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Which of the following statements is false about trees?
- a)The maximum number of nodes in a binary tree of height h is 2h+1 - 1
- b)A binary tree T has n nodes of degree two, then the number of leaf nodes is n + 1
- c)The number of leaves in a 3 - ary tree with n internal nodes is 2(n - 1) + 3
- d)A binary tree T has n leaf nodes, then the number of nodes of degree two in T is n
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Which of the following statements is false about trees?a)The maximum n...
False Statement: Option D
Explanation:
A binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child. In a binary tree, nodes can have a degree of either zero, one, or two. The degree of a node is the number of children it has.
Let's analyze each statement to determine which one is false:
Statement A: The maximum number of nodes in a binary tree of height h is 2h+1 - 1.
This statement is true. In a binary tree, the number of nodes at each level doubles as we move down the tree. The total number of nodes in a binary tree of height h can be calculated using the formula 2h+1 - 1.
Statement B: If a binary tree T has n nodes of degree two, then the number of leaf nodes is n - 1.
This statement is true. In a binary tree, a leaf node has a degree of zero, meaning it has no children. If a binary tree has n nodes of degree two, it means that there are n - 1 internal nodes (nodes with degree two) because the root node cannot have degree two. The remaining n - 1 nodes must be leaf nodes.
Statement C: The number of leaves in a 3-ary tree with n internal nodes is 2(n - 1) / 3.
This statement is true. A 3-ary tree is a tree in which each node can have at most three children. For a 3-ary tree with n internal nodes, the number of leaf nodes can be calculated using the formula 2(n - 1) / 3. This formula takes into account that each internal node can have up to three children, with the exception of the root node.
Statement D: If a binary tree T has n leaf nodes, then the number of nodes of degree two in T is n.
This statement is false. If a binary tree has n leaf nodes, it means that there are n - 1 internal nodes (nodes with degree two) because the root node cannot have degree two. Therefore, the number of nodes of degree two in a binary tree with n leaf nodes is always less than n.
In conclusion, the false statement is option D. The number of nodes of degree two in a binary tree with n leaf nodes is always less than n.
Explanation:
A binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child. In a binary tree, nodes can have a degree of either zero, one, or two. The degree of a node is the number of children it has.
Let's analyze each statement to determine which one is false:
Statement A: The maximum number of nodes in a binary tree of height h is 2h+1 - 1.
This statement is true. In a binary tree, the number of nodes at each level doubles as we move down the tree. The total number of nodes in a binary tree of height h can be calculated using the formula 2h+1 - 1.
Statement B: If a binary tree T has n nodes of degree two, then the number of leaf nodes is n - 1.
This statement is true. In a binary tree, a leaf node has a degree of zero, meaning it has no children. If a binary tree has n nodes of degree two, it means that there are n - 1 internal nodes (nodes with degree two) because the root node cannot have degree two. The remaining n - 1 nodes must be leaf nodes.
Statement C: The number of leaves in a 3-ary tree with n internal nodes is 2(n - 1) / 3.
This statement is true. A 3-ary tree is a tree in which each node can have at most three children. For a 3-ary tree with n internal nodes, the number of leaf nodes can be calculated using the formula 2(n - 1) / 3. This formula takes into account that each internal node can have up to three children, with the exception of the root node.
Statement D: If a binary tree T has n leaf nodes, then the number of nodes of degree two in T is n.
This statement is false. If a binary tree has n leaf nodes, it means that there are n - 1 internal nodes (nodes with degree two) because the root node cannot have degree two. Therefore, the number of nodes of degree two in a binary tree with n leaf nodes is always less than n.
In conclusion, the false statement is option D. The number of nodes of degree two in a binary tree with n leaf nodes is always less than n.
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Which of the following statements is false about trees?a)The maximum n...
A binary tree T has n nodes of degree two, then the number of leaf nodes is n + 1. Conversely, a binary tree, T, has n leaf nodes, then the number of nodes of degree two in T is n - 1.
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Which of the following statements is false about trees?a)The maximum number of nodes in a binary tree of height h is 2h+1 - 1b)A binary tree T has n nodes of degree two, then the number of leaf nodes is n + 1c)The number of leaves in a 3 - ary tree with n internal nodes is 2(n - 1) + 3d)A binary tree T has n leaf nodes, then the number of nodes of degree two in T is nCorrect answer is option 'D'. Can you explain this answer?
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Which of the following statements is false about trees?a)The maximum number of nodes in a binary tree of height h is 2h+1 - 1b)A binary tree T has n nodes of degree two, then the number of leaf nodes is n + 1c)The number of leaves in a 3 - ary tree with n internal nodes is 2(n - 1) + 3d)A binary tree T has n leaf nodes, then the number of nodes of degree two in T is nCorrect answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 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 Which of the following statements is false about trees?a)The maximum number of nodes in a binary tree of height h is 2h+1 - 1b)A binary tree T has n nodes of degree two, then the number of leaf nodes is n + 1c)The number of leaves in a 3 - ary tree with n internal nodes is 2(n - 1) + 3d)A binary tree T has n leaf nodes, then the number of nodes of degree two in T is nCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements is false about trees?a)The maximum number of nodes in a binary tree of height h is 2h+1 - 1b)A binary tree T has n nodes of degree two, then the number of leaf nodes is n + 1c)The number of leaves in a 3 - ary tree with n internal nodes is 2(n - 1) + 3d)A binary tree T has n leaf nodes, then the number of nodes of degree two in T is nCorrect answer is option 'D'. Can you explain this answer?.
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