May 10, 2014
Seriously, just watch it.
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Seriously, just watch it.
Counting The Number Of Ways You Can Put Items Into A Shopping Cart: A Combinatorial Explosion Problem
This problem illustrates how common, every day Web functionality presents the test designer with a staggeringly large number of execution paths.
Imagine you have a shopping cart which can contain up to 100 different items in varying quantities. There are about 150 different items to choose from.
Now imagine you have been asked to design an automated test that exercises all possible combinations of items, in all valid quantities including zero.
How many variables do we need to think about here? There are 3 variables:
capacity of the cart,
number of different items, and
how many of each item is available
How would you describe the complexity of this test? The number of paths that need be excercised exhibits factorial or O(n!) growth as we put more items into the cart.
How long would you expect this test to take to run? There are over 10^45 ways (that's the sum of 150 choose i as i grows from 1 to 100) to fill the cart with just one of each item. That's just one of each item, we haven't even considered different quantities of items yet.
Assuming one test per microsecond, runtime exceeds the age of the universe (only about 4 * 10^17 seconds). And that still is just a fraction of the number of paths that would be encountered in the the full test case as described above; where not just all possible combinations of items, but also all possible combinations in all valid quantities from 0 to 100, would be tested. I didn't bother to do the math on that one, but it's a lot of paths :)
This is a bad test. Besides being impossible to implement, what are we proving by testing every combination that we can't prove by just testing a few edge cases?
15 trillion trillion—The number of possible routes a driver with just 25 packages to deliver can choose from. As illustrated by the classic traveling salesman problem, the mathematical phenomenon that makes figuring out the best delivery routes so difficult is called a combinatorial explosion.
"The Astronomical Math Behind UPS’ New Tool to Deliver Packages Faster" via Wired
That's one hell of a logistics problem...