(v, B)) = B
7. remove(v, add(u, B)) = add(u, remove(v, B)) if v ≠ u

The predicate isEmpty(B) may be defined with the following additional axioms.

8. isEmpty(new()) = true
9. isEmpty(add(v, B)) = false

Also known as multi-set.

Generalization (I am a kind of ...)
abstract data type.

See also set, list.

Note: A bag, or multi-set, is a set where values may be repeated. Inserting 2, 1, 2 into an empty set gives the set {1, 2}. Inserting those values into an empty bag gives {1, 2, 2}. From another point of view, a set is unordered, too, but has each value at most once.

Author: PEB

If you have suggestions, corrections, or comments, please get in touch with Paul E. Black.

Entry modified Tue Jan 11 16:17:02 2005.
HTML page formatted Wed Oct 26 09:47:12 2005.

Cite this as:
Paul E. Black, "bag", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
http://www.nist.gov/dads/HTML/bag.html