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In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The number of leaf nodes in the binary tree is
- a)10
- b)11
- c)12
- d)15
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a binary tree, the number of internal nodes of degree 1 is 5, and t...
In a binary tree, the number of leaf nodes is always 1 more than number of internal nodes with 2 children, refer
So, Number of Leaf Nodes = Number of Internal nodes with 2 children + 1 Number of Leaf Nodes = 10 + 1 Number of Leaf Nodes = 11
So, Number of Leaf Nodes = Number of Internal nodes with 2 children + 1 Number of Leaf Nodes = 10 + 1 Number of Leaf Nodes = 11
Most Upvoted Answer
In a binary tree, the number of internal nodes of degree 1 is 5, and t...
Solution:
Given the number of internal nodes of degree 1 = 5,
and number of internal nodes of degree 2 = 10.
Let the number of leaf nodes be 'L'.
Total number of nodes in the binary tree = Internal nodes + Leaf nodes.
Therefore, Total number of nodes = 5 + 10 + L = 15 + L.
Let's consider the degrees of all the nodes in the binary tree.
Each internal node can have either 1 or 2 child nodes.
Therefore, the total number of child nodes of all internal nodes = (1 * Number of internal nodes of degree 1) + (2 * Number of internal nodes of degree 2)
= (1 * 5) + (2 * 10) = 25.
Each leaf node has degree 0.
Therefore, the total number of child nodes of all leaf nodes = (0 * Number of leaf nodes) = 0.
Total number of child nodes = Number of parent nodes.
Therefore, Total number of internal nodes = 25.
Now, Total number of nodes = Internal nodes + Leaf nodes.
15 + L = 25.
L = 10.
Therefore, the number of leaf nodes in the binary tree is 10.
Hence, the correct answer is option B.
Given the number of internal nodes of degree 1 = 5,
and number of internal nodes of degree 2 = 10.
Let the number of leaf nodes be 'L'.
Total number of nodes in the binary tree = Internal nodes + Leaf nodes.
Therefore, Total number of nodes = 5 + 10 + L = 15 + L.
Let's consider the degrees of all the nodes in the binary tree.
Each internal node can have either 1 or 2 child nodes.
Therefore, the total number of child nodes of all internal nodes = (1 * Number of internal nodes of degree 1) + (2 * Number of internal nodes of degree 2)
= (1 * 5) + (2 * 10) = 25.
Each leaf node has degree 0.
Therefore, the total number of child nodes of all leaf nodes = (0 * Number of leaf nodes) = 0.
Total number of child nodes = Number of parent nodes.
Therefore, Total number of internal nodes = 25.
Now, Total number of nodes = Internal nodes + Leaf nodes.
15 + L = 25.
L = 10.
Therefore, the number of leaf nodes in the binary tree is 10.
Hence, the correct answer is option B.
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In a binary tree, the number of internal nodes of degree 1 is 5, and the number of internal nodes of degree 2 is 10. The number of leaf nodes in the binary tree isa)10b)11c)12d)15Correct answer is option 'B'. Can you explain this answer?
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