project euler problem 413

One child number

This problem is an interesting dynamic programming problem. It does not take me too long to figure out  how to solve the problem. 

I first used a lazy vector to handle the key component of the problem. It soon works after I fixed a couple of bugs. The issue was that my code ran too slow. I then found a better format to reorganize the data, the hashmap! The hashmap use less memory and better performance. But I did not write out a very detailed plan. It proved that this was a unwise decision. I made several stupid mistake and sometime contradictory implementation.  It takes me several hours debugging the code and actually making a plan during debugging. I should write out the plan before coding even if it is a rewrite. Finally I got it write again, the code runs for 6 seconds.

project euler problem 469

Empty Chairs

This is an interesting problem. But it is simple if one find the shortcut. I would not tell anything about the shortcut. It is fast to solve but you lose a lot to learn if you are only interested in the solution to be submitted. 

I investigated the problem a little bit and then find a recurrent equation. It is routine to find the differential equation that needs to be solved. I asked "Mr. wolframalpha" to solve the equation for me, then the problem becomes easy and clear. When I got the final solution, I was surprised that the result is related to one of Euler's well known contribution to math. I hope everyone can enjoy the problem.