(A) Nearest Neighbor Problem:

In this .py file, we solve the Nearest Neighbor problem:
given a set of points in Euclidean space, if we pick a single point
from the set, which other point is closest to the point we chose?

We compare 2 methods:
    1) exhaustive search: calculate all of the distances!
    2) building a K neighbors classifier tree (a multi-dimensional binary tree)

Method 2 requires us to assemble a data structure, so of course it is
slower in the short term. However, provided we have the tree, the search
goes from O(n) to O(logn) time.

(B) Machine Learning Application:

We want our computer to correctly label a digit given a 32x32 pixel image. 
To do this, we stack each image into a 32**2 length vector, and treat them as
nodes in scipy's version of a KD Tree.

Once the tree is built from training data, we act as if we are going to insert
a new node into the tree. Then, within a fixed distance, we count the number
of 'neighbor' nodes in this proximity associated with each digit 0-9.

Whichever digit has the most neighbors wins!




File Contents:
    exaustive_search()   - brute force approach that calculates the distance
                           to all nodes in a set to a target node
    KDTNode              - individual node for KDTree
    KDTree               - tree with methods to find, insert, and query
    KNeighborsClassifier - Fits a training set of nodes with labels to an 
                           instance of scipy's KDTree. Has a predict function
                           to predict which label should be assigned to 
                           a new "target node"
    run()                - Uses a KNeighborsClassifier to build a KDTree
                           from our data set of digits and outputs the accuracy.