Question:
Which of the following are the applications of binary search?
(A) Telephone Directory
(B) Finding the element with a minimum or maximum value in a sorted list
(C) Implementing routing tables
(D) Indexing in database
Choose the correct answer from the options given below:
Which of the following are the applications of binary search?
(A) Telephone Directory
(B) Finding the element with a minimum or maximum value in a sorted list
(C) Implementing routing tables
(D) Indexing in database
Choose the correct answer from the options given below:
(A) Telephone Directory
(B) Finding the element with a minimum or maximum value in a sorted list
(C) Implementing routing tables
(D) Indexing in database
Choose the correct answer from the options given below:
Show Hint
Binary search strictly requires monotonic or sorted data.
Any structure arranged in sorted order (dictionaries, database indexes, sorted arrays) utilizes binary search.
Routing tables prefer trie-based structures due to prefix matching requirements.
Any structure arranged in sorted order (dictionaries, database indexes, sorted arrays) utilizes binary search.
Routing tables prefer trie-based structures due to prefix matching requirements.
Updated On: Sep 7, 2026
- (A), (B) and (D) only
- (A), (B) and (C) only
- (A), (B), (C) and (D)
- (B), (C) and (D) only
Show Solution
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The Correct Option is A
Solution and Explanation
Concept:
Binary search is an efficient divide-and-conquer algorithm used to locate a specific target value within a sorted collection.
It operates with a logarithmic time complexity of \(O(\log n)\) by repeatedly comparing the target to the middle element and halving the search space.
Step 1: Analyzing Individual Applications:
(A) Telephone Directory:
A physical or electronic telephone directory is organized alphabetically (sorted order).
Searching for a name is efficiently accomplished using the divide-and-conquer principles of binary search.
(B) Finding an element with minimum or maximum value in a sorted list:
In specialized sorted arrangements, such as rotated sorted arrays or unimodal sequences, modified binary search is standardly applied to find extremes in \(O(\log n)\) time.
(D) Indexing in database:
Database systems organize index blocks (such as B-trees and B+ trees) in sorted order, applying binary search internally to rapidly traverse index nodes and fetch records.
(C) Implementing routing tables:
Network routing tables generally employ longest-prefix matching algorithms implemented via Trie data structures, hash tables, or specialized hardware like TCAM (Ternary Content-Addressable Memory), rather than basic binary search.
Step 2: Conclusion:
Statements (A), (B), and (D) directly represent recognized practical applications of binary search.
Final Answer:
Therefore, the correct choice is (A), which corresponds to (A), (B), and (D) only.
Binary search is an efficient divide-and-conquer algorithm used to locate a specific target value within a sorted collection.
It operates with a logarithmic time complexity of \(O(\log n)\) by repeatedly comparing the target to the middle element and halving the search space.
Step 1: Analyzing Individual Applications:
(A) Telephone Directory:
A physical or electronic telephone directory is organized alphabetically (sorted order).
Searching for a name is efficiently accomplished using the divide-and-conquer principles of binary search.
(B) Finding an element with minimum or maximum value in a sorted list:
In specialized sorted arrangements, such as rotated sorted arrays or unimodal sequences, modified binary search is standardly applied to find extremes in \(O(\log n)\) time.
(D) Indexing in database:
Database systems organize index blocks (such as B-trees and B+ trees) in sorted order, applying binary search internally to rapidly traverse index nodes and fetch records.
(C) Implementing routing tables:
Network routing tables generally employ longest-prefix matching algorithms implemented via Trie data structures, hash tables, or specialized hardware like TCAM (Ternary Content-Addressable Memory), rather than basic binary search.
Step 2: Conclusion:
Statements (A), (B), and (D) directly represent recognized practical applications of binary search.
Final Answer:
Therefore, the correct choice is (A), which corresponds to (A), (B), and (D) only.
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