#20 ### Question: Time and Space complexity for bidirectional search is _______### Answer Choices:- \( O(b^{d}) \)- \( O(bd) \)- \( O(1) \)- \( \mathbf{O(b^{d/2})} \) [Selected]### Explanation:Bidirectional search is an algorithm used to find the shortest path between a start node and a goal node in a graph. It simultaneously searches forward from the start node and backward from the goal node until the two searches meet. This algorithm is known for its efficient time and space performance, particularly in exponential search spaces.Here, \( b \) represents the branching factor (the average number of children per node), and \( d \) represents the depth of the shallowest solution. The time and space complexity of bidirectional search is \( O(b^{d/2}) \) because it effectively reduces the search depth by half, as two simultaneous searches cover half the depth each.### Detailed Explanation of the Selected Answer:- **\( O(b^{d}) \)**: This complexity is typically associated with a simple breadth-first search which explores all nodes up to depth \( d \), resulting in exponential growth in the number of nodes.- **\( O(bd) \)**: This is not a correct representation of the time and space complexity for bidirectional search.- **\( O(1) \)**: This would imply a constant time and space complexity, which is not feasible for search algorithms in large, branching graphs.- **\( \( \mathbf{O(b^{d/2})} \)**[Selected]: This option correctly represents the complexity of bidirectional search. By splitting the search into two simultaneous searches that meet in the middle, the search space is significantly reduced, achieving exponential speedup compared to other search strategies.Understanding the complexities of different search algorithms helps in selecting the right approach for solving problems efficiently.

Here we have to find the correct option for the given questionQ. Time and space complexity for…

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Engineering

Computer Science

Time and Space complexity for bidirectional search is 0 0(69) O(bd) O(1) 0(6/2)

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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