An engineer attempting to read

The four years that I have spent at Columbia has by far been the best four of my adolescence. I say adolescence because one of the important things I learned in my time here is that college aged students are in no way real adults (nor do they really want to be). But I strongly feel that the time I have spent at Columbia has adequately prepared me for the future, for adulthood and for the many unknowns ahead, and for that I am grateful.

Yet, I cannot help but look back and realize that unlike many others, I did not truly find a home here. Like many of the other places I have lived, the culture and environment at Columbia is geared towards a specific archetype. Because the sum of my gender, race, interests, personality etc do not meet those requirements, I did not find the same sense of belonging here that many others did. While Columbia may pride itself on its diversity and stress the celebration of differences, if you deviate from the norm, you will have a hard time fitting in, just like at any other place. When my 18-year-old self set foot here for NSOP, I had felt that this could finally be a place that I could call home. But I was naive and wrong. Instead, this was a place that taught me that there are no magical places where everyone fits in but rather it is up to us, as the next generation, to create less prejudiced environments and build greater communities. 

We see above the skill tree for the game Path of Exile.  The Problem that we are posed with is such. Given the Skill Tree above, what is the best path/nodes for maximum game play. 

Problem: The Skill Tree Problem

Input: Given a Skill Tree in the form of a graph G and k, the number of nodes you are allowed to select.

Output: Find the most OP Path.

This is rather simple for say a game like Borderlands 

Players are restricted by their level and have the option on building out three separate trees (although since they are all connected to a root node, it's basically one tree).

However, we see that this can scale up dramatically, as is the case of Path of Exile. In fact, the Skill Tree Problem is probably NP Complete since this can probably be reduced to the infamous Traveling Salesman Problem (Will attempt to prove this some other time or leave as an exercise to the reader =P)

How to Solve: NP complete problems are in the set of NP problems and the set of NP hard problems and are therefore difficult to solve.

In fact, NP stands for Non-deterministic Polynomial meaning this problem can be solved by a Non-deterministic Turing Machine in Polynomial Time. Usually, we approximate NP Complete problems through the use of dynamic programming and greedy algorithms. For practicality these approximations suffice.