kt←{⎕ML←1                       ⍝ Knight's Tour Chess Problem.
    ⍺←1 ⋄ sreq←⍺ ⋄ nsqs←×/⍵     ⍝ no. of solutions required, default: 1.
    kdef←,0 1∘.⌽1 ¯1∘.,2 ¯2     ⍝ vector of relative knight's moves.
    net←(⊂,⍳⍵)∩¨↓(⍳⍵)∘.+kdef    ⍝ absolute moves from each square.
    ⍳∘(⍳⍵)¨↑⍬{                  ⍝ initially empty placement vector.
        sreq=⍴⍵:⍵               ⍝ found required no. of solutions: stop.
        path←⍺⍺,⊂⍺              ⍝ extended placement vector.
        nsqs=⍴path:⍵,⊂path      ⍝ solution: accumulate.
        nxt←(⊂⍺)⊃⍵⍵             ⍝ moves from current square.
        0=⍴nxt:⍵                ⍝ stitched: back out.
        net←⍵⍵~¨⊂⊂⍺             ⍝ compressed net.
        ord←nxt[⍒↑⍴¨net[nxt]]   ⍝ tightest-rightmost order.
        ↑path ∇∇ net/ord,⊂⍵     ⍝ pursue remaining possibilities.
    }net/(⌽,⍳⍵),⊂0⍴⊂⍬           ⍝ from each starting position.
}

code_colours

test script

Back to: notes

Back to: Workspaces