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78bfc38b81
| Author | SHA1 | Date |
|---|---|---|
 Oliver Payne
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78bfc38b81 | |
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Oliver Payne
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1bc48e4e78 |
96
2-42.rkt
96
2-42.rkt
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@ -74,6 +74,102 @@
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(not (memv (negative-intercept kth-position)
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(map negative-intercept pre-kth-positions))))))
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;; ;; Output
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;; (((1 . 1) (5 . 2) (8 . 3) (6 . 4) (3 . 5) (7 . 6) (2 . 7) (4 . 8))
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;; ((1 . 1) (6 . 2) (8 . 3) (3 . 4) (7 . 5) (4 . 6) (2 . 7) (5 . 8))
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;; ((1 . 1) (7 . 2) (4 . 3) (6 . 4) (8 . 5) (2 . 6) (5 . 7) (3 . 8))
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;; ((1 . 1) (7 . 2) (5 . 3) (8 . 4) (2 . 5) (4 . 6) (6 . 7) (3 . 8))
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;; ((2 . 1) (4 . 2) (6 . 3) (8 . 4) (3 . 5) (1 . 6) (7 . 7) (5 . 8))
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;; ((2 . 1) (5 . 2) (7 . 3) (1 . 4) (3 . 5) (8 . 6) (6 . 7) (4 . 8))
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;; ((2 . 1) (5 . 2) (7 . 3) (4 . 4) (1 . 5) (8 . 6) (6 . 7) (3 . 8))
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;; ((2 . 1) (6 . 2) (1 . 3) (7 . 4) (4 . 5) (8 . 6) (3 . 7) (5 . 8))
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;; ((2 . 1) (6 . 2) (8 . 3) (3 . 4) (1 . 5) (4 . 6) (7 . 7) (5 . 8))
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;; ((2 . 1) (7 . 2) (3 . 3) (6 . 4) (8 . 5) (5 . 6) (1 . 7) (4 . 8))
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;; ((2 . 1) (7 . 2) (5 . 3) (8 . 4) (1 . 5) (4 . 6) (6 . 7) (3 . 8))
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;; ((2 . 1) (8 . 2) (6 . 3) (1 . 4) (3 . 5) (5 . 6) (7 . 7) (4 . 8))
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;; ((3 . 1) (1 . 2) (7 . 3) (5 . 4) (8 . 5) (2 . 6) (4 . 7) (6 . 8))
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;; ((3 . 1) (5 . 2) (2 . 3) (8 . 4) (1 . 5) (7 . 6) (4 . 7) (6 . 8))
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;; ((3 . 1) (5 . 2) (2 . 3) (8 . 4) (6 . 5) (4 . 6) (7 . 7) (1 . 8))
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;; ((3 . 1) (5 . 2) (7 . 3) (1 . 4) (4 . 5) (2 . 6) (8 . 7) (6 . 8))
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;; ((3 . 1) (5 . 2) (8 . 3) (4 . 4) (1 . 5) (7 . 6) (2 . 7) (6 . 8))
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;; ((3 . 1) (6 . 2) (2 . 3) (5 . 4) (8 . 5) (1 . 6) (7 . 7) (4 . 8))
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;; ((3 . 1) (6 . 2) (2 . 3) (7 . 4) (1 . 5) (4 . 6) (8 . 7) (5 . 8))
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;; ((3 . 1) (6 . 2) (2 . 3) (7 . 4) (5 . 5) (1 . 6) (8 . 7) (4 . 8))
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;; ((3 . 1) (6 . 2) (4 . 3) (1 . 4) (8 . 5) (5 . 6) (7 . 7) (2 . 8))
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;; ((3 . 1) (6 . 2) (4 . 3) (2 . 4) (8 . 5) (5 . 6) (7 . 7) (1 . 8))
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;; ((3 . 1) (6 . 2) (8 . 3) (1 . 4) (4 . 5) (7 . 6) (5 . 7) (2 . 8))
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;; ((3 . 1) (6 . 2) (8 . 3) (1 . 4) (5 . 5) (7 . 6) (2 . 7) (4 . 8))
