Stirling numbers of the first kind: Difference between revisions
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19710908747055261109287881673376044669240511161402863823515728791076863288440277983854056472903481625299174865860036734731122707870406148096000000000000000000 |
19710908747055261109287881673376044669240511161402863823515728791076863288440277983854056472903481625299174865860036734731122707870406148096000000000000000000 |
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</pre> |
</pre> |
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=={{header|Ruby}}== |
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{{trans|D}} |
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<lang ruby>$cache = {} |
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def sterling1(n, k) |
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if n == 0 and k == 0 then |
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return 1 |
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end |
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if n > 0 and k == 0 then |
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return 0 |
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end |
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if k > n then |
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return 0 |
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end |
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key = [n, k] |
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if $cache[key] then |
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return $cache[key] |
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end |
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value = sterling1(n - 1, k - 1) + (n - 1) * sterling1(n - 1, k) |
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$cache[key] = value |
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return value |
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end |
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MAX = 12 |
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def main |
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print "Unsigned Stirling numbers of the first kind:\n" |
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print "n/k" |
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for n in 0 .. MAX |
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print "%10d" % [n] |
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end |
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print "\n" |
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for n in 0 .. MAX |
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print "%-3d" % [n] |
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for k in 0 .. n |
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print "%10d" % [sterling1(n, k)] |
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end |
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print "\n" |
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end |
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print "The maximum value of S1(100, k) =\n" |
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previous = 0 |
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for k in 1 .. 100 |
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current = sterling1(100, k) |
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if previous < current then |
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previous = current |
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else |
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print previous, "\n" |
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print "(%d digits, k = %d)\n" % [previous.to_s.length, k - 1] |
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break |
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end |
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end |
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end |
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main()</lang> |
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{{out}} |
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<pre>Unsigned Stirling numbers of the first kind: |
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n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 |
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0 1 |
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1 0 1 |
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2 0 1 1 |
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3 0 2 3 1 |
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4 0 6 11 6 1 |
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5 0 24 50 35 10 1 |
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6 0 120 274 225 85 15 1 |
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7 0 720 1764 1624 735 175 21 1 |
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8 0 5040 13068 13132 6769 1960 322 28 1 |
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9 0 40320 109584 118124 67284 22449 4536 546 36 1 |
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10 0 362880 1026576 1172700 723680 269325 63273 9450 870 45 1 |
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11 0 3628800 10628640 12753576 8409500 3416930 902055 157773 18150 1320 55 1 |
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12 0 39916800 120543840 150917976 105258076 45995730 13339535 2637558 357423 32670 1925 66 1 |
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The maximum value of S1(100, k) = |
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19710908747055261109287881673376044669240511161402863823515728791076863288440277983854056472903481625299174865860036734731122707870406148096000000000000000000 |
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(158 digits, k = 5)</pre> |
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=={{header|Sidef}}== |
=={{header|Sidef}}== |
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