Pascal's triangle: Difference between revisions
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=== Recursive(slow) === |
=== Recursive(slow) === |
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In the spirit of the Haskell "think in whole lists" solution here is a list-driven, minimalist solution: |
In the spirit of the Haskell "think in whole lists" solution here is a list-driven, minimalist solution: |
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<lang groovy>pascal = { n -> n <= 1 ? [1] : |
<lang groovy>pascal = { n -> (n <= 1) ? [1] : GroovyCollections.transpose([[0] + pascal(n - 1), pascal(n - 1) + [0]]).collect { it.sum() } }</lang> |
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However, this solution is horribly inefficient (O(''n'' |
However, this solution is horribly inefficient (O(''n''**2)). It slowly grinds to a halt on a reasonably powerful PC after about line 25 of the triangle. |
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Program for unformatted output: |
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<lang groovy>(1..20).each { println "${it}: ${pascal(it)}" }</lang> |
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Output: |
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<pre>1: [1] |
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2: [1, 1] |
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3: [1, 2, 1] |
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4: [1, 3, 3, 1] |
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5: [1, 4, 6, 4, 1] |
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6: [1, 5, 10, 10, 5, 1] |
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7: [1, 6, 15, 20, 15, 6, 1] |
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8: [1, 7, 21, 35, 35, 21, 7, 1] |
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9: [1, 8, 28, 56, 70, 56, 28, 8, 1] |
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10: [1, 9, 36, 84, 126, 126, 84, 36, 9, 1] |
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11: [1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1] |
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12: [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1] |
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13: [1, 12, 66, 220, 495, 792, 924, 792, 495, 220, 66, 12, 1] |
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14: [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13, 1] |
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15: [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003, 2002, 1001, 364, 91, 14, 1] |
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16: [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435, 5005, 3003, 1365, 455, 105, 15, 1] |
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17: [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1] |
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18: [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310, 24310, 19448, 12376, 6188, 2380, 680, 136, 17, 1] |
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19: [1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758, 48620, 43758, 31824, 18564, 8568, 3060, 816, 153, 18, 1] |
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20: [1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582, 92378, 92378, 75582, 50388, 27132, 11628, 3876, 969, 171, 19, 1]</pre> |
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=={{header|Haskell}}== |
=={{header|Haskell}}== |