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Algorithms

This category collects posts where we dig into algorithms and how APL expresses them. You’ll find worked examples covering sorting and ordering, performance tuning, real-world methods like D’Hondt apportionment, and classic puzzles like Krypto, all explored through actual APL code, benchmarks, and step-by-step reasoning.

A New Stack for the APL Challenge

In: Algorithms, APL Competitions, Implementation

In February 2026, the APL Challenge quietly launched its next round on a rewritten stack. The previous infrastructure was retired and replaced by... Read

By

Adám Brudzewsky

June 2026

Towards Improvements to Stencil

In: Algorithms, APL Language, Implementation, Tips and Tricks

Background The stencil operator ⌺ was introduced in Dyalog version 16.0 in 2017. Recently we received some feedback (OK, complaints) that (a) stencil does... Read

By

Roger Hui

June 2020

Ascending and Descending

In: Algorithms, APL Language

Lexicographic Ordering Lexicographic ordering is what the APL primitives ⍋ and ⍒ provide: ⎕io←0 ⍝ ⎕io delenda est ⎕rl←7*5 ⍝ to get... Read

By

Roger Hui

February 2019

Krypto

In: Algorithms, Recreational

In the 2016 Year Game, the task was to generate the numbers 0 to 100 using APL primitives and the digits 2 0 1 6 in that order. For example, 20=16 ×2016... Read

By

Roger Hui

May 2017

Beauty and the Beast

In: Algorithms, APL Language, CXO, Raspberry Pi, Recreational

Finally, the last accessory I ordered for my Raspberry Pi Zero (that’s the little red thing behind my keyboard) has arrived – an Acer 43″... Read

By

Morten Kromberg

March 2017

Charting Reaction Times on the Raspberry Pi

In: Algorithms, APL Language, CXO, Raspberry Pi, SharpPlot

Earlier this week I collected some reaction timer data on my Pi using the BBC micro:bit as an input device. I only produced an “ASCII art” chart at... Read

By

Morten Kromberg

March 2017

APL Exercises

In: Algorithms

These exercises are designed to introduce APL to a high school senior adept in mathematics. The entire set of APL Exercises has the following sections:... Read

By

Roger Hui

September 2016

50847534

In: Algorithms, APL Language, Musings

⎕io←0 throughout. I was re-reading A Mathematician’s Apology before recommending it to Suki Tekverk, our summer intern, and came across a statement... Read

By

Roger Hui

September 2016

Shuffle Faster Please!

In: Algorithms, APL Language

Andy reported that in the shuffle QA some functions take a long time: m9249 “4½ days so far” rankop 21.5 hours... Read

By

Roger Hui

May 2016

The Halting Problem Rendered in APL

In: Algorithms

The halting problem is the problem of determining, from a description of a program and an input, whether the program will finish running or continue to run... Read

By

Roger Hui

April 2016

Quicksort in APL Revisited

In: Algorithms, APL Language, Tips and Tricks

A message in the Forum inquired on sorting strings in APL with a custom comparison function. First, sorting strings without a custom comparison function... Read

By

Roger Hui

February 2016

Permutations

In: Algorithms, APL Language

I started composing a set of APL exercises in response to a query from a new APL enthusiast who attended Morten’s presentation at Functional Conf,... Read

By

Roger Hui

July 2015

In Praise of Magic Functions: Part II

In: Algorithms, APL Language

Part I of this post was concerned with the development speed and execution speed of magic functions and should be read before this post. Benefitting from... Read

By

Roger Hui

June 2015

In Praise of Magic Functions: Part I

In: Algorithms, APL Language

A magic function is an APL-coded (dfn) computation in the C source of the interpreter. For example, some cases of ∧.= are coded as... Read

By

Roger Hui

June 2015

Changes of Heart

In: Algorithms, APL Language

Karen Shaw started the ball rolling (hearts afluttering?) by asking Jay Foad to come up with a one-liner for St. Valentine’s Day; he then solicited... Read

By

Roger Hui

February 2015

Solving the 2014 APL Problem Solving Competition – Cryptography Problem 3

In: Algorithms, APL Language, APL Problem Solving Competition

This post is the continuation of the series where we examine some of the problems selected for the 2014 APL Problem Solving Competition. In this post... Read

By

Jay Foad

February 2015

Solving the 2014 APL Problem Solving Competition – Cryptography Problem 2

In: Algorithms, APL Language, APL Problem Solving Competition

This post is the continuation of the series where we examine some of the problems selected for the 2014 APL Problem Solving Competition. In this post... Read

By

Jay Foad

January 2015

Solving the 2014 APL Problem Solving Competition – Cryptography Problem 1

In: Algorithms, APL Language, APL Problem Solving Competition

This post is a continuation of the series where we examine some of the problems selected for the 2014 APL Problem Solving Competition. I’ll start by... Read

By

Jay Foad

January 2015

The Diamond Kata

In: Algorithms, APL Language

Acknowledgments Morten Kromberg is the other co-author of this text but the blogging software prevents his being listed as such. We are indebted to Jay Foad,... Read

By

Roger Hui

January 2015

Three-and-a-bit

In: Algorithms, APL Language, Tips and Tricks

The most obvious expression for computing π in APL is ○1. But what if you can’t remember how ○ works, or your O key is broken, or you feel like... Read

By

Jay Foad

January 2015

Solving the 2014 APL Problem Solving Competition – it’s as easy as 1 1 2 3…

In: Algorithms, APL Language, APL Problem Solving Competition, Tips and Tricks

The winners of the 2014 APL Problem Solving Competition were recognized at the Dyalog ’14 user meeting and had a chance to share their... Read

By

Brian Becker

November 2014

Why Dyalog ’14 was a Shear Delight

In: Algorithms, APL Language, Dyalog '14

Recent versions of Microsoft Windows support touch screens, which of course means that applications can respond to events originating from touches. Microsoft... Read

By

John Daintree

October 2014

Turning to a Heading with an MPU-9150

In: Algorithms, CTO, Raspberry Pi, Robots

As the odour of fried electronics dissipates in the air, I’m unexpectedly afforded the opportunity to write this blog post a day or two earlier than... Read

By

Morten Kromberg

September 2014

Dancing with the Bots

In: Algorithms, APL Language, CTO, Raspberry Pi, Robots

Last week the ‘bots were busy preparing for the J Language Conference in Toronto, where they made their first public appearance together. Upon returning... Read

By

Morten Kromberg

August 2014

Aligning Diff Output

In: Algorithms, APL Language, CTO

‘Bots are off limits this week so here is a story from this year’s Iverson College – a fantastic week spent in the company of a wonderful mixture of... Read

By

Morten Kromberg

July 2014

Algorithms

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