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Please explain what's space efficiency for depth-first search and breadth-first search of a graph(not a tree). That is what the extra space needs for these

Please explain what's space efficiency for depth-first search and breadth-first search of a graph(not a tree). That is what the extra space needs for these two methods? And what the worst case and except average case for the space complexity for depth-first search and breadth-first search of a graph(not a tree)?

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