Stirling numbers of the second kind: Difference between revisions
Stirling numbers of the second kind (view source)
Revision as of 00:44, 6 February 2021
, 3 years ago→{{header|Ruby}}: added Ruby
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</pre>
=={{header|Ruby}}==
<lang ruby>@memo = {}
def sterling2(n, k)
key = [n,k]
return @memo[key] if @memo.key?(key)
return 1 if n.zero? and k.zero?
return 0 if n.zero? or k.zero?
return 1 if n == k
return 0 if k > n
res = k * sterling2(n-1, k) + sterling2(n - 1, k-1)
@memo[key] = res
end
r = (0..12)
puts "Sterling2 numbers:"
puts "n/k #{r.map{|n| "%11d" % n}.join}"
r.each do |row|
print "%-4s" % row
puts "#{(0..row).map{|col| "%11d" % sterling2(row, col)}.join}"
end
puts "\nMaximum value from the sterling2(100, k)";
puts (1..100).map{|a| sterling2(100,a)}.max
</lang>
{{out}}<pre>Sterling2 numbers:
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
Maximum value from the L(100, *) row:
7769730053598745155212806612787584787397878128370115840974992570102386086289805848025074822404843545178960761551674
</pre>
=={{header|Sidef}}==
<lang ruby>func S2(n, k) { # Stirling numbers of the second kind
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