From e5a82c427e28bd3533c86c075b7d5610b5fb864a Mon Sep 17 00:00:00 2001
From: Marshall Lochbaum <mwlochbaum@gmail.com>
Date: Mon, 13 Jul 2020 23:06:33 -0400
Subject: Selected functions from Hui\'s 50

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+# A history of APL in 50 functions
+# But they're BQN functions
+# Still about APL history though
+# Also not all the functions are here yet
+# https://www.jsoftware.com/papers/50/
+
+# Utilities
+Words ← (⊢-˜¬×+`)∘=⟜' '⊸⊔  # Split string on spaces
+
+# 0
+ArrayLogic ← (>-<)⟜0
+! 1‿¯1‿0‿1 ≡ ArrayLogic 5‿¯2.7‿0‿6
+
+# 1
+Average ← +´÷≠
+! 3 ≡ Average 2‿1‿6
+
+# 2
+# x⌹x=x is an alternate way to get the average of vector x.
+# There's no reason to do it this way in BQN (or APL, really).
+
+# 3
+IndexOfSelfie ← ⊐˜
+! 0‿1‿2‿3‿4‿1 ≡ IndexOfSelfie "Selfie"
+
+# 4
+BarChart ← ".⎕"⊏˜>⌜⟜(↕⌈´)
+! {
+  bc ← BarChart 3‿1‿4‿1‿5‿9
+  bc ≡ 6‿9⥊"⎕⎕⎕......⎕........⎕⎕⎕⎕.....⎕........⎕⎕⎕⎕⎕....⎕⎕⎕⎕⎕⎕⎕⎕⎕"
+}
+
+# 5
+ParenthesesNesting ← +`1‿¯1‿0⊏˜"()"⊐⊢
+! {
+  pn ← ParenthesesNesting "⍵((∇<S),=S,(∇>S))⍵⌷⍨?≢⍵"
+  pn ≡ 0‿1‿2‿2‿2‿2‿1‿1‿1‿1‿1‿2‿2‿2‿2‿1‿0‿0‿0‿0‿0‿0‿0
+}
+
+# 6
+PerfectShuffle ← ⊢⊏˜·⍋∘⍒≠⥊0‿1˜
+! "IAJBKCLDMENFOGPHQ" ≡ PerfectShuffle "ABCDEFGHIJKLMNOPQ"
+
+# 7
+_quicksort ← {Cmp←𝔽 ⋄ S←{p←𝕩Cmp˜𝕩⊏˜•Rand≠𝕩 ⋄ ∾1‿0‿1𝕩{S⍟𝕨𝕗/˜0𝕏p}¨<‿=‿>}⍟(1<≠)}
+! 1‿2‿2‿3‿5‿7‿9‿10‿10‿10‿11‿14‿16 ≡ -_quicksort 2‿2‿7‿10‿10‿11‿3‿10‿14‿5‿9‿1‿16
+! {
+  Cmp ← ≢◶0‿(-´∘⍋∾○<)¨
+  srt ← Words "Anna Fi JD Jay Jd John Morten Roger Scott Zeus"
+  srt ≡ Cmp _quicksort Words "Fi Jay John Morten Roger JD Jd Anna Scott Zeus"
+}
+
+# 8
+PascalsTriangle ← {>𝕩↑¨0(∾+∾˜)⍟(↕𝕩)⥊1}
+! (>⟨1‿0‿0‿0⋄1‿1‿0‿0⋄1‿2‿1‿0⋄1‿3‿3‿1⟩) ≡ PascalsTriangle 4
+! 1‿1‿2‿3‿5‿8‿13‿21‿34‿55 ≡ { 𝕩 ↑ +´¨ (+⌜˜↕𝕩) ⊔○⥊ PascalsTriangle 𝕩 } 10
+
+# 9
+GoldenRatio ← +⟜÷´¨∘(1↓↑) ⥊⟜1
+! 1e¯5 > | (GoldenRatio 16) - 1‿2‿1.5‿1.66667‿1.6‿1.625‿1.61538‿1.61905‿1.61765‿1.61818‿1.61798‿1.61806‿1.61803‿1.61804‿1.61803‿1.61803
+
+# 10
+NewtonsMethod ← (2 ÷˜ ⊢ + ÷)´¨∘(1↓↑) ⥊
+! 1e¯5 > | (7 NewtonsMethod 2) - 2‿1.5‿1.41667‿1.41422‿1.41421‿1.41421‿1.41421
+
+# 11
+InnerProduct ← (+´<˘)∘(ר)⎉1‿2
+! (>⟨2‿3⋄4‿1⟩) ≡ (>⟨1‿0⋄¯1‿1⟩) InnerProduct >⟨2‿3⋄6‿4⟩
+
+# 12
+CayleysTheorem ← {R←∾⊐⊢ ⋄ (R𝕩) ≡ R ⊏˜⌜˜ <˘R𝕩}
+! {
+  t ← 2‿2⊸⥊¨ (⌽2|⌊∘÷⟜2⍟(↕4))¨ 9‿6‿7‿11‿13‿14
+  g ← (≠´<˘)∘(∧¨)⎉1‿2⌜˜t
+  CayleysTheorem g
+}
+
+# 14
+IntervalIndex ← 1-˜≠∘⊣(⊣↓⊢⍋⊸⊏+`∘>)⍋∘∾  # Or ⍋, of course
+! 0‿2‿3‿2‿4‿1‿0‿2‿¯1 ≡ ¯1‿2‿3‿7‿8.5 IntervalIndex 0‿4‿7‿6‿11‿2‿1‿3‿¯5
+! 0‿1‿0‿¯1‿4‿4 ≡ "Fi Jay John Morten Roger" IntervalIndex○Words "JD Jd Geoff Anna Scott Zeus"
+
+# 15
+CentralLimit ← { 41 ↑ /⁼ (5×↕40) ⍋ +´<˘ •Rand 𝕩⥊21 }
+# 5‿8 ⥊ CentralLimit 10 1e3
+
+# 17
+SeventeenTwentyNine ← {F:
+  c ← 3⋆˜1+↕200
+  t ← (<⌜˜↕200) × +⌜˜c
+  d ← ⍷⊸⊐⊸⊔ ⥊t
+  ⌊´ ⊑¨ (2=≠¨)⊸/ d
+}
+# ! 1729 ≡ SeventeenTwentyNine⟨⟩  # slow
+
+# 24
+SymmetricArray ← ⍉⊸≡ ∧ 1⊸⍉⊸≡
+! SymmetricArray +⌜´ 3⥊<2‿3‿7‿11
+
+# 34
+_pow ← {𝔽´𝔽˜⍟(/2|⌊∘÷⟜2⍟(↕·⌈2⋆⁼⊢)𝕩)𝕨}
+! 847288609443 ≡ 3 ×_pow 25
+
+# 38
+Hanoi ← {¯1↓(⥊⊢≍⎉0˜≠⥊⊑⊑⟨1‿5‿2⋄0‿3‿4⟩˜)⍟𝕩⥊1}
+! 0‿1‿3‿0‿4‿5‿0 ≡ Hanoi 3
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