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Lets get started so today were gonna look at one of my favorite puzzles I'll say right at the beginning that the coding associated with the puzzle is fairly straightforward, but the analysis associated with this puzzle is quite intricate and in particular if you're going to have to do worst-case analysis which is really a good thing to for you to learn about because asymptotic analysis in algorithms is all about the worst case alright so keep that in mind when you try to come up with answers to my questions always keep in mind that I'm going to be asking for what happens in the worst case know in the context of our puzzle which is called the crystal ball puzzle and its fairly popular in the literature though I've generalized it a little you have the situation where you're supposed to figure out the hardness coefficient of a crystal ball and in the generalized version you have a set of identical crystal balls right so how do you find this hardness coefficient well you go up to this Shanghai Tower that has 128 floors one through 128, and you drop this ball from say floor one so just you're standing here and let's say you just drop it from there, or you go up to floor to, and you drop the ball and the hardness coefficient is defined as the highest floor from which you can drop the ball and the ball does not break okay so what this means is if floor F the ball doesn't break, and it breaks at f 1 then the hardness coefficient is F and you can assume a monotone a city properly that says that if it did not break at floor F then it won't break this implies that it won't break it at any floor less than or equal to F okay which makes sense right I'm not otherwise it would be kind of complicated it would be random and everyone is able to do any interesting analysis um so the easy a version of the puzzle of course which is not particularly interesting is if you need it to get this exactly right so your job depends on getting that number exactly right, so there's no shortcuts you got to get it right you can't be off by one either way and I you have only one ball right, so you only have one ball so what can you do if you only have one ball, and you have to get it exactly right try every floor right and more important I try from lower floors to higher floors right, so you drop it at floor one I saw one ball you drop from floor one and if it in and if it breaks than your hardness coefficient is you return zero but then if you keep going and it, and it lets say you drop I've got a dot from floor 65, and it breaks and you've gone in order then the hardness coefficient is 64 okay right, so that's easy enough theres theres no optimization here it's the only thing you can do so that's why it's not particularly interesting now if you have identical crystal balls that are guaranteed they were manufactured in exactly the same way etc, etc then obviously things get a lot more interesting because you can try to minimize something, and I'm gonna write it over here because...
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