GatherBy

Group elements by the value of a function, in order of first appearance.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageGatherBy✓↗

GatherBy(list, f)elements grouped by $f(element)$, in first-appearance order.

Typed signatures

Type	Package	Applies
(indexed_collection<T>, (T) any -> any) -> list<list<T>> where T	combinatorics	always

Domain: Collections

Details

• Gather with the equivalence "same $f$ value" instead of plain equality.

Examples

Basic #

Grouped by residue mod 3

live ↗

In$\mathrm{GatherBy}(\bigl\lbrack1, 2, 3, 4, 5, 6, 7\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}\bmod3)$Out$\bigl\lbrack\bigl\lbrack1, 4, 7\bigr\rbrack, \bigl\lbrack2, 5\bigr\rbrack, \bigl\lbrack3, 6\bigr\rbrack\bigr\rbrack$

Grouped by absolute value

live ↗

In$\mathrm{GatherBy}(\bigl\lbrack-2, 1, 2, -1, 3\bigr\rbrack, \mathrm{Abs})$Out$\bigl\lbrack\bigl\lbrack-2, 2\bigr\rbrack, \bigl\lbrack1, -1\bigr\rbrack, \bigl\lbrack3\bigr\rbrack\bigr\rbrack$

Groups by the value of a test, odds first because $1$ appears first

live ↗

In$\mathrm{GatherBy}(\bigl\lbrack1, 2, 3, 4, 5\bigr\rbrack, \mathrm{IsOdd})$Out$\bigl\lbrack\bigl\lbrack1, 3, 5\bigr\rbrack, \bigl\lbrack2, 4\bigr\rbrack\bigr\rbrack$

Grouping by a key function: here the first element of each pair

live ↗

In$\mathrm{GatherBy}(\bigl\lbrack\bigl\lbrack a, 1\bigr\rbrack, \bigl\lbrack b, 1\bigr\rbrack, \bigl\lbrack a, 2\bigr\rbrack, \bigl\lbrack d, 1\bigr\rbrack, \bigl\lbrack b, 3\bigr\rbrack\bigr\rbrack, \mathrm{First})$Out$\bigl\lbrack\bigl\lbrack\bigl\lbrack a, 1\bigr\rbrack, \bigl\lbrack a, 2\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack b, 1\bigr\rbrack, \bigl\lbrack b, 3\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack d, 1\bigr\rbrack\bigr\rbrack\bigr\rbrack$

Scope #

Pairs grouped by their last element

live ↗

In$\mathrm{GatherBy}(\bigl\lbrack\bigl\lbrack a, 1\bigr\rbrack, \bigl\lbrack b, 2\bigr\rbrack, \bigl\lbrack c, 1\bigr\rbrack\bigr\rbrack, \mathrm{Last})$Out$\bigl\lbrack\bigl\lbrack\bigl\lbrack a, 1\bigr\rbrack, \bigl\lbrack c, 1\bigr\rbrack\bigr\rbrack, \bigl\lbrack\bigl\lbrack b, 2\bigr\rbrack\bigr\rbrack\bigr\rbrack$

Applications #

Grouping by residue gives the classes mod $3$ without writing an equivalence

live ↗

In$\mathrm{GatherBy}(1..10, \operatorname{\_1}↦\operatorname{\_1}\bmod3)$Out$\bigl\lbrack\bigl\lbrack1, 4, 7, 10\bigr\rbrack, \bigl\lbrack2, 5, 8\bigr\rbrack, \bigl\lbrack3, 6, 9\bigr\rbrack\bigr\rbrack$

About

Examples	6
Checked against	Wolfram Language 6 agree
Crosswalk	Wolfram Language

See also: Gather, SplitBy, SortBy