WEBVTT 00:00:00.000 --> 00:00:02.000 00:00:02.000 --> 00:00:08.866 As another example, let's write a function that determines if a number is a multiple of a factor. 00:00:08.866 --> 00:00:11.466 We can use the remainder function. 00:00:11.466 --> 00:00:18.532 However, if the factor is zero, we will see an error message telling us not to divide by zero. 00:00:18.533 --> 00:00:25.966 We want to return the answer false if factor is zero, so we can add another condition checking that factor is non-zero. 00:00:25.966 --> 00:00:32.566 By putting that condition first, we can rely on short-cut evaluation. 00:00:32.566 --> 00:00:35.799 To trace the function on inputs 10 and 5, 00:00:35.800 --> 00:00:42.566 we first substitute 10 in for number and 5 in for factor in the expression returned by the function. 00:00:42.566 --> 00:00:46.366 We now start to evaluate the expression from left to right. 00:00:46.366 --> 00:00:52.899 The first smaller expression is true, so we can substitute the value true for the first expression. 00:00:52.900 --> 00:00:56.000 Can we use short-cut evaluation to stop early? 00:00:56.000 --> 00:01:03.166 No, since we are using "and", we can only stop early if have a smaller expression that evaluates to false. 00:01:03.166 --> 00:01:10.399 So now we evaluate the expression 10 remainder 5 to obtain 0, which we place instead of 10 remainder 5 in the expression. 00:01:10.400 --> 00:01:15.166 This results in the expression 0 equals 0, which evaluates to true. 00:01:15.166 --> 00:01:20.166 Finally, the expression "True" and "True" is evaluated to obtain "True". 00:01:20.166 --> 00:01:26.366 On the other hand, on inputs 10 and 0, the first expression evaluates to False. 00:01:26.366 --> 00:01:33.599 Since we are using short-cut evalution, we can now conclude that the value of the entire expression is "False". 00:01:33.600 --> 00:01:39.266 This not only saved time, but saved us from the program failing due to an error message. 00:01:39.266 --> 00:01:45.899 That is, since we never evaluated the second smaller expression, we didn't try to divide by zero. 00:01:45.900 --> 00:01:51.033 Notice that the only time we would divide by zero would be if the second input were zero. 00:01:51.033 --> 00:01:54.466 But that is exactly when we would get to stop early. 00:01:54.466 --> 00:02:01.999 Short-cut evaluation ensures that we never see an error message, no matter what integers the inputs are. 00:02:02.000 --> 00:02:09.966 We can also take advantage of short-cut evaluation in writing a function to determine whether the first character in a string is the letter "a". 00:02:09.966 --> 00:02:18.166 This function seems fine except that trying to find the first character of an empty string will result in an error message. 00:02:18.166 --> 00:02:24.299 We want to return false in that case anyway, so we can add a condition that will be false for the empty string. 00:02:24.300 --> 00:02:30.600 Again, we put the condition first to take advantage of short-cut evaluation. 00:02:30.600 --> 00:02:39.200 As in the previous example, we can trace the behaviour of our function by placing the input value everywhere in the expression returned by the function. 00:02:39.200 --> 00:02:48.066 Moving from left to right, we first evaluate the length of the string "dog" to obtain 3, and then compare 3 and 0 to obtain "True". 00:02:48.066 --> 00:02:52.799 We don't get to stop early, since we only get to stop early when we see "False". 00:02:52.800 --> 00:02:59.000 We next determine the first character in "dog", and then compare it to "a" to obtain "False". 00:02:59.000 --> 00:03:04.966 This means that the entire expression is false, since the value of "True and False" is False. 00:03:04.966 --> 00:03:12.866 When the input is the empty string, the length is 0, and hence the value of the first expression is "False". 00:03:12.866 --> 00:03:15.866 By short-cut evaluation, we get to stop early, 00:03:15.866 --> 00:03:20.566 and returns "False" without ever trying to find the first character in the string. 00:03:20.566 --> 00:03:29.766 This is very good, because it meant that we avoided applying the index 0 to an empty string, which would have resulted in an error message. 00:03:29.766 --> 00:03:37.499 Again, short-cut evaluation saved the day: it is only when there is an empty string that the first expression will evaluate to false, 00:03:37.500 --> 00:03:44.600 and that is precisely when we want to stop evaluating expressions before hitting the second one. 00:03:44.600 --> 00:03:49.766 Keep short-cut evaluation in mind to avoid errors such as division by zero, 00:03:49.766 --> 00:03:52.799 extracting a character from an empty string, 00:03:52.800 --> 00:03:55.433 and adding non-numbers. 00:03:55.433 --> 00:04:04.999 Judicious ordering of conditions can allow you to take advantage of short-cut evaluation to circumvent these problems.