Stirling numbers of the second kind: Difference between revisions
→{{header|Factor}}
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7769730053598745155212806612787584787397878128370115840974992570102386086289805848025074822404843545178960761551674
</pre>
=={{header|D}}==
{{trans|Java}}
<lang d>import std.bigint;
import std.conv;
import std.functional;
import std.stdio;
alias sterling2 = memoize!sterling2Impl;
BigInt sterling2Impl(int n, int k) {
if (n == 0 && k == 0) {
return BigInt(1);
}
if ((n > 0 && k == 0) || (n == 0 && k > 0)) {
return BigInt(0);
}
if (n == k) {
return BigInt(1);
}
if (k > n) {
return BigInt(0);
}
return BigInt(k) * sterling2(n - 1, k) + sterling2(n - 1, k - 1);
}
void main() {
writeln("Stirling numbers of the second kind:");
int max = 12;
write("n/k");
for (int n = 0; n <= max; n++) {
writef("%10d", n);
}
writeln;
for (int n = 0; n <= max; n++) {
writef("%-3d", n);
for (int k = 0; k <= n; k++) {
writef("%10s", sterling2(n, k));
}
writeln;
}
writeln("The maximum value of S2(100, k) = ");
auto previous = BigInt(0);
for (int k = 1; k <= 100; k++) {
auto current = sterling2(100, k);
if (current > previous) {
previous = current;
} else {
writeln(previous);
auto ps = previous.to!string;
writefln("(%d digits, k = %d)", ps.length, k - 1);
break;
}
}
}</lang>
{{out}}
<pre>Stirling numbers of the second kind:
n/k 0 1 2 3 4 5 6 7 8 9 10 11 12
0 1
1 0 1
2 0 1 1
3 0 1 3 1
4 0 1 7 6 1
5 0 1 15 25 10 1
6 0 1 31 90 65 15 1
7 0 1 63 301 350 140 21 1
8 0 1 127 966 1701 1050 266 28 1
9 0 1 255 3025 7770 6951 2646 462 36 1
10 0 1 511 9330 34105 42525 22827 5880 750 45 1
11 0 1 1023 28501 145750 246730 179487 63987 11880 1155 55 1
12 0 1 2047 86526 611501 1379400 1323652 627396 159027 22275 1705 66 1
The maximum value of S2(100, k) =
7769730053598745155212806612787584787397878128370115840974992570102386086289805848025074822404843545178960761551674
(115 digits, k = 28)</pre>
=={{header|Factor}}==
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