Editing Approximation Algorithms (section)

== <span style="color: #FFFFFF;">Remembering</span> ==
* '''Approximation Algorithm''' — An algorithm used to find "Near-Optimal" solutions to "Optimization Problems" (usually NP-Hard ones) in "Polynomial Time."
* '''Optimization Problem''' — A problem where you want to "Minimize" a cost (e.g., fuel) or "Maximize" a gain (e.g., profit).
* '''NP-Hard''' — A class of problems (like 'The Traveling Salesman') for which "No fast, perfect algorithm" is known to exist.
* '''Approximation Ratio (Alpha)''' — The "Guarantee" of quality: e.g., a "2-approximation" algorithm is guaranteed to be "No more than 2x as bad" as the perfect answer.
* '''Greedy Algorithm''' — A simple type of approximation that "Makes the best choice right now" and "Never looks back" (e.g., 'Take the biggest coin first').
* '''Heuristic''' — A "Rule of Thumb" or "Guess" that works well in practice but has "No Mathematical Guarantee" of success.
* '''PTAS (Polynomial-Time Approximation Scheme)''' — A "Golden Algorithm" that lets you "Choose your accuracy": you can get a "1% error" if you are willing to "Wait longer."
* '''Knapsack Problem''' — A classic problem: "Given items with different 'Weights' and 'Values,' which ones fit in your bag to get the 'Most Value'?"
* '''Traveling Salesman Problem (TSP)''' — The most famous challenge: finding the shortest route to visit many cities.
* '''Local Search''' — Starting with a "Random" solution and "Tweaking" it (moving a city in the route) to see if it "Gets better."
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