public static int maxPath(int[][] a, int row, int col) {
    if(row<rows) { //while still more rows
        if(max[row][col]>0) //we've found this subtree's max path before
            return max[row][col]; //get it
        else { //we've yet to find this subtree's max path
            //set the max path for this subtree with the current value plus the
            //greater of the left subtree's max path and the right subtree's max path
            max[row][col]=a[row][col]+max(maxPath(a, row+1, col), maxPath(a, row+1, col+1));
            return max[row][col]; //return the result
        }
    }
    return 0; //end of triangle
}