# 6.10. More generalization¶

As another example of generalization, imagine you wanted a program that would print a multiplication table of any size, not just the 6x6 table. You could add a parameter to printMultTable:

void printMultTable (int high) {
int i = 1;
while (i <= high) {
printMultiples (i);
i = i + 1;
}
}


I replaced the value 6 with the parameter high. If I call printMultTable with the argument 7, I get

1   2   3   4   5   6
2   4   6   8   10   12
3   6   9   12   15   18
4   8   12   16   20   24
5   10   15   20   25   30
6   12   18   24   30   36
7   14   21   28   35   42


which is fine, except that I probably want the table to be square (same number of rows and columns), which means I have to add another parameter to printMultiples, to specify how many columns the table should have.

Just to be annoying, I will also call this parameter high, demonstrating that different functions can have parameters with the same name (just like local variables):

void printMultiples (int n, int high) {
int i = 1;
while (i <= high) {
cout << n * i << "   ";
i = i + 1;
}
cout << endl;
}

void printMultTable (int high) {
int i = 1;
while (i <= high) {
printMultiples (i, high);
i = i + 1;
}
}


Notice that when I added a new parameter, I had to change the first line of the function (the interface or prototype), and I also had to change the place where the function is called in printMultTable. As expected, this program generates a square 7x7 table:

1   2   3   4   5   6   7
2   4   6   8   10   12   14
3   6   9   12   15   18   21
4   8   12   16   20   24   28
5   10   15   20   25   30   35
6   12   18   24   30   36   42
7   14   21   28   35   42   49


The active code below uses the updated printMultTable function. Notice that with generalization, we can create multiplication tables of multiple sizes by simply changing the parameter passed into printMultTable. Run the active code to see what happens!

When you generalize a function appropriately, you often find that the resulting program has capabilities you did not intend. For example, you might notice that the multiplication table is symmetric, because $$ab = ba$$, so all the entries in the table appear twice. You could save ink by printing only half the table. To do that, you only have to change one line of printMultTable. Change

printMultiples (i, high);


to

printMultiples (i, i);


and you get

1
2   4
3   6   9
4   8   12   16
5   10   15   20   25
6   12   18   24   30   36
7   14   21   28   35   42   49


I’ll leave it up to you to figure out how it works.

The active code below prints half the multiplication table. We can achieve this by replacing the printMultiples (i, high) in printMultTable with printMultiples (i, i). Run the active code to see what happens!