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A binary tree with n > 1 nodes has n1, n2 and n3 nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.
Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?
Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?
- a)2 * n1 - 3
- b)n2 + 2 * n1 - 2
- c)n3 - n2
- d)n2 + n1 - 2
Correct answer is option 'A'. Can you explain this answer?
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A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one...
With reference to figure of answer of previous question:
Most Upvoted Answer
A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one...
Given:
- A binary tree with n nodes
- n1 nodes of degree one
- n2 nodes of degree two
- n3 nodes of degree three
To Find:
- The number of edges remaining at the end of the process
Approach:
1. Let's first calculate the total number of edges in the initial tree.
2. Each node of degree one contributes to one edge, so the total number of edges contributed by nodes of degree one is n1.
3. Each node of degree two contributes to two edges, so the total number of edges contributed by nodes of degree two is 2 * n2.
4. Each node of degree three contributes to three edges, so the total number of edges contributed by nodes of degree three is 3 * n3.
5. Therefore, the total number of edges in the initial tree is n1 + 2 * n2 + 3 * n3.
Process:
1. While there remains a node v of degree two in the tree:
- Add an edge between the two neighbors of v
- Remove v from the tree
2. Each time a node of degree two is removed, two edges are added.
3. Since there are initially n2 nodes of degree two, the total number of edges added during this process is 2 * n2.
Final Number of Edges:
1. The initial number of edges is n1 + 2 * n2 + 3 * n3.
2. The number of edges added during the process is 2 * n2.
3. Therefore, the final number of edges remaining at the end of the process is (n1 + 2 * n2 + 3 * n3) + 2 * n2 = 2 * n1 - 3.
Answer:
The correct answer is option 'A' - 2 * n1 - 3.
- A binary tree with n nodes
- n1 nodes of degree one
- n2 nodes of degree two
- n3 nodes of degree three
To Find:
- The number of edges remaining at the end of the process
Approach:
1. Let's first calculate the total number of edges in the initial tree.
2. Each node of degree one contributes to one edge, so the total number of edges contributed by nodes of degree one is n1.
3. Each node of degree two contributes to two edges, so the total number of edges contributed by nodes of degree two is 2 * n2.
4. Each node of degree three contributes to three edges, so the total number of edges contributed by nodes of degree three is 3 * n3.
5. Therefore, the total number of edges in the initial tree is n1 + 2 * n2 + 3 * n3.
Process:
1. While there remains a node v of degree two in the tree:
- Add an edge between the two neighbors of v
- Remove v from the tree
2. Each time a node of degree two is removed, two edges are added.
3. Since there are initially n2 nodes of degree two, the total number of edges added during this process is 2 * n2.
Final Number of Edges:
1. The initial number of edges is n1 + 2 * n2 + 3 * n3.
2. The number of edges added during the process is 2 * n2.
3. Therefore, the final number of edges remaining at the end of the process is (n1 + 2 * n2 + 3 * n3) + 2 * n2 = 2 * n1 - 3.
Answer:
The correct answer is option 'A' - 2 * n1 - 3.
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A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?a)2 * n1- 3b)n2+ 2 * n1- 2c)n3- n2d)n2+ n1- 2Correct answer is option 'A'. 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 A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?a)2 * n1- 3b)n2+ 2 * n1- 2c)n3- n2d)n2+ n1- 2Correct answer is option 'A'. 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 A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?a)2 * n1- 3b)n2+ 2 * n1- 2c)n3- n2d)n2+ n1- 2Correct answer is option 'A'. Can you explain this answer?.
A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?a)2 * n1- 3b)n2+ 2 * n1- 2c)n3- n2d)n2+ n1- 2Correct answer is option 'A'. 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 A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?a)2 * n1- 3b)n2+ 2 * n1- 2c)n3- n2d)n2+ n1- 2Correct answer is option 'A'. 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 A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?a)2 * n1- 3b)n2+ 2 * n1- 2c)n3- n2d)n2+ n1- 2Correct answer is option 'A'. Can you explain this answer?.
Solutions for A binary tree with n > 1 nodes has n1, n2and n3nodes of degree one, two and three respectively. The degree of a node is defined as the number of its neighbors.Starting with the above tree, while there remains a node v of degree two in the tree, add an edge between the two neighbors of v and then remove v from the tree. How many edges will remain at the end of the process?a)2 * n1- 3b)n2+ 2 * n1- 2c)n3- n2d)n2+ n1- 2Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Computer Science Engineering (CSE).
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