Uniform cost search vs dijkstra - Explain the difference.

 Every computer science student (including myself, when I was doing my bachelor's in CS) probably encountered the famous single-source shortest path Dijkstra's algorithm (DA). If you also took an introductory course on artificial intelligence (as I did a few years ago, during my bachelor's), you should have also encountered some search algorithms, in particular, the uniform-cost search (UCS).

A few articles on the web (such as the Wikipedia article on DA) say that DA (or a variant of it) is equivalent to the UCS. The famous Norvig and Russell's book Artificial Intelligence: A Modern Approach (3rd edition) even states

The two-point shortest-path algorithm of Dijkstra (1959) is the origin of uniform-cost search. These works also introduced the idea of explored and frontier sets (closed and open lists).

How exactly is THE equivalent to UCS?

Answered by Amit Sinha

Uniform cost search vs dijkstra, both are logically equivalent (i.e. they process the same vertices in the same order), but they do it differently. In particular, the main practical difference between the single-source DA and UCS is that, in DA, all nodes are initially inserted in a priority queue, while in UCS nodes are inserted lazily.

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