# Ordering

Ordering[list]

gives the positions in list at which each successive element of Sort[list] appears.

Ordering[list,n]

gives the positions in list at which the first n elements of Sort[list] appear.

Ordering[list,-n]

gives the positions of the last n elements of Sort[list].

Ordering[list,n,p]

gives positions in list of elements of Sort[list,p].

# Details • In a numerical list, Ordering[list,n] gives the positions of the n smallest elements. Ordering[list,-n] gives the positions of the n largest elements.
• If there are several smallest elements in list, Ordering[list,1] will give only the position of the one that appears first.
• list[[Ordering[list]]] is the same as Sort[list].
• Ordering[list,seq] is equivalent to Take[Ordering[list],seq].
• Ordering[list,UpTo[n]] returns n positions, or as many as are available.
• Ordering[list,All,p] gives the position at which all elements of list appear in Sort[list,p].
• Ordering can be used on expressions with any head, not only List.

# Examples

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## Basic Examples(4)

Find the ordering that sorts a list:

 In:= Out= Apply the ordering:

 In:= Out= Find the positions of the 4 smallest elements in a list:

 In:= Out= Find the position of the largest element:

 In:= Out= Find the ordering of values in an Association:

 In:= Out= ## Properties & Relations(2)

Introduced in 2000
(4.1)
|
Updated in 2015
(10.3)