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|D}}== |
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{{trans|Java}} |
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<lang d>import std.bigint; |
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import std.functional; |
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import std.stdio; |
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alias sterling1 = memoize!sterling1Impl; |
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BigInt sterling1Impl(int n, int k) { |
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if (n == 0 && k == 0) { |
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return BigInt(1); |
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} |
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if (n > 0 && k == 0) { |
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return BigInt(0); |
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} |
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if (k > n) { |
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return BigInt(0); |
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} |
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return sterling1(n - 1, k - 1) + (n - 1) * sterling1(n - 1, k); |
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} |
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void main() { |
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writeln("Unsigned Stirling numbers of the first kind:"); |
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int max = 12; |
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write("n/k"); |
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foreach (n; 0 .. max + 1) { |
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writef("%10d", n); |
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} |
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writeln; |
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foreach (n; 0 .. max + 1) { |
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writef("%-3d", n); |
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foreach (k; 0 .. n + 1) { |
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writef("%10s", sterling1(n, k)); |
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} |
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writeln; |
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} |
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writeln("The maximum value of S1(100, k) = "); |
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auto previous = BigInt(0); |
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foreach (k; 1 .. 101) { |
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auto current = sterling1(100, k); |
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if (previous < current) { |
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previous = current; |
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} else { |
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import std.conv; |
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writeln(previous); |
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writefln("(%d digits, k = %d)", previous.to!string.length, k - 1); |
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break; |
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} |
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} |
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}</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|Factor}}== |
=={{header|Factor}}== |