---
title: "Mixed-radix generation -"
author: ["Samuel Ortion"]
date: 2024-04-15T00:00:00+02:00
draft: true
pseudocode: true
---

In its draft on Generating all \\(n\\) tuples, of The Art of Computer Programming, Knuth presents the following algorithm for the generation of $n$-tuples (<a href="#citeproc_bib_item_1">Knuth 2002</a>).

<pre id="hello-world-code" class="pseudocode">
    \begin{algorithm}
    \caption{Mixed-radix generation}
    \begin{algorithmic}
    \State \textbf{M1.} [Initialize.] Set $a_j \gets 0$ for $0 \leq j \leq n$, and set $m_0 \gets 2$.
    \State \textbf{M2.} [Visit.] Visit the \(n\)-tuple $(a_1, ..., a_n)$ (The program that wants to examine all $n$-tuples now does its thing.)
    \State \textbf{M3.} [Prepare to add one.] Set $j \gets n$.
    \State \textbf{M4.} [Carry if necessary.] If $a_j = m_j - 1$, set $a_j \gets 0$, $j \gets j - 1$ and repeat this step.
    \State \textbf{M5.} [Increase, unless done.] If $j = 0$, terminate the algorithm. Otherwise set $a_j \gets a_j + 1$ and go back to step M2.
    \end{algorithmic}
    \end{algorithm}
</pre>

## References

<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
  <div class="csl-entry"><a id="citeproc_bib_item_1"></a>Knuth, Donald E. 2002. <i>A Draft of Section 7.2.1.1: Generating All N-Tuples</i>. Vol. 4a. 5 vols. The Art of Computer Programming.</div>
</div>