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;; ((3 . 1) (6 . 2) (8 . 3) (2 . 4) (4 . 5) (1 . 6) (7 . 7) (5 . 8))
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;; ((3 . 1) (7 . 2) (2 . 3) (8 . 4) (5 . 5) (1 . 6) (4 . 7) (6 . 8))
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;; ((3 . 1) (7 . 2) (2 . 3) (8 . 4) (6 . 5) (4 . 6) (1 . 7) (5 . 8))
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;; ((3 . 1) (8 . 2) (4 . 3) (7 . 4) (1 . 5) (6 . 6) (2 . 7) (5 . 8))
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;; ((4 . 1) (1 . 2) (5 . 3) (8 . 4) (2 . 5) (7 . 6) (3 . 7) (6 . 8))
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;; ((4 . 1) (1 . 2) (5 . 3) (8 . 4) (6 . 5) (3 . 6) (7 . 7) (2 . 8))
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;; ((4 . 1) (2 . 2) (5 . 3) (8 . 4) (6 . 5) (1 . 6) (3 . 7) (7 . 8))
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;; ((4 . 1) (2 . 2) (7 . 3) (3 . 4) (6 . 5) (8 . 6) (1 . 7) (5 . 8))
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;; ((4 . 1) (2 . 2) (7 . 3) (3 . 4) (6 . 5) (8 . 6) (5 . 7) (1 . 8))
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;; ((4 . 1) (2 . 2) (7 . 3) (5 . 4) (1 . 5) (8 . 6) (6 . 7) (3 . 8))
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;; ((4 . 1) (2 . 2) (8 . 3) (5 . 4) (7 . 5) (1 . 6) (3 . 7) (6 . 8))
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;; ((4 . 1) (2 . 2) (8 . 3) (6 . 4) (1 . 5) (3 . 6) (5 . 7) (7 . 8))
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;; ((4 . 1) (6 . 2) (1 . 3) (5 . 4) (2 . 5) (8 . 6) (3 . 7) (7 . 8))
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;; ((4 . 1) (6 . 2) (8 . 3) (2 . 4) (7 . 5) (1 . 6) (3 . 7) (5 . 8))
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;; ((4 . 1) (6 . 2) (8 . 3) (3 . 4) (1 . 5) (7 . 6) (5 . 7) (2 . 8))
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;; ((4 . 1) (7 . 2) (1 . 3) (8 . 4) (5 . 5) (2 . 6) (6 . 7) (3 . 8))
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;; ((4 . 1) (7 . 2) (3 . 3) (8 . 4) (2 . 5) (5 . 6) (1 . 7) (6 . 8))
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;; ((4 . 1) (7 . 2) (5 . 3) (2 . 4) (6 . 5) (1 . 6) (3 . 7) (8 . 8))
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;; ((4 . 1) (7 . 2) (5 . 3) (3 . 4) (1 . 5) (6 . 6) (8 . 7) (2 . 8))
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;; ((4 . 1) (8 . 2) (1 . 3) (3 . 4) (6 . 5) (2 . 6) (7 . 7) (5 . 8))
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;; ((4 . 1) (8 . 2) (1 . 3) (5 . 4) (7 . 5) (2 . 6) (6 . 7) (3 . 8))
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;; ((4 . 1) (8 . 2) (5 . 3) (3 . 4) (1 . 5) (7 . 6) (2 . 7) (6 . 8))
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;; ((5 . 1) (1 . 2) (4 . 3) (6 . 4) (8 . 5) (2 . 6) (7 . 7) (3 . 8))
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;; ((5 . 1) (1 . 2) (8 . 3) (4 . 4) (2 . 5) (7 . 6) (3 . 7) (6 . 8))
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;; ((5 . 1) (1 . 2) (8 . 3) (6 . 4) (3 . 5) (7 . 6) (2 . 7) (4 . 8))
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;; ((5 . 1) (2 . 2) (4 . 3) (6 . 4) (8 . 5) (3 . 6) (1 . 7) (7 . 8))
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;; ((5 . 1) (2 . 2) (4 . 3) (7 . 4) (3 . 5) (8 . 6) (6 . 7) (1 . 8))
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;; ((5 . 1) (2 . 2) (6 . 3) (1 . 4) (7 . 5) (4 . 6) (8 . 7) (3 . 8))
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;; ((5 . 1) (2 . 2) (8 . 3) (1 . 4) (4 . 5) (7 . 6) (3 . 7) (6 . 8))
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;; ((5 . 1) (3 . 2) (1 . 3) (6 . 4) (8 . 5) (2 . 6) (4 . 7) (7 . 8))
