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A complete n-ary tree is one in which every node has 0 or n sons. If x is the number of internal nodes of a complete n-ary tree, the number of leaves in it is given by
- a)x (n - 1) +1
- b)xn - 1
- c)xn + 1
- d)x(n + 1)
Correct answer is option 'A'. Can you explain this answer?
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A complete n-ary tree is one in which every node has 0 or n sons. If x...
In n-ary tree the total number of vertices are m = nx + 1
Where x: number of internal nodes and let l be the number of leaf nodes.
x + l = nx +1
l = (n - 1)x + 1
So number of leaf nodes in n-ary tree with x internal nodes is (n - 1) x + 1.
Where x: number of internal nodes and let l be the number of leaf nodes.
x + l = nx +1
l = (n - 1)x + 1
So number of leaf nodes in n-ary tree with x internal nodes is (n - 1) x + 1.
Most Upvoted Answer
A complete n-ary tree is one in which every node has 0 or n sons. If x...
Explanation:
To understand why the correct answer is option 'A', let's break down the problem and analyze it step by step.
Definition:
A complete n-ary tree is a tree in which every node has either 0 or n children.
Internal Nodes:
Internal nodes are the nodes that have at least one child. In a complete n-ary tree, all internal nodes have exactly n children.
Leaves:
Leaves are the nodes that do not have any children. In other words, leaves are the nodes that have 0 children.
Number of Internal Nodes:
Let x be the number of internal nodes of a complete n-ary tree. This means that there are x nodes in the tree that have n children each.
Number of Leaves:
To determine the number of leaves in the tree, we need to consider the following:
- Each internal node has exactly n children.
- The tree is complete, so all internal nodes have n children.
Calculating the number of leaves:
Since each internal node has n children, the total number of children in the tree is x * n.
Since each node, except for the leaves, is a child of an internal node, the total number of nodes in the tree is x + x * n.
To find the number of leaves, we subtract the number of internal nodes from the total number of nodes:
Number of Leaves = Total number of nodes - Number of internal nodes
Number of Leaves = (x + x * n) - x
Simplifying the equation further:
Number of Leaves = x * n
Conclusion:
Therefore, the number of leaves in a complete n-ary tree with x internal nodes is given by the equation:
Number of Leaves = x * n
This matches with option 'A': x(n - 1) + 1, where x(n - 1) represents the total number of nodes excluding the root node, and the "+ 1" accounts for the root node itself.
Hence, option 'A' is the correct answer.
To understand why the correct answer is option 'A', let's break down the problem and analyze it step by step.
Definition:
A complete n-ary tree is a tree in which every node has either 0 or n children.
Internal Nodes:
Internal nodes are the nodes that have at least one child. In a complete n-ary tree, all internal nodes have exactly n children.
Leaves:
Leaves are the nodes that do not have any children. In other words, leaves are the nodes that have 0 children.
Number of Internal Nodes:
Let x be the number of internal nodes of a complete n-ary tree. This means that there are x nodes in the tree that have n children each.
Number of Leaves:
To determine the number of leaves in the tree, we need to consider the following:
- Each internal node has exactly n children.
- The tree is complete, so all internal nodes have n children.
Calculating the number of leaves:
Since each internal node has n children, the total number of children in the tree is x * n.
Since each node, except for the leaves, is a child of an internal node, the total number of nodes in the tree is x + x * n.
To find the number of leaves, we subtract the number of internal nodes from the total number of nodes:
Number of Leaves = Total number of nodes - Number of internal nodes
Number of Leaves = (x + x * n) - x
Simplifying the equation further:
Number of Leaves = x * n
Conclusion:
Therefore, the number of leaves in a complete n-ary tree with x internal nodes is given by the equation:
Number of Leaves = x * n
This matches with option 'A': x(n - 1) + 1, where x(n - 1) represents the total number of nodes excluding the root node, and the "+ 1" accounts for the root node itself.
Hence, option 'A' is the correct answer.
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A complete n-ary tree is one in which every node has 0 or n sons. If x is the number of internal nodes of a complete n-ary tree, the number of leaves in it is given bya)x (n - 1) +1b)xn - 1c)xn + 1d)x(n + 1)Correct answer is option 'A'. Can you explain this answer?
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A complete n-ary tree is one in which every node has 0 or n sons. If x is the number of internal nodes of a complete n-ary tree, the number of leaves in it is given bya)x (n - 1) +1b)xn - 1c)xn + 1d)x(n + 1)Correct answer is option 'A'. 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 A complete n-ary tree is one in which every node has 0 or n sons. If x is the number of internal nodes of a complete n-ary tree, the number of leaves in it is given bya)x (n - 1) +1b)xn - 1c)xn + 1d)x(n + 1)Correct answer is option 'A'. 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 A complete n-ary tree is one in which every node has 0 or n sons. If x is the number of internal nodes of a complete n-ary tree, the number of leaves in it is given bya)x (n - 1) +1b)xn - 1c)xn + 1d)x(n + 1)Correct answer is option 'A'. Can you explain this answer?.
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