collatz.txt

⍝ The Collatz conjecture. All sequences terminate at 1
⍝ If the number is even, cut it in half.
⍝ If the number is odd, triple it and add one.
⍝ Repeat...

scalar←{
    {                  ⍝ scalar function
        2|⍵:1+3×⍵      ⍝ odd
        ⍵÷2            ⍝ even
    }⍣{⍺=1}¨⍵         ⍝ applied under each
}

vector←{
    {                ⍝ vector function
        p←2|⍵        ⍝ parity
        u←⍵÷2-p      ⍝ half of evens
        v←p+u×1+2×p  ⍝ 1+3× odds
        ∪v~1         ⍝ without 1s and duplication
    }⍣{⍺≡⍬}⍵         ⍝ Applied to whole vector
}

⍝ Working with vectors is much faster than working on individual elements.
⍝ Also, notice how we embed logical boolean values into the data?!  Very clever!

      vector time ⍳1e6
00.60
      scalar time ⍳1e6
01:45.85

Counting brace depth
 ⍝ Array thinking:
      brace2←{(+\⍵='(')-(+\⍵=')')}
      brace3←{+\1 ¯1 0['()'⍳⍵]}