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Dijksta's algorithm for finding the shortest path in a weighted graph. Even if you don't care about graph theory, you should still watch the video to enjoy the quality of the explanation. Sure it is pretty, but the merits go well beyond that. Notice how the example is small, but just big enough to include the tricky cases of the algorithm. Even the asides are beautifully done; when the narrator talks about using a priority queue, the little animation does the right heap percolation thing :-)