Give the time and space complexity of the Tree Search version of Depth-First Search (DFS), in terms of the branching factor b and the maximum depth m of the search tree.Write your answer using big-O notation, and if you need to use powers then write them in TeX notation. For example, n squared would be written as n^2. If the algorithm has worst-case complexity n squared, it would be written as O(n^2).
Question
Give the time and space complexity of the Tree Search version of Depth-First Search (DFS), in terms of the branching factor b and the maximum depth m of the search tree.Write your answer using big-O notation, and if you need to use powers then write them in TeX notation. For example, n squared would be written as n^2. If the algorithm has worst-case complexity n squared, it would be written as O(n^2).
Solution
The time complexity of the Tree Search version of Depth-First Search (DFS) is O(b^m), where b is the branching factor and m is the maximum depth of the search tree. This is because in the worst-case scenario, the algorithm will have to explore all nodes in the tree, which is the number of leaves in a perfectly balanced tree, or b^m.
The space complexity of DFS is O(bm), because in the worst-case scenario, the algorithm will have to store one node at each level of the tree in the stack for backtracking purposes. This results in bm nodes stored in the stack in the worst-case scenario.
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