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|Kotlin}}== |
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{{trans|Java}} |
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<lang scala>import java.math.BigInteger |
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fun main() { |
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println("Unsigned Stirling numbers of the first kind:") |
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val max = 12 |
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print("n/k") |
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for (n in 0..max) { |
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print("%10d".format(n)) |
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} |
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println() |
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for (n in 0..max) { |
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print("%-3d".format(n)) |
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for (k in 0..n) { |
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print("%10s".format(sterling1(n, k))) |
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} |
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println() |
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} |
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println("The maximum value of S1(100, k) = ") |
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var previous = BigInteger.ZERO |
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for (k in 1..100) { |
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val current = sterling1(100, k) |
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previous = if (current!! > previous) { |
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current |
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} else { |
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println("$previous\n(${previous.toString().length} digits, k = ${k - 1})") |
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break |
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} |
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} |
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} |
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private val COMPUTED: MutableMap<String, BigInteger?> = HashMap() |
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private fun sterling1(n: Int, k: Int): BigInteger? { |
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val key = "$n,$k" |
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if (COMPUTED.containsKey(key)) { |
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return COMPUTED[key] |
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} |
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if (n == 0 && k == 0) { |
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return BigInteger.valueOf(1) |
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} |
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if (n > 0 && k == 0) { |
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return BigInteger.ZERO |
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} |
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if (k > n) { |
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return BigInteger.ZERO |
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} |
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val result = sterling1(n - 1, k - 1)!!.add(BigInteger.valueOf(n - 1.toLong()).multiply(sterling1(n - 1, k))) |
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COMPUTED[key] = result |
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return result |
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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|Perl}}== |
=={{header|Perl}}== |