A solution to project euler 61 in BQN

euler61.bqn

n ← 6
k ← 4

d ← ↕n
poly ← (0.5×d+1)≍¨(-0.5×d-1)
limits ← ⌈{a‿b‿c: (2×a)÷˜-b-√(טb)-4×a×c}¨ poly ∾⌜ -10⋆k-1‿0
values ← poly {+´𝕨×(ט𝕩)‿𝕩}¨ {a‿b:<a+↕b-a}˘limits # the numbers to be tested
perm ← (n-1) ∾˘˜ (≍↕0){∾˝(0∾˘1+𝕩)⊸⊏˘⍒˘=⌜˜↕𝕨}´-⟜↕n-1 # distinct cycles of number class

{
	x ← 𝕩  
	w ← / 0‿0 ⍉ ∨˝∘∧⎉1‿∞´ m ← x {(100|𝕨)=⌜⌊𝕩÷100}¨ 1⌽x # adjacency matrices of consecutive number classes
	(×≠w)◶@‿{𝕩⋄ # is a cycle possible?
		path  ← ⟨⊑w⟩
		reach ← (⊑w) ⊏˘¨ 1↓mc ← ∨˝∘∧⎉1‿∞˜`⌾⌽ m # progressive reachability 
		reach {path ∾↩ ⊑/𝕨∧(⊢´path)⊏𝕩}¨ ¯1↓m # find path backwards
		•Show +´ path ⊑¨ x
	} @
}¨ <˘perm⊏values