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;; ((5 . 1) (3 . 2) (1 . 3) (7 . 4) (2 . 5) (8 . 6) (6 . 7) (4 . 8))
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;; ((5 . 1) (3 . 2) (8 . 3) (4 . 4) (7 . 5) (1 . 6) (6 . 7) (2 . 8))
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;; ((5 . 1) (7 . 2) (1 . 3) (3 . 4) (8 . 5) (6 . 6) (4 . 7) (2 . 8))
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;; ((5 . 1) (7 . 2) (1 . 3) (4 . 4) (2 . 5) (8 . 6) (6 . 7) (3 . 8))
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;; ((5 . 1) (7 . 2) (2 . 3) (4 . 4) (8 . 5) (1 . 6) (3 . 7) (6 . 8))
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;; ((5 . 1) (7 . 2) (2 . 3) (6 . 4) (3 . 5) (1 . 6) (4 . 7) (8 . 8))
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;; ((5 . 1) (7 . 2) (2 . 3) (6 . 4) (3 . 5) (1 . 6) (8 . 7) (4 . 8))
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;; ((5 . 1) (7 . 2) (4 . 3) (1 . 4) (3 . 5) (8 . 6) (6 . 7) (2 . 8))
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;; ((5 . 1) (8 . 2) (4 . 3) (1 . 4) (3 . 5) (6 . 6) (2 . 7) (7 . 8))
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;; ((5 . 1) (8 . 2) (4 . 3) (1 . 4) (7 . 5) (2 . 6) (6 . 7) (3 . 8))
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;; ((6 . 1) (1 . 2) (5 . 3) (2 . 4) (8 . 5) (3 . 6) (7 . 7) (4 . 8))
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;; ((6 . 1) (2 . 2) (7 . 3) (1 . 4) (3 . 5) (5 . 6) (8 . 7) (4 . 8))
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;; ((6 . 1) (2 . 2) (7 . 3) (1 . 4) (4 . 5) (8 . 6) (5 . 7) (3 . 8))
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;; ((6 . 1) (3 . 2) (1 . 3) (7 . 4) (5 . 5) (8 . 6) (2 . 7) (4 . 8))
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;; ((6 . 1) (3 . 2) (1 . 3) (8 . 4) (4 . 5) (2 . 6) (7 . 7) (5 . 8))
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;; ((6 . 1) (3 . 2) (1 . 3) (8 . 4) (5 . 5) (2 . 6) (4 . 7) (7 . 8))
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;; ((6 . 1) (3 . 2) (5 . 3) (7 . 4) (1 . 5) (4 . 6) (2 . 7) (8 . 8))
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;; ((6 . 1) (3 . 2) (5 . 3) (8 . 4) (1 . 5) (4 . 6) (2 . 7) (7 . 8))
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;; ((6 . 1) (3 . 2) (7 . 3) (2 . 4) (4 . 5) (8 . 6) (1 . 7) (5 . 8))
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;; ((6 . 1) (3 . 2) (7 . 3) (2 . 4) (8 . 5) (5 . 6) (1 . 7) (4 . 8))
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;; ((6 . 1) (3 . 2) (7 . 3) (4 . 4) (1 . 5) (8 . 6) (2 . 7) (5 . 8))
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;; ((6 . 1) (4 . 2) (1 . 3) (5 . 4) (8 . 5) (2 . 6) (7 . 7) (3 . 8))
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;; ((6 . 1) (4 . 2) (2 . 3) (8 . 4) (5 . 5) (7 . 6) (1 . 7) (3 . 8))
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;; ((6 . 1) (4 . 2) (7 . 3) (1 . 4) (3 . 5) (5 . 6) (2 . 7) (8 . 8))
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;; ((6 . 1) (4 . 2) (7 . 3) (1 . 4) (8 . 5) (2 . 6) (5 . 7) (3 . 8))
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;; ((6 . 1) (8 . 2) (2 . 3) (4 . 4) (1 . 5) (7 . 6) (5 . 7) (3 . 8))
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;; ((7 . 1) (1 . 2) (3 . 3) (8 . 4) (6 . 5) (4 . 6) (2 . 7) (5 . 8))
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;; ((7 . 1) (2 . 2) (4 . 3) (1 . 4) (8 . 5) (5 . 6) (3 . 7) (6 . 8))
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;; ((7 . 1) (2 . 2) (6 . 3) (3 . 4) (1 . 5) (4 . 6) (8 . 7) (5 . 8))
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;; ((7 . 1) (3 . 2) (1 . 3) (6 . 4) (8 . 5) (5 . 6) (2 . 7) (4 . 8))
