As the size of the pyramid increases the obvious algorithm (walking all the routes down the tree) is going to fall afoul of the time limit pretty quickly, as are several alternative algorithms you might try. So a pyramid 100 or 1000 levels deep very rapidly falls out of the time limit unless you choose the right algorithm because there are 2^(n-1) paths for a n-level pyramid. I’d suggested a…much bigger dataset as one of the judgement datasets One that took my reference implementation about 15 seconds.
This was a contest for high school kids c. 2001 and was going to involve 4 problems across 6 hours. The prof making the decision thought it was a bit much for them to figure out why the algorithm they were likely to try wasn’t working in time (noting that the only feedback they were going to get was along the lines of “failed for time on judgement dataset 3 with 10000 layers”, that it was because it was a poor choice of algorithm rather than some issue in their implementation, and then to devise a faster algorithm and implement and debug that all ideally within 1.5 hours.
For example, the algorithm I used for my reference solution started one layer above the bottom of the pyramid, checked the current number against either child it could be summed with, replaced the current number with the larger sum and continued in that fashion up the pyramid layer by layer. So, comparison, add, store for each number in the pyramid above the bottom layer. When you process the number at the top of the pyramid, that’s the final result. It’s simple and it’s fast. But it requires looking at the problem upside down, which is admittedly a useful skill.
I mean it’s basically solving one of those labyrinth puzzles in a puzzle book by starting at the finish and working your way to the start, avoiding all the wrong turns. 😄 It’s the smart solution. 😉 But yeah, maybe they had a point with the “no feedback” issue. In Advent of Code, at least you get to see your final input data.
As the size of the pyramid increases the obvious algorithm (walking all the routes down the tree) is going to fall afoul of the time limit pretty quickly, as are several alternative algorithms you might try. So a pyramid 100 or 1000 levels deep very rapidly falls out of the time limit unless you choose the right algorithm because there are 2^(n-1) paths for a n-level pyramid. I’d suggested a…much bigger dataset as one of the judgement datasets One that took my reference implementation about 15 seconds.
This was a contest for high school kids c. 2001 and was going to involve 4 problems across 6 hours. The prof making the decision thought it was a bit much for them to figure out why the algorithm they were likely to try wasn’t working in time (noting that the only feedback they were going to get was along the lines of “failed for time on judgement dataset 3 with 10000 layers”, that it was because it was a poor choice of algorithm rather than some issue in their implementation, and then to devise a faster algorithm and implement and debug that all ideally within 1.5 hours.
For example, the algorithm I used for my reference solution started one layer above the bottom of the pyramid, checked the current number against either child it could be summed with, replaced the current number with the larger sum and continued in that fashion up the pyramid layer by layer. So, comparison, add, store for each number in the pyramid above the bottom layer. When you process the number at the top of the pyramid, that’s the final result. It’s simple and it’s fast. But it requires looking at the problem upside down, which is admittedly a useful skill.
I mean it’s basically solving one of those labyrinth puzzles in a puzzle book by starting at the finish and working your way to the start, avoiding all the wrong turns. 😄 It’s the smart solution. 😉 But yeah, maybe they had a point with the “no feedback” issue. In Advent of Code, at least you get to see your final input data.