How to resolve the algorithm Stirling numbers of the second kind step by step in the FreeBASIC programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Stirling numbers of the second kind step by step in the FreeBASIC programming language

Table of Contents

Problem Statement

Stirling numbers of the second kind, or Stirling partition numbers, are the number of ways to partition a set of n objects into k non-empty subsets. They are closely related to Bell numbers, and may be derived from them.

Stirling numbers of the second kind obey the recurrence relation:

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Stirling numbers of the second kind step by step in the FreeBASIC programming language

Source code in the freebasic programming language

dim as integer S2(0 to 12, 0 to 12)   'initially set with zeroes
dim as ubyte n, k
dim as string outstr

function padto( i as ubyte, j as integer ) as string
    return wspace(i-len(str(j)))+str(j)
end function

for k = 0 to 12   'calculate table
    S2(k,k)=1
next k
for n = 1 to 11
    for k = 1 to 12
        S2(n+1,k) = k*S2(n,k) + S2(n,k-1)
    next k
next n

print "Stirling numbers of the second kind"
print
outstr = "   k"
for k=0 to 12
    outstr += padto(12, k)
next k
print outstr
print " n"
for n = 0 to 12
    outstr = padto(2, n)+"  "
    for k = 0 to 12
        outstr += padto(12, S2(n, k))
    next k
    print outstr
next n

  

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