Print Pascal's Triangle using recursion

Question

I'm trying to develop a program that prints out Pascal's Triangle using recursion. Here are my codes:

public class PascalTriangle {
    public static int[] computePT(int k) {
        int[] pt = new int[k + 1];
        if (k == 0) {
            pt[0] = 1;
            return pt;
        } else {
            int[] ppt = computePT(k - 1);
            pt[0] = pt[k] = 1;
            for (int i = 1; i < ppt.length; i++) {
                pt[i] = ppt[i - 1] + ppt[i];
            }
        }
        return pt;
    }
}

public class PascalTriangleDriver {
    public static void main(String args[]) {
        int k = 10;

        int arr[] = PascalTriangle.computePT(k);

        for (int i = 0; i < arr.length; i++)
            System.out.print(arr[i] + " ");

        System.out.println();
    }
}

The code runs perfectly, however my issue is that I want to modify my PascalTriangle code (not the PascalTriangleDriver code) such that when k=10, for example, it prints out:

1 9 36 84 126 126 84 36 9 1

instead of:

1 10 45 120 210 252 210 120 45 10 1

Answer 1

You seem to have made an off-by-1 error. One simple way to solve this is to write another method that calls your original method with k-1:

// this is your original method, just renamed:
private static int[] computePTImpl(int k) {
    int[] pt = new int[k + 1];
    if (k == 0) {
        pt[0] = 1;
        return pt;
    } else {
        int[] ppt = computePT(k - 1);
        pt[0] = pt[k] = 1;
        for (int i = 1; i < ppt.length; i++) {
            pt[i] = ppt[i - 1] + ppt[i];
        }
    }
    return pt;
}

// you will call this method:
public static int[] computePT(int k) {
    return computePT(k - 1);
}

Alternatively, you can actually fix your code by replacing ks with k-1s:

public static int[] computePT(int k) {
    int[] pt = new int[k]; // note the change
    if (k == 1) { // note the change
        pt[0] = 1;
        return pt;
    } else {
        int[] ppt = computePT(k - 1);
        pt[0] = pt[k - 1] = 1; // note the change
        for (int i = 1; i < ppt.length; i++) {
            pt[i] = ppt[i - 1] + ppt[i];
        }
    }
    return pt;
}

Note that we don't change the recursive call because if we did, we would be saying that the k-th row of Pascal's triangle depends on the k-2-th row, which is not true.