29 lines
1.4 KiB
Markdown
29 lines
1.4 KiB
Markdown
---
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title: "Mixed-radix generation -"
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author: ["Samuel Ortion"]
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date: 2024-04-15T00:00:00+02:00
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draft: true
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pseudocode: true
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---
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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>).
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<pre id="hello-world-code" class="pseudocode">
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\begin{algorithm}
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\caption{Mixed-radix generation}
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\begin{algorithmic}
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\State \textbf{M1.} [Initialize.] Set $a_j \gets 0$ for $0 \leq j \leq n$, and set $m_0 \gets 2$.
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\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.)
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\State \textbf{M3.} [Prepare to add one.] Set $j \gets n$.
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\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.
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\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.
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\end{algorithmic}
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\end{algorithm}
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</pre>
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## References
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<style>.csl-entry{text-indent: -1.5em; margin-left: 1.5em;}</style><div class="csl-bib-body">
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<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>
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</div>
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