MapIndexed

f applied to each part together with its position path, a list.

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

MapIndexed(f, list){f(a1, {1}), f(a2, {2}), …} — the index is a LIST, not a bare integer

MapIndexed(f, list, levelspec)f goes on every part in those levels (as in Level), innermost first, with its full position path

Typed signatures

Type	Package	Applies
(function: any, list<any>, any?) -> list<any>	combinatorics	always

Domain: Collections

Details

• The index arrives as a position path, {i} at the top level, not i; with a level spec, a part at depth 2 gets {i, j}, and so on.
• Without a level spec, f goes on the top-level parts only.

Examples

Basic #

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack a, b, c\bigr\rbrack)$Out$\bigl\lbrack f(a, \bigl\lbrack1\bigr\rbrack), f(b, \bigl\lbrack2\bigr\rbrack), f(c, \bigl\lbrack3\bigr\rbrack)\bigr\rbrack$

Each element is passed with its position as a list

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack a, b, c, d\bigr\rbrack)$Out$\bigl\lbrack f(a, \bigl\lbrack1\bigr\rbrack), f(b, \bigl\lbrack2\bigr\rbrack), f(c, \bigl\lbrack3\bigr\rbrack), f(d, \bigl\lbrack4\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d, k\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack1\bigr\rbrack), f(\bigl\lbrack c, d, k\bigr\rbrack, \bigl\lbrack2\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d, k\bigr\rbrack\bigr\rbrack, \bigl\lbrack2\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack f(a, \bigl\lbrack1, 1\bigr\rbrack), f(b, \bigl\lbrack1, 2\bigr\rbrack)\bigr\rbrack, \bigl\lbrack f(c, \bigl\lbrack2, 1\bigr\rbrack), f(d, \bigl\lbrack2, 2\bigr\rbrack), f(k, \bigl\lbrack2, 3\bigr\rbrack)\bigr\rbrack\bigr\rbrack$

Scope #

Only the outermost level is mapped, so the position is $[1]$

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In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack)$Out$\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack1\bigr\rbrack)\bigr\rbrack$

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In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 2)$Out$\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack2\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack f(\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack)\bigr\rbrack\bigr\rbrack$

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In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, 3)$Out$\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack, \bigl\lbrack1, 1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d, \bigl\lbrack k\bigr\rbrack\bigr\rbrack\bigr\rbrack, ∞)$Out$\bigl\lbrack f(\bigl\lbrack f(a, \bigl\lbrack1, 1\bigr\rbrack), f(b, \bigl\lbrack1, 2\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1\bigr\rbrack), f(\bigl\lbrack f(c, \bigl\lbrack2, 1\bigr\rbrack), f(d, \bigl\lbrack2, 2\bigr\rbrack), f(\bigl\lbrack f(k, \bigl\lbrack2, 3, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack2, 3\bigr\rbrack)\bigr\rbrack, \bigl\lbrack2\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d, \bigl\lbrack k\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack-1\bigr\rbrack)$Out$\bigl\lbrack\bigl\lbrack f(a, \bigl\lbrack1, 1\bigr\rbrack), f(b, \bigl\lbrack1, 2\bigr\rbrack)\bigr\rbrack, \bigl\lbrack f(c, \bigl\lbrack2, 1\bigr\rbrack), f(d, \bigl\lbrack2, 2\bigr\rbrack), \bigl\lbrack f(k, \bigl\lbrack2, 3, 1\bigr\rbrack)\bigr\rbrack\bigr\rbrack\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, -1)$Out$\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack f(a, \bigl\lbrack1, 1, 1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1, 1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1\bigr\rbrack)\bigr\rbrack$

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In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, -2)$Out$\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack a\bigr\rbrack, \bigl\lbrack1, 1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack\bigl\lbrack\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack\bigr\rbrack\bigr\rbrack, -3)$Out$\bigl\lbrack f(\bigl\lbrack f(\bigl\lbrack\bigl\lbrack a\bigr\rbrack\bigr\rbrack, \bigl\lbrack1, 1\bigr\rbrack)\bigr\rbrack, \bigl\lbrack1\bigr\rbrack)\bigr\rbrack$

live ↗

In$\mathrm{MapIndexed}(f, \bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack0, 1\bigr\rbrack)$Out$f(\bigl\lbrack f(a, \bigl\lbrack1\bigr\rbrack), f(b, \bigl\lbrack2\bigr\rbrack)\bigr\rbrack, \bigl\lbrack\bigr\rbrack)$

Applications #

Tags each term with its index

live ↗

In$\mathrm{MapIndexed}(\mathrm{Labeled}, \bigl\lbrack x^2, x+y, y^2, y^3\bigr\rbrack)$Out$\bigl\lbrack\mathrm{Labeled}(x^2, \bigl\lbrack1\bigr\rbrack), \mathrm{Labeled}(x+y, \bigl\lbrack2\bigr\rbrack), \mathrm{Labeled}(y^2, \bigl\lbrack3\bigr\rbrack), \mathrm{Labeled}(y^3, \bigl\lbrack4\bigr\rbrack)\bigr\rbrack$

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In$\mathrm{First}(\mathrm{Last}(\mathrm{Reap}(\mathrm{MapIndexed}(()↦\mathrm{Sow}(\operatorname{\_2}), \bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c\bigr\rbrack, \bigl\lbrack\bigl\lbrack d\bigr\rbrack\bigr\rbrack\bigr\rbrack, \bigl\lbrack1, ∞\bigr\rbrack))))$Out$\bigl\lbrack\bigl\lbrack1, 1\bigr\rbrack, \bigl\lbrack1, 2\bigr\rbrack, \bigl\lbrack1\bigr\rbrack, \bigl\lbrack2, 1\bigr\rbrack, \bigl\lbrack2\bigr\rbrack, \bigl\lbrack3, 1, 1\bigr\rbrack, \bigl\lbrack3, 1\bigr\rbrack, \bigl\lbrack3\bigr\rbrack\bigr\rbrack$

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In$\sum\mathrm{MapIndexed}(()↦\operatorname{\_1}x^{\mathrm{First}(\operatorname{\_2})}, \bigl\lbrack a, b, c, d, k\bigr\rbrack)$Out$kx^5+dx^4+cx^3+bx^2+ax$

About

Examples	17
Checked against	Wolfram Language 17 agree
Crosswalk	Wolfram Language

See also: MapThread, Level