Learn to Program with C_ Learn to Program using the Popular C Programming Language ( PDFDrive )

Chapter 7 ■ Functions
When main is executed,
• printf prints a heading
• The for loop is executed with n assuming the values 0, 1, 2, 3, 4, 5, 6, 7. For
each value of n, factorial is called with n as its argument. The factorial is
calculated and returned to the place in printf from where it was called.
We have deliberately used a variable called n in main to illustrate that this n does not (and
cannot) conflict with the parameter n of factorial. Suppose n in main is stored in memory
location 865 and has the value 3. The call factorial(n) stores the value of n, i.e. 3, in a temporary
location (472, say) and this temporary location is passed to factorial where it is known as n. This
is illustrated as follows:
865 3 472 3
n in main
n in factorial
We now have two locations called n. When in factorial, n refers to location 472; when in
main, n refers to location 865; factorial has no access whatsoever to location 865.
It does not happen here, but if factorial were to change the value of n, it is the value in
location 472 that would be changed; the value in location 865 would not be affected. When
factorial finishes, location 472 is discarded – that n no longer exists.
From another point of view, factorial is oblivious to the actual argument that was used to
call it since it sees only the argument’s value, not how it was derived.
We used n in main as a loop variable to illustrate the point above. However, we could have
used any variable. In particular, we could have used h and there would be no conflict with the
local variable h of the function factorial. When in factorial, h refers to the local variable; when
in main, h refers to the h declared in main.
7.7.2 Combinations
Suppose there are 7 people on a committee. How many subcommittees of 3 people can be
formed? The answer is denoted by 7 C 3
and calculated as follows:
7!
4! 3!
This gives us a value of 35. We say there are 35 combinations of 7 objects taken 3 at a time.
In general, n C r
denotes the number of combinations of n objects taken r at a time and is
calculated by the formula:
n!
n-
r ! r !
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