Day 24: add explanation

Author: thatguyintech

day24/README.md

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+Today's challenge is a continuation of [yesterday's](../day23)!
+
+## Ideas
+
+I wanted to take a different approach to this question; instead of doing a
+full brute-force exploration on all combinations of the inputArray,
+construct a graph and then do DFS from every node to find a possible 
+Hamiltonian path. The existence of a path would verify whether there is
+a desired arrangement of the strings.
+
+I can construct the graph in `O(N<sup>2</sup>)` time where `N` is the number of 
+elements in the inputArray, and also the number of vertices in my graph. I check
+every possible pair of strings to see whether they differ by exactly one place,
+and add an edge in the graph between the two if so.
+
+I can then run DFS from each node in `N * O(N) = O(N<sup>2</sup>)` time (this
+analysis doesn't seem right to me actually) to complete the algorithm.
+
+Overall, it comes out to a runtime of `O(n<sup>2</sup>)`. The space complexity
+scales in proportion to the number of vertices and edges I need to keep track
+of in my graph. Vertices increase with every additional element in the inputArray.
+Edges increase when there are higher frequencies of words in the inputArray
+that are closer to each other in edit distance.
+
+## Code
+
+[Python](./stringsRearrangementBacktracking.py) (unfinished)
+
+## Follow up
+