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## Pure Functions

A function is considered a pure function if the result depends only on the arguments, and it has no side effects like modifying an argument or outputting something. The only result of calling a pure function is the return value.

One example is after, which compares two Times and returns a bool that indicates whether the first operand comes after the second:

bool after (Time& time1, Time& time2) {
if (time1.hour > time2.hour) return true;
if (time1.hour < time2.hour) return false;

if (time1.minute > time2.minute) return true;
if (time1.minute < time2.minute) return false;

if (time1.second > time2.second) return true;
return false;
}

What is the result of this function if the two times are equal? Does that seem like the appropriate result for this function? If you were writing the documentation for this function, would you mention that case specifically?

A second example is addTime, which calculates the sum of two times. For example, if it is 9:14:30, and your breadmaker takes 3 hours and 35 minutes, you could use addTime to figure out when the bread will be done.

Here is a rough draft of this function that is not quite right:

Time addTime (Time& t1, Time& t2) {
Time sum;
sum.hour = t1.hour + t2.hour;
sum.minute = t1.minute + t2.minute;
sum.second = t1.second + t2.second;
return sum;
}

Here is an example of how to use this function. If currentTime contains the current time and breadTime contains the amount of time it takes for your breadmaker to make bread, then you could use addTime to figure out when the bread will be done.

Time currentTime = { 9, 14, 30.0 };
Time breadTime = { 3, 35, 0.0 };
printTime (doneTime);

The output of this program is 12:49:30, which is correct. On the other hand, there are cases where the result is not correct. Can you think of one?

The problem is that this function does not deal with cases where the number of seconds or minutes adds up to more than 60. When that happens we have to "carry" the extra seconds into the minutes column, or extra minutes into the hours column.

Here's a second, corrected version of this function.

Time addTime (Time& t1, Time& t2) {
Time sum;
sum.hour = t1.hour + t2.hour;
sum.minute = t1.minute + t2.minute;
sum.second = t1.second + t2.second;

if (sum.second >= 60.0) {
sum.second -= 60.0;
sum.minute += 1;
}
if (sum.minute >= 60) {
sum.minute -= 60;
sum.hour += 1;
}
return sum;
}

Although it's correct, it's starting to get big. Later, I will suggest an alternate approach to this problem that will be much shorter.

This code demonstrates two operators we have not seen before, += and -=. These operators provide a concise way to increment and decrement variables. For example, the statement sum.second -= 60.0; is equivalent to sum.second = sum.second - 60;

Last Update: 2005-12-05