Split

Split a list into runs of identical adjacent elements.

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

Split(list)runs of adjacent equal elements.

Split(list, test)runs on which adjacent elements agree by a custom two-argument test.

Typed signatures

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

Domain: Collections

Details

• Runs, not groups: only ADJACENT equal elements join a run, so the same value can appear in several separate runs. See Gather to group every occurrence together regardless of position.

Examples

Basic #

Runs, not groups: the two runs of 1 stay apart

live ↗

In$\mathrm{Split}(\bigl\lbrack1, 1, 2, 2, 2, 3, 1, 1\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack1, 1\bigr\rbrack, \bigl\lbrack2, 2, 2\bigr\rbrack, \bigl\lbrack3\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack\bigr\rbrack$

Symbolic elements

live ↗

In$\mathrm{Split}(\bigl\lbrack a, a, b, b, b, a\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack a, a\bigr\rbrack, \bigl\lbrack b, b, b\bigr\rbrack, \bigl\lbrack a\bigr\rbrack\bigr\rbrack$

Runs of equal neighbours are grouped

live ↗

In$\mathrm{Split}(\bigl\lbrack a, a, a, b, b, a, a, c\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack a, a, a\bigr\rbrack, \bigl\lbrack b, b\bigr\rbrack, \bigl\lbrack a, a\bigr\rbrack, \bigl\lbrack c\bigr\rbrack\bigr\rbrack$

Scope #

A test between neighbours: split into increasing runs

live ↗

In$\mathrm{Split}(\bigl\lbrack1, 2, 3, 5, 4, 6\bigr\rbrack, \mathrm{Less})$Out$\bigl\lbrack\bigl\lbrack1, 2, 3, 5\bigr\rbrack, \bigl\lbrack4, 6\bigr\rbrack\bigr\rbrack$

The empty list

live ↗

In$\mathrm{Split}(\bigl\lbrack\bigr\rbrack)$Out$\bigl\lbrack\bigr\rbrack$

Breaks wherever the list stops increasing, giving increasing runs

live ↗

In$\mathrm{Split}(\bigl\lbrack1, 2, 3, 4, 3, 2, 1, 5, 6, 7, 4, 3\bigr\rbrack, \mathrm{Less})$Out$\bigl\lbrack\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \bigl\lbrack3\bigr\rbrack, \bigl\lbrack2\bigr\rbrack, \bigl\lbrack1, 5, 6, 7\bigr\rbrack, \bigl\lbrack4\bigr\rbrack, \bigl\lbrack3\bigr\rbrack\bigr\rbrack$

Breaks wherever the list stops decreasing

live ↗

In$\mathrm{Split}(\bigl\lbrack1, 2, 3, 4, 3, 2, 1, 5, 6, 7, 4, 3\bigr\rbrack, \mathrm{Greater})$Out$\bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack2\bigr\rbrack, \bigl\lbrack3\bigr\rbrack, \bigl\lbrack4, 3, 2, 1\bigr\rbrack, \bigl\lbrack5\bigr\rbrack, \bigl\lbrack6\bigr\rbrack, \bigl\lbrack7, 4, 3\bigr\rbrack\bigr\rbrack$

Groups primes whose consecutive gaps are below $4$

live ↗

In$\mathrm{Split}(\mathrm{Array}(\mathrm{NthPrime}, 20), (\operatorname{\_1}, \operatorname{\_2})↦\operatorname{\_2}-\operatorname{\_1}\lt4)$Out$\bigl\lbrack\bigl\lbrack2, 3, 5, 7\bigr\rbrack, \bigl\lbrack11, 13\bigr\rbrack, \bigl\lbrack17, 19\bigr\rbrack, \bigl\lbrack23\bigr\rbrack, \bigl\lbrack29, 31\bigr\rbrack, \bigl\lbrack37\bigr\rbrack, \bigl\lbrack41, 43\bigr\rbrack, \bigl\lbrack47\bigr\rbrack, \bigl\lbrack53\bigr\rbrack, \bigl\lbrack59, 61\bigr\rbrack, \bigl\lbrack67\bigr\rbrack, \bigl\lbrack71\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{Split}(\bigl\lbrack a, a, a, b, a, b, b, a, a, a, c, a\bigr\rbrack, \mathrm{UnsameQ})$Out$\bigl\lbrack\bigl\lbrack a\bigr\rbrack, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack b\bigr\rbrack, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack b\bigr\rbrack, \bigl\lbrack b\bigr\rbrack, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack a\bigr\rbrack, \bigl\lbrack c\bigr\rbrack, \bigl\lbrack a\bigr\rbrack\bigr\rbrack$

