Java: Calculating binomial coefficient

问题:

I have the following programm calculating the binomial coefficient of two integers. But I want to change the programm, that it calculates and saves only the necessary coefficients for the solution. The problem is that I have really no idea how to it, right now. The Code

 public static long binomialIteration(int n, int k)


{
     if(k<0 || n<k)
     {
         return 0;
     }
     long[][] h= new long[n+1][n+1];
     for(int i=0; i<=n; i++)
     {
         h[i][0]=h[i][i]=1;    
     }
     for(int i=1;i<=n;i++)
     {
         for(int j=0; j<=i; j++)
         {
             h[i][j] = (j==0 ? 0: h[i-1][j-1]) + (i == j ? 0 : h[i-1][j]);
         }
     }
     return h[n][k];
 }

回答1:

Do you want to keep your code afterall? Because you can also compute the binominal coefficient recursively, which would reduce your function to these 4 lines:

static long binomi(int n, int k) {
        if ((n == k) || (k == 0))
            return 1;
        else
            return binomi(n - 1, k) + binomi(n - 1, k - 1);
    }

回答2:

What about this Code from this site

 private static long binomial(int n, int k)
    {
        if (k>n-k)
            k=n-k;

        long b=1;
        for (int i=1, m=n; i<=k; i++, m--)
            b=b*m/i;
        return b;
    }

回答3:

You don't say which coefficients youi need. If you need C(N,n) for some fixed N, you could translate the C code below, which uses a one dimensional array. After the call, C[n] will hold the binomial coefficient C(N,n) for 0<=m<=N, as long as N is at most 66 -- if you need bigger N you will need to use an integral type with more bits.

static  int64_t*    pascals_triangle( int N)
{
int n,k;
int64_t*    C = calloc( N+1, sizeof *C);
    for( n=0; n<=N; ++n)
    {   C[n] = 1;
        k = n;
        while( --k>0)
        {   C[k] += C[k-1];
        }
    }
    return C;
}