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;; ((7 . 1) (3 . 2) (8 . 3) (2 . 4) (5 . 5) (1 . 6) (6 . 7) (4 . 8))
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;; ((7 . 1) (4 . 2) (2 . 3) (5 . 4) (8 . 5) (1 . 6) (3 . 7) (6 . 8))
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;; ((7 . 1) (4 . 2) (2 . 3) (8 . 4) (6 . 5) (1 . 6) (3 . 7) (5 . 8))
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;; ((7 . 1) (5 . 2) (3 . 3) (1 . 4) (6 . 5) (8 . 6) (2 . 7) (4 . 8))
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;; ((8 . 1) (2 . 2) (4 . 3) (1 . 4) (7 . 5) (5 . 6) (3 . 7) (6 . 8))
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;; ((8 . 1) (2 . 2) (5 . 3) (3 . 4) (1 . 5) (7 . 6) (4 . 7) (6 . 8))
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;; ((8 . 1) (3 . 2) (1 . 3) (6 . 4) (2 . 5) (5 . 6) (7 . 7) (4 . 8))
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;; ((8 . 1) (4 . 2) (1 . 3) (3 . 4) (6 . 5) (2 . 6) (7 . 7) (5 . 8)))
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;; Exercise 2.43
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;; This is slower than the first version from the book because
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@ -1,92 +1,49 @@
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;; EXERCISE 2.42
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(define (queens board-size)
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(define (queen-cols k)
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(if (= k 0)
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(list empty-board)
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(filter
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(lambda (positions) (safe? k positions))
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(flatmap
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(lambda (rest-of-queens)
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(map (lambda (new-row)
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(adjoin-position new-row k rest-of-queens))
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(enumerate-interval 1 board-size)))
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(queen-cols (- k 1))))))
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(queen-cols board-size))
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(define empty-board '())
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(define (position row col) (cons row col))
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(define (row position) (car position))
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(define (col position) (cdr position))
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(define (intercepts horiz pos neg) (list horiz pos neg))
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(define (horiz intercepts) (car intercepts))
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(define (pos intercepts) (cadr intercepts))
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(define (neg intercepts) (caddr intercepts))
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(define (col-k-pos k positions)
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(car (filter (lambda (x) (= (col x) k)) positions)))
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; Compute the y-intercepts of the horizontal line the line
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; of gradient +1 and the line of gradient -1 through the
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; given position. Any two positions that share one of these
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; intercepts put are not safe wrt each other.
