Anonymous user
Stirling numbers of the second kind: Difference between revisions
Stirling numbers of the second kind (view source)
Revision as of 11:18, 30 January 2020
, 4 years ago→{{header|Phix}}
Line 543:
Maximum value from the S2(100, *) row: 7769730053598745155...3545178960761551674 (115 digits)
</pre>
=={{header|Python}}==
{{trans|Java}}
<lang Python>
computed = {}
def sterling2(n, k):
key = str(n) + "," + str(k)
if key in computed.keys():
return computed[key]
if n == k == 0:
return 1
if (n > 0 and k == 0) or (n == 0 and k > 0):
return 0
if n == k:
return 1
if k > n:
return 0
result = k * sterling2(n - 1, k) + sterling2(n - 1, k - 1)
computed[key] = result
return result
print("Stirling numbers of the second kind:")
MAX = 12
print("n/k".ljust(10), end="")
for n in range(MAX + 1):
print(str(n).rjust(10), end="")
print()
for n in range(MAX + 1):
print(str(n).ljust(10), end="")
for k in range(n + 1):
print(str(sterling2(n, k)).rjust(10), end="")
print()
print("The maximum value of S2(100, k) = ")
previous = 0
for k in range(1, 100 + 1):
current = sterling2(100, k)
if current > previous:
previous = current
else:
print("{0}\n({1} digits, k = {2})\n".format(previous, len(str(previous)), 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>
| |||