 In this video, we provide the solution to question number 12 for practice exam number two for math 1030, in which case we're asked to use the backflow algorithm to compute the critical time priority list for the project whose project diagram is illustrated below. So we have to come up with the critical time priority list, but we have to also show our work by computing the critical times of each of these tasks. So I want a little bit more space here. So I'm going to write their critical times in each of these boxes here. So starting at the very end, the end gets zero here. Who are the neighbors of the end? You get K, which has 20 plus a zero as its critical time. You have J, whose critical time is going to be five plus a zero like so. So then who precedes J? That's only H. H, it has processing time of five, five plus five is 10. We get that one. G only precedes K, whose critical time was 20. 20 plus four is 24 naturally here. I only precedes K. So we're going to take 15 plus 20 and get 35 like so. Looking at E here, whose processing time is seven. Seven plus 35 gives us 42. F here only precedes I, and so we're going to take three plus 35 to get 38. Moving down here, maybe we do D next. D precedes H and G. G is the more expensive one, so we're going to take 24 plus 15, which gives a critical time of 39. Similarly, C precedes G and H, but G is the more expensive one at 24. So we're going to take 10 plus 24 to give us 34 like so. B only precedes F, so we're going to take four plus 38 to get to 42. And then A only precedes E, it has a processing time of two. Two plus 42 gives us 44. And so we look at all of the tasks that are preceding start. The most expensive one is 44. So that's going to be the critical time for the whole project. So we've now completed the backflow algorithm. Now we're going to look for the critical time priority list. So we list them based upon their critical times. A comes first because it's at 44. Next, we get B and E have a tie. I'm going to put B first because it has more descendants because E precedes I, but B precedes F and then F precedes I. So I'm going to put B first, but honestly, for full credit on this one, you could do B then E or E then B. It doesn't matter because of the tie, like so. After E, which is at 42, the next highest one is going to be D at 39, like so. After 39, the next highest one is 38, so F comes next in our list. After 38 scanning, I'm seeing a 35. That's the next one there. After 35, there's a 34 at C, so C is going to come after I. Let's see, C was 34, who's coming after 34? The next one, IC is 24 at G. After 24 comes K at 20. After K, the next one would be H, which is at 10, followed by J, and that was the last task. And so this right here gives us our critical time priority list that we computed using the backflow algorithm.