Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > How many distinct binary search trees can be ...
Start Learning for Free
How many distinct binary search trees can be created out of 4 distinct keys?
- a)5
- b)14
- c)24
- d)35
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
How many distinct binary search trees can be created out of 4 distinct...
Total number of distinct binary search tree with n nodes (key)
Most Upvoted Answer
How many distinct binary search trees can be created out of 4 distinct...
Introduction:
In this problem, we need to determine the number of distinct binary search trees that can be created using 4 distinct keys. A binary search tree is a binary tree in which the left subtree contains keys less than the root, and the right subtree contains keys greater than the root.
Approach:
To solve this problem, we can use the concept of Catalan numbers. Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. The formula to calculate the nth Catalan number is given by:
C(n) = (2n)! / (n+1)! * n!
where n is the number of keys.
Explanation:
Let's calculate the number of distinct binary search trees using the given formula:
C(4) = (2*4)! / (4+1)! * 4!
= 8! / 5! * 4!
= (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1) * (4 * 3 * 2 * 1)
= (8 * 7 * 6) / (4 * 3 * 2 * 1)
= 56 / 24
= 14
Therefore, the number of distinct binary search trees that can be created using 4 distinct keys is 14.
Conclusion:
The correct answer is option 'B', which states that there are 14 distinct binary search trees that can be created out of 4 distinct keys.
In this problem, we need to determine the number of distinct binary search trees that can be created using 4 distinct keys. A binary search tree is a binary tree in which the left subtree contains keys less than the root, and the right subtree contains keys greater than the root.
Approach:
To solve this problem, we can use the concept of Catalan numbers. Catalan numbers are a sequence of natural numbers that occur in various counting problems, often involving recursively defined objects. The formula to calculate the nth Catalan number is given by:
C(n) = (2n)! / (n+1)! * n!
where n is the number of keys.
Explanation:
Let's calculate the number of distinct binary search trees using the given formula:
C(4) = (2*4)! / (4+1)! * 4!
= 8! / 5! * 4!
= (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (5 * 4 * 3 * 2 * 1) * (4 * 3 * 2 * 1)
= (8 * 7 * 6) / (4 * 3 * 2 * 1)
= 56 / 24
= 14
Therefore, the number of distinct binary search trees that can be created using 4 distinct keys is 14.
Conclusion:
The correct answer is option 'B', which states that there are 14 distinct binary search trees that can be created out of 4 distinct keys.
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Similar Computer Science Engineering (CSE) Doubts
Top Courses for Computer Science Engineering (CSE)View all
Top Courses for Computer Science Engineering (CSE)
Question Description
How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer?.
How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer?.
Solutions for How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
Download more important topics, notes, lectures and mock test series for Computer Science Engineering (CSE) Exam by signing up for free.
Here you can find the meaning of How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer?, a detailed solution for How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice How many distinct binary search trees can be created out of 4 distinct keys?a)5b)14c)24d)35Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
|
|
Explore Courses for Computer Science Engineering (CSE) exam
|
|
Signup to solve all Doubts
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup