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Unrank a Lexicographic List of Integer Compositions

ZIO · 2022 · Zonal Informatics Olympiad · P4

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combinatorics · compositions · lexicographic-order

The organizer’s problem statement is available at the official source link.

ordered groups

Lists are grouped by their sum

Enumerate positive-integer lists by increasing total, then lexicographically within each total.

State table
sum klexicographic composition
k(1,...,1)
k(1,...,2,...)
k(k)
  1. 1

    Skip earlier groups

    A k-list is an ordered list of positive integers summing to k.
  2. 2

    Unrank lexicographically

    Count each sum-group and skip whole groups before the target position.
  3. 3

    Compute requested value

    Unrank within the matching group, then compute the requested sum or product.
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