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(define (compute-intercepts position)
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(intercepts (row position)
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(- (row position) (col position))
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(+ (row position) (col position))))
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(define (checks pos1 pos2)
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(if (= (col pos1) (col pos2))
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#f
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(let ((int1 (compute-intercepts pos1))
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(int2 (compute-intercepts pos2)))
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(or (= (horiz int1) (horiz int2))
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(= (pos int1) (pos int2))
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(= (neg int1) (neg int2))))))
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(define (adjoin-position row col rest-of-queens)
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(append rest-of-queens (list (position row col))))
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; Calculuate the intercepts of each of the position. If any
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; match, then the k-th position is not safe.
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(define (safe? k positions)
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(if (= (col (car positions)) k) #t ; Need to only check with first k-1
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(let* ((k-pos (col-k-pos k positions))
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(k-int (compute-intercepts k-pos))
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(int (compute-intercepts (car positions))))
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(and (not (= (horiz int) (horiz k-int)))
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(not (= (pos int) (pos k-int)))
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(not (= (neg int) (neg k-int)))
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(safe? k (cdr positions))))))
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(define (enumerate-interval low high)
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(if (> low high)
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'()
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(cons low (enumerate-interval (+ low 1) high))))
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(define (list-ref l n)
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(if (= n 0) (car l)
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(list-ref (cdr l) (- n 1))))
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(define (eight-queens)
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;; Not sure how to get a procedure to create (amb 1 ... n) for
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;; arbitrary n without doing quasiquote, unsplice, etc, so fix for
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;; n=8.
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(define (queens)
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(define (position row col) (cons row col))
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(define (row position) (car position))
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(define (col position) (cdr position))
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(define (positive-intercept position)
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(- (row position) (col position)))
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(define (negative-intercept position)
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(+ (row position) (col position)))
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(define (safe? k positions)
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(let ((kth-position (list-ref positions (- k 1)))
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(pre-kth-positions (cdr (reverse positions))))
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;; If the row, positive or negative intercept of the k-th position
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;; is equal to any of the first k-1 positions, then the k-th
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;; position is not safe.
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;; Better would be: look at columns up to k and check that row
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;; and intercepts are distinct.
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(if (memv (row kth-position) (map row pre-kth-positions))
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false
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(if (memv (positive-intercept kth-position)
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(map positive-intercept pre-kth-positions))
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(if (< k 2) true
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(let ((kth-position (list-ref positions (- k 1)))
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(pre-kth-positions (cdr (reverse positions))))
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;; If the row, positive or negative intercept of the k-th position
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;; is equal to any of the first k-1 positions, then the k-th
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;; position is not safe.
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(if (memv (row kth-position) (map row pre-kth-positions))
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false
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(if (memv (negative-intercept kth-position)
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(map negative-intercept pre-kth-positions))
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(if (memv (positive-intercept kth-position)
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(map positive-intercept pre-kth-positions))
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false
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true)))))
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(let ((queens
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(map (lambda (col) (position (amb 1 2 3 4 5 6 7 8) col))
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'(1 2 3 4 5 6 7 8))))
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(and-map (lambda (k) (safe? k queens))
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'(1 2 3 4 5 6 7 8))
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queens))
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(if (memv (negative-intercept kth-position)
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(map negative-intercept pre-kth-positions))
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false
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true))))))
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(define (queens-add-columns current-queens column)
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(if (> column 8) current-queens
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(let ((new-queens
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(append current-queens
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(list (position (amb 1 2 3 4 5 6 7 8) column)))))
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(require (safe? column new-queens))
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(queens-add-columns new-queens (+ column 1)))))
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(queens-add-columns '() 1))
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@ -164,6 +164,7 @@
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(list 'null? null?)
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(list 'list list)
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(list 'reverse reverse)
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(list 'append append)
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(list 'memq memq)
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(list 'memv memv)
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(list 'member member)
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