SortBy

The collection sorted by the value of a function on each element.

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

SortBy(collection, f)sorted by $f(element)$, ascending; elements with equal keys come out in canonical order. SortBy(c, [f]), with the key function in a list, is stable, keeping input order on ties.

Typed signatures

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

Domain: Collections

Examples

Basic #

Sorted by absolute value

live ↗

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

Pairs sorted by their last element

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In$\mathrm{SortBy}(\bigl\lbrack\bigl\lbrack a, 2\bigr\rbrack, \bigl\lbrack c, 1\bigr\rbrack, \bigl\lbrack d, 3\bigr\rbrack\bigr\rbrack, \mathrm{Last})$Out$\bigl\lbrack\bigl\lbrack c, 1\bigr\rbrack, \bigl\lbrack a, 2\bigr\rbrack, \bigl\lbrack d, 3\bigr\rbrack\bigr\rbrack$

Equal sort keys now follow Wolfram's tie order (our own convention changing, not a known value).

live ↗

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

live ↗

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

Sorts by residue mod $3$; ties come out in canonical order

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In$\mathrm{SortBy}(1..10, \operatorname{\_1}↦\operatorname{\_1}\bmod3)$Out$\bigl\lbrack3, 6, 9, 1, 4, 7, 10, 2, 5, 8\bigr\rbrack$

Scope #

Sorted by the square of each element

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In$\mathrm{SortBy}(\bigl\lbrack4, -5, 1, 3, -2\bigr\rbrack, \operatorname{\_1}↦\operatorname{\_1}^2)$Out$\bigl\lbrack1, -2, 3, 4, -5\bigr\rbrack$

Sorting by $-x$ gives descending order

live ↗

In$\mathrm{SortBy}(\bigl\lbrack3, 1, 2\bigr\rbrack, \mathrm{Negate})$Out$\bigl\lbrack3, 2, 1\bigr\rbrack$

Sorted by key length

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In$\mathrm{SortBy}(\bigl\lbrack\text{dog}, \text{zebra}, \text{donkey}, \text{anteater}, \text{fish}\bigr\rbrack, \mathrm{StringLength})$Out$\bigl\lbrack\text{dog}, \text{fish}, \text{zebra}, \text{donkey}, \text{anteater}\bigr\rbrack$

live ↗

In$\mathrm{SortBy}(\bigl\lbrack\sqrt{1+e^{-10i}}, e^{2+i}, e^{-1+2i}, e^{i}\bigr\rbrack, \mathrm{Abs})$Out$\bigl\lbrack e^{-1+2i}, \sqrt{1+i\sin(-10)+\cos(-10)}, i\sin(1)+\cos(1), e^{2+i}\bigr\rbrack$

live ↗

In$\mathrm{SortBy}(\bigl\lbrack e, π, \sin(1), \sqrt{2}\bigr\rbrack, N)$Out$\bigl\lbrack\sin(1), \sqrt{2}, e, π\bigr\rbrack$

live ↗

In$\mathrm{SortBy}(\bigl\lbrack1, \sqrt{1+1/e^{10}}, e^{2+i}, e^{-1+2i}, e^{i}\bigr\rbrack, \operatorname{\_1}↦N(\vert\operatorname{\_1}\vert))$Out$\bigl\lbrack e^{-1+2i}, 1, i\sin(1)+\cos(1), \sqrt{1+1/e^{10}}, e^{2+i}\bigr\rbrack$

Elements with equal keys come out in canonical order, so SortBy is not stable

live ↗

In$\mathrm{SortBy}(\bigl\lbrack\text{bb}, \text{a}, \text{cc}, \text{aa}, \text{b}\bigr\rbrack, \mathrm{StringLength})$Out$\bigl\lbrack\text{a}, \text{b}, \text{aa}, \text{bb}, \text{cc}\bigr\rbrack$

A list of key functions sorts by each in turn and keeps input order for what ties on all of them

live ↗

In$\mathrm{SortBy}(\bigl\lbrack\text{bb}, \text{a}, \text{cc}, \text{aa}, \text{b}\bigr\rbrack, \bigl\lbrack\mathrm{StringLength}\bigr\rbrack)$Out$\bigl\lbrack\text{a}, \text{b}, \text{bb}, \text{cc}, \text{aa}\bigr\rbrack$

live ↗

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

live ↗

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

Applications #

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In$\mathrm{SortBy}(\mathrm{exprs}, \mathrm{err})$Out$\mathrm{SortBy}(\mathrm{exprs}, \mathrm{err})$

Properties #

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In$\mathrm{SortBy}(\mathrm{list}, \mathrm{Abs})$Out$\mathrm{SortBy}(\mathrm{list}, \mathrm{Abs})$

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In$\mathrm{SortBy}(\mathrm{list}, \mathrm{First})$Out$\mathrm{SortBy}(\mathrm{list}, \mathrm{First})$

About

Examples	18
Checked against	Wolfram Language 17 agree1 differ
Crosswalk	Wolfram Language

See also: Sort, GatherBy