I found that in some tutorial the breadth first search
the shallow nodes are expanded before deeper nodes.
I am really confused what is the meaning of each of them?
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Terms “shallow” and “deep” come from visualizing your graph with the starting node at the top: the “depth” of a node is the number of edges that you need to traverse in order to get to that node from the starting node. The statement about BFS tells you that nodes with fewer edges between them and the starting node are discovered before nodes separated from the start by more edges.