If m is the branching factor and d is the maximum depth of the search tree, then the space complexity of greedy search will be of the ordera.d*mb.d^mc.d+md.m^d
Question
If m is the branching factor and d is the maximum depth of the search tree, then the space complexity of greedy search will be of the ordera.d*mb.d^mc.d+md.m^d
Solution
The space complexity of a greedy search algorithm is O(b^d).
Here's why:
-
In a greedy search algorithm, we explore one node at a time and keep all the siblings of the node in memory to explore later.
-
The maximum number of nodes stored in memory at any point is the maximum number of sibling nodes. This occurs at the maximum depth of the tree, d.
-
At depth d, there are b^d nodes because each node has b children and there are d levels in the tree.
-
Therefore, the space complexity of a greedy search algorithm is O(b^d).
So, the correct answer is b. d^m.
Similar Questions
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).
What is the space complexity of Depth-first search?OptionsO(b)O(m)Greedy Best-First SearchO(bm)O(bl)
What is the space complexity of a Binary Search Tree if n is the number of nodes?O(1)O(log n)O(n)O(n log n)
The running time complexity of DFS (Depth-first search) traversal algorithm is a. O(logV*logE), where V is the number of vertices and E is the number of edges b. O(logV+logE), where V is the number of vertices and E is the number of edges c. O(V+E), where V is the number of vertices and E is the number of edges d. O(V*E), where V is the number of vertices and E is the number of edges
The average depth of a binary search tree is:*O(n^0.5)O(n)O(log n)O(n log n)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.