Traveling Salesman and technical interviewing techniques.

Author: linkel

7-case-studies/TravelingSalesman.md

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+## TSP
+
+Optimization problem. What's the fastest way for our salesman to get home given a graph? 
+
+Apparently this is used in microchip design and DNA sequencing. 
+
+## Category: NP-Hard
+
+NP-Hard means known algorithm in polynomial time. That is, things like O(n^2), O(n), O(2). 
+
+## Two algo solution types
+
+Exact, which will be in pseudo polynomial time.
+
+Approximate, which will find a near-optimal solution in a quicker time (some of which are actually polynomial time!).
+
+### Exact Algo
+
+- Brute Force: Takes factorial time. O(n!)
+- Dynamic Programming: 
+    - Held-Karp Algorithm: O(n^2 * 2^n)
+
+### Approximation Algo
+
+- Christofides Algorithm: turns the graph into a tree, starting node is a root, and traverses through it in a way such that it guarantees that the result it finds is at most 50% longer than the shortest route. 
+
+- There exist some slight improvements on this algo, but the Christofides one is the main one.