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19 lines
847 B
APL
19 lines
847 B
APL
⍝ N-Queens — count solutions to placing N non-attacking queens on N×N
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⍝
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⍝ A solution is encoded as a permutation P of 1..N where P[i] is the
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⍝ column of the queen in row i. Rows and columns are then automatically
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⍝ unique (it's a permutation). We must additionally rule out queens
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⍝ sharing a diagonal: |i-j| = |P[i]-P[j]| for any pair.
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⍝
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⍝ Backtracking via reduce — the classic Roger Hui style:
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⍝ queens ← {≢{⍵,¨⍨↓(0=∊(¨⍳⍴⍵)≠.+|⍵)/⍳⍴⍵}/(⍳⍵)⍴⊂⍳⍵}
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⍝
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⍝ Plain reading:
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⍝ permute 1..N, keep those where no two queens share a diagonal.
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⍝
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⍝ Known solution counts (OEIS A000170):
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⍝ N 1 2 3 4 5 6 7 8 9 10
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⍝ q(N) 1 0 0 2 10 4 40 92 352 724
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queens ← {≢({(i j)←⍺⍵ ⋄ (|i-j)≠|(P[i])-(P[j])}⌿permutations ⍵)}
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