Best way to generate Pascal Triangle

Question

I am using the concept of level order traversal to generate Pascal Triangle.

Here is the code snippet:

void printPascalTriangle(int n)
{
    int line=1,Q[50]={0},f=-1,r=-1,prev,t;

    Enqueue(Q,&f,&r,1);
    Enqueue(Q,&f,&r,0);

    prev=0;
    while(line!=n)
    {
            t = Dequeue(Q,&f,&r);

            if( !t )
            {
                    line++;
                    prev = 0;
                    Enqueue(Q,&f,&r,1);

                    if(!isEmpty(&r))
                            Enqueue(Q,&f,&r,0);

                    printf("\n");
            }
            else
            {
                    printf("%d ", t);
                    Enqueue(Q,&f,&r,prev+t);
                    prev = t;
            }
    }
}

The complete code is here:

The advantage with this approach is that its space complexity is O(N) where N is the number of lines.

Is there any better way of doing the same?

Answer 1

Since your only concern is space-complexity, and you're using int (as opposed to some sort of big-integer type of potentially unbounded size), you can actually achieve space complexity of O(1) by using these two facts:

• C(n, 0) = 1 for 0 ≤ n
• C(n, k+1) = C(n, k) × (n − k) / (k + 1) for 0 ≤ k < n

These two facts mean that you can compute each element using only the previous element of the same row, so you never have to save more than one element at a time.

(By C(n, k) I mean the element in row n, position k of Pascal's triangle, assuming that rows and positions are numbered starting from 0.)