giles
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26 lines
1.2 KiB
APL
26 lines
1.2 KiB
APL
⍝ Quicksort — the classic Roger Hui one-liner
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⍝
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⍝ Q ← {1≥≢⍵:⍵ ⋄ (∇⍵⌿⍨⍵<p),(p=⍵)/⍵,∇⍵⌿⍨⍵>p←⍵⌷⍨?≢⍵}
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⍝
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⍝ Read right-to-left:
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⍝ ?≢⍵ : pick a random index in 1..length
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⍝ ⍵⌷⍨… : take that element as pivot p
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⍝ ⍵>p : boolean — elements greater than pivot
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⍝ ∇⍵⌿⍨… : recursively sort the > partition
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⍝ (p=⍵)/⍵ : keep elements equal to pivot
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⍝ ⍵<p : boolean — elements less than pivot
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⍝ ∇⍵⌿⍨… : recursively sort the < partition
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⍝ , : catenate ⟨less⟩ ⟨equal⟩ ⟨greater⟩
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⍝ 1≥≢⍵:⍵ : guard — base case for length ≤ 1
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⍝
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⍝ Stability: not stable on duplicates (but eq-class is preserved as a block).
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⍝ Worst case O(N²) on already-sorted input with deterministic pivot;
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⍝ randomized pivot selection gives expected O(N log N).
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⍝
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⍝ Examples:
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⍝ Q 3 1 4 1 5 9 2 6 5 3 5 → 1 1 2 3 3 4 5 5 5 6 9
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⍝ Q ⍳0 → ⍬ (empty)
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⍝ Q ,42 → 42
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quicksort ← {1≥≢⍵:⍵ ⋄ p←⍵⌷⍨?≢⍵ ⋄ (∇⍵⌿⍨⍵<p),(p=⍵)/⍵,∇⍵⌿⍨⍵>p}
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