The Viterbi and Dijkstra algorithms look similar, the difference between the two:
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Dijkstra's algorithm adapts to a wider range. Viterbi's algorithm is used in special directed acyclic graphs, while Dijkstra's algorithm can be used in most graph structures (directed and undirected, cyclic and acyclic can be used).
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The search process is similar, but the search order is different. Dijkstra selects the shortest node to search at each step, while Viterbi searches layer by layer in topological order.
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Dijkstra is based on a greedy idea, while Viterbi is a dynamic programming idea.