Dynamic programming approach to calculating Stirling's Number

Question

int s_dynamic(int n,int k) {
    int maxj = n-k;

    int *arr = new int[maxj+1];

    for (int i = 0; i <= maxj; ++i)
        arr[i] = 1;

    for (int i = 1; i <= k; ++i)
        for(int j = 1; j <= maxj; ++j)
            arr[j] += i*arr[j-1];

    return arr[maxj];
}

Here's my attempt at determining Stirling numbers using Dynamic Programming.

It is defined as follows:

S(n,k) = S(n-1,k-1) + k S(n-1,k), if 1 < k < n

S(n,k) = 1, if k=1 ou k=n

Seems ok, right? Except when I run my unit test...

partitioningTest ..\src\Test.cpp:44 3025 == s_dynamic(9,3) expected:    3025    but was:    4414    

Can anyone see what I'm doing wrong?

Thanks!

BTW, here's the recursive solution:

int s_recursive(int n,int k) {
    if (k == 1 || k == n)
        return 1;

    return s_recursive(n-1,k-1) + k*s_recursive(n-1,k);
}

Answer 1

Found the bug. You already computed your dynamic array of Stirlings numbers for k=1 (S(n,1)=1 for all n). You should start computing S(n,2) - that is:

for (int i = 2; i <= k; ++i) //i=2, not 1
  for(int j = 1; j <= maxj; ++j)
    arr[j] += i*arr[j-1];