Project Euler/6
From charlesreid1
Project Euler Problem 6
The sum of the squares of the first 10 integers is x.
The square of the sum of the first 10 integers is y.
Their difference is y-x.
Find this for the first 100 integers.
Project Euler Link: https://projecteuler.net/problem=6
Link to solution, git.charlesreid1.com: https://charlesreid1.com:3000/cs/euler/src/master/Problem006.java
Principle: this utilizes two summations that are useful to know off the top of your head. If you do, it makes this an O(1) problem. If not, it makes it an O(N) problem.
The two summations are:
$ \sum_{i=1}^{n} i = \dfrac{n(n+1)}{2} $
and
$ \sum_{i=1}^{n} i^2 = \dfrac{n(n+1)(2n+1)}{6} $
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