Algorithms for All Equal

Video Commentary

Solution #1

Solution #2

Solution #3

Solution #4

Using the prefix variants of Maximum and Minimum:

Using MinMax function:

Solution #5

Convenience is essential for a calculator. While the above solutions are simple, they are not obvious for casual users.

So there is dedicated ‘All Equal’ function.

It is the prefix form of ‘=’.
By default, this form is opted in to avoid confusion for the beginners.

Why the glyph ‘=̂’

For three numbers a, b, and c to be equal, they have to satisfy the condition:
a = b   and   b = c   and   a = c

Writing using the logical ‘and’ symbol:
a = b   ∧   b = c   ∧   a = c

So the glyph is a reflection of the condition.

Any Equal

If any pair of a, b, and c are equal, they satisfy:
a = b   or   b = c   or   a = c

Using the logical ‘or’ symbol:
a = b   ∨   b = c   ∨   a = c

So the glyph for ‘Any Equal’ is =̌

Example

Duplicate Zeros

From Weekly Challenge 333 – Task 2
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Leap Year

From Exercism
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First Missing Positive

From LeetCode
Video Commentary

The Count function (⧻) gives you the number of elements in a list.

The Remove function (~) removes a particular element from a list.
Later you will find it useful to think of Remove as ‘Without’.

Putting it altogether:

Count Negative Numbers in a Matrix

From LeetCode
Video Commentary

The Count function (⧻) gives you the number of elements in a matrix.

What’s more, it can count the occurrence of a particular number:
here 4 only appears once in the matrix.

To find the negative numbers, we start by setting the condition

The 1s in the above conditional matrix are the locations of the negative numbers.
All we need to do is to count the 1s.

So there are 4 negative numbers.

Sign of the Product of an Array

From LeetCode
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Minimum Average of Smallest and Largest

From LeetCode
Video Commentaries: Original, Follow Up

We are going for a simple solution — choosing elegance over efficiency.

•⃒ is the median function. The median of two numbers is same as the average.

Richest Customer Wealth

From LeetCode
Video Commentary

For illustration, we will use a simpler example than the one in LeetCode.

First we will need to sum up the numbers for each row.
For the first row, it will be 1 + 2 + 3, and 5 + 5 + 5 for the second row, etc.

In other words we need to inject (▷) addition (+) between each number.

By default, inject works horizontally along the x-axis, also known as axis 1. You can specify axis 1 for inject, it will appear as a subscript. You get the same result.

As an aside, to get the sum for each column, specify axis 2 for inject.

To find the richest customer, we use the maximum operator |̊

However, it has no effect.
Like inject, maximum also works horizontally. To find the maximum column wise, we specify 2 for the axis:

Prime Numbers

Finding primes between 2 to 50.

Ken Iverson’s APL solution on Wikipedia

(2 = +⌿ 0 = (⍳N) ∘.| ⍳N) / ⍳N

Using the fact that for numbers 1 to N, a prime only has 2 factors — itself and 1.

In our case, for numbers 2 to N, a prime has only one factor.

The ‘multiplication table’ APL solution.

(~ m ∊ m ∘.× m) / m ← 1↓⍳50

It’s short and sweet. Definitely not fast.

Sort by Parity

From LeetCode
Video Commentary

Maximum Count of Positive and Negative Integer

From LeetCode
Video: 1 Problem, 24 Languages

Spaces are used to separate items in the list.
Optionally we can use comma or semicolon for the sake of clarity.

Usually ⧻ counts how many elements in a list.
Here ⧻₁ counts how many elements satisfied the condition.
And you can use ⧻₀ to count what’s false.

Alternatively we can use the infix form of the maximum operator:

Optimum Solution

Maximize Prefix Score

LeetCode
Video: Why I Love BQN So Much! (vs Python)

As a multi-line solution:

Alternative without variable assignment:

R⃣ can be used to break up longer statements into shorter ones.

While R⃣ makes complex expressions easier to write, it sometimes makes the expression harder to understand. To understand line 3, you have know line 2. And R⃣ from line 2 has a difference meaning to R⃣ from line 3. So use sparingly.

Height Checker

From LeetCode
Video commentary

It’s easier to read in 2 lines.

Let’s use ⧻₁ to show our intention better.

We can use R instead of a normal variable.
R stands for result from a previous statement.
So if you have ‘1 + 2 ; R + 6’, you get 9 as R = 1 + 2 = 3

R allows us to break down a complex expression into smaller simpler chunks.

Max Difference Between Increasing Elements

From LeetCode
Video: Functional vs Array Programming

Using a different style of bracket for legibility:

Elimination Sort

From APL Quest
Video commentary

Multiples of 3 or 5

From Project Euler
Video commentary

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.

Introducing ·❘·
While ÷ means division, ·❘· means divisible.
So 6 ·❘· 3 = 1 (true) and 6 ·❘· 4 = 0 (false).

Similar expression but factoring out 3 and 5.

Moment of truth — let’s find all the multiples under 1000:

Sum of Squares

Video commentary

Difference Between Ones and Zeros

From LeetCode
Video commentary

Left and Right Sum Differences

From LeetCode
Video commentary

We can make the solution easier to read with fewer nested parentheses.

The above makes use of the absolute value of the difference in the form of:

When use in the infix form, it becomes the absolute difference:

Now we can remove the outer parentheses:

We can go one step further us of the fact that nested list is ignored, that is
[ [ 1 2 3 ] ] evaluates to [ 1 2 3 ] …
Let’s use square brackets for clarity:

‘What sums up 2020?’

From Advent of Code
Video commentary

The result of line 1, 𝗥, is the coordinate of 2020, expressed as a 2-dimensional complex number. The column is the real part ℜ while row is the imaginary part ℑ.

Splitting coordinates into separate ‘normal’ numbers can be done with the handy function Complex Number to List — ‘ℂ › 𝕃’:

Check if Matrix is X-Matrix

From LeetCode
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