Comparing Dijkstra's and Prim's Algorithms

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This is a video walking through & contrasting Dijkstra's Algorithm & Prim's Algorithm based on the greedy choices each algorithm is optimized to make.

Prim's algorithm optimizes for the min-cost edge that connects the subset of vertices not in the minimum spanning tree to the subset of vertices in the minimum spanning tree we are trying to expand. We ensure every iteration we are choosing the min-cost edge that crosses the cut (wikipedia: a 'cut' is a partition of the vertices of a graph into two disjoint subsets).

Dijkstra's algorithm optimizes for the shortest cost path to get from the start vertex to a given vertex. We ensure every iteration we are improving our tentative costs from a fully optimized vertex.