Applications #

Sorting first merges all equal elements into one run each

live ↗

In$\mathrm{Split}(\mathrm{Sort}(\bigl\lbrack a, a, a, b, b, a, a, c, c, c\bigr\rbrack))$Out$\bigl\lbrack\bigl\lbrack a, a, a, a, a\bigr\rbrack, \bigl\lbrack b, b\bigr\rbrack, \bigl\lbrack c, c, c\bigr\rbrack\bigr\rbrack$

Splits wherever the sign changes

live ↗

In$\mathrm{Split}(\bigl\lbrack3, 0, -4, 3, 3, -2, 0, -3, -4, 5\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦\mathrm{sgn}(\operatorname{\_1})=\mathrm{sgn}(\operatorname{\_2}))$Out$\bigl\lbrack\bigl\lbrack3\bigr\rbrack, \bigl\lbrack0\bigr\rbrack, \bigl\lbrack-4\bigr\rbrack, \bigl\lbrack3, 3\bigr\rbrack, \bigl\lbrack-2\bigr\rbrack, \bigl\lbrack0\bigr\rbrack, \bigl\lbrack-3, -4\bigr\rbrack, \bigl\lbrack5\bigr\rbrack\bigr\rbrack$

Splits only where a negative is followed by a positive

live ↗

In$\mathrm{Split}(\bigl\lbrack3, 0, -4, 3, 3, -2, 0, -3, -4, 5\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦¬(\mathrm{sgn}(\operatorname{\_1})\lt0∧0\lt\mathrm{sgn}(\operatorname{\_2})))$Out$\bigl\lbrack\bigl\lbrack3, 0, -4\bigr\rbrack, \bigl\lbrack3, 3, -2, 0, -3, -4\bigr\rbrack, \bigl\lbrack5\bigr\rbrack\bigr\rbrack$

Splits only where a positive is followed by a negative

live ↗

In$\mathrm{Split}(\bigl\lbrack3, 0, -4, 3, 3, -2, 0, -3, -4, 5\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦¬(0\lt\mathrm{sgn}(\operatorname{\_1})∧\mathrm{sgn}(\operatorname{\_2})\lt0))$Out$\bigl\lbrack\bigl\lbrack3, 0, -4, 3, 3\bigr\rbrack, \bigl\lbrack-2, 0, -3, -4, 5\bigr\rbrack\bigr\rbrack$

Run-length encoding: each run becomes a value and a count

live ↗

In$\mathrm{Map}(\operatorname{\_1}↦\bigl\lbrack\mathrm{First}(\operatorname{\_1}), \mathrm{Length}(\operatorname{\_1})\bigr\rbrack, \mathrm{Split}(\bigl\lbrack a, a, a, b, b, a, a, c, c, c\bigr\rbrack))$Out$\bigl\lbrack\bigl\lbrack a, 3\bigr\rbrack, \bigl\lbrack b, 2\bigr\rbrack, \bigl\lbrack a, 2\bigr\rbrack, \bigl\lbrack c, 3\bigr\rbrack\bigr\rbrack$

Properties #

Equal values separated by others stay in separate runs

live ↗

In$\mathrm{Split}(\bigl\lbrack a, a, a, b, b, a, a, c, c, c\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack a, a, a\bigr\rbrack, \bigl\lbrack b, b\bigr\rbrack, \bigl\lbrack a, a\bigr\rbrack, \bigl\lbrack c, c, c\bigr\rbrack\bigr\rbrack$

Neat examples #

live ↗

In$\mathrm{NestList}(\operatorname{\_1}↦\mathrm{Flatten}(\mathrm{Map}(\operatorname{\_1}↦\bigl\lbrack\mathrm{Length}(\operatorname{\_1}), \mathrm{First}(\operatorname{\_1})\bigr\rbrack, \mathrm{Split}(\operatorname{\_1}))), \bigl\lbrack1\bigr\rbrack, 8)$Out$\bigl\lbrack\bigl\lbrack1\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack, \bigl\lbrack2, 1\bigr\rbrack, \bigl\lbrack1, 2, 1, 1\bigr\rbrack, \bigl\lbrack1, 1, 1, 2, 2, 1\bigr\rbrack, \bigl\lbrack3, 1, 2, 2, 1, 1\bigr\rbrack, \bigl\lbrack1, 3, 1, 1, 2, 2, 2, 1\bigr\rbrack, \bigl\lbrack1, 1, 1, 3, 2, 1, 3, 2, 1, 1\bigr\rbrack, \bigl\lbrack3, 1, 1, 3, 1, 2, 1, 1, 1, 3, 1, 2, 2, 1\bigr\rbrack\bigr\rbrack$

About

Examples	16
Checked against	Wolfram Language 16 agree
Crosswalk	Wolfram Language

See also: Gather, SplitBy, Partition