project euler problem 086

Cuboid route

Among the first 100 problems, this one is not easy.

Since my old code was lost, I rewrote it. It still took me three  hours to get it work in a relatively efficient way. It takes less than 1ms for my optimized version to get the correct answer. 

Update 10/05/2017,  I found my previous code for this problem is not efficient because I did not choose the number range carefully and I need to set the maximum to be large enough to get a correct answer for n=1e11.  It is a little bit tricky to find an appropriate limit for the pythagorean triangle numbers. There is still room to make improvement, but I will live with it since I have already passed the projecteuler+ tests for this problem. 

project euler problem 040

Champernowne's constant

This number appeared at least 3 times in all 400 problems. This is the easiest one. Problem 305 is much more difficult than 40. I used binary search on this problem. Simple and fast. I remember that the first time I saw this problem, I solved it by hand. It is not difficult since the number of digits involved is so small.

Update: Binary search is still an overkill if we use a function to count the numbers of digits up to n. With some simple math, the problem can be further simplified. since the numbers with one digit is 9 and with two digits is 90, etc.