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A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?
- a)6
- b)3
- c)4
- d)5
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A complete n-ary tree is a tree in which each node has n children or n...
For an n-ary tree where each node has n children or no children, following relation holds
L = (n-1)*I + 1
Where L is the number of leaf nodes and I is the number of internal nodes.
Where L is the number of leaf nodes and I is the number of internal nodes.
Let us find out the value of n for the given data.
L = 41 , I = 10
41 = 10*(n-1) + 1
(n-1) = 4
n = 5
41 = 10*(n-1) + 1
(n-1) = 4
n = 5
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Community Answer
A complete n-ary tree is a tree in which each node has n children or n...
Given:
- L = 41 (number of leaves)
- I = 10 (number of internal nodes)
To find:
The value of n, the number of children each node has in the complete n-ary tree.
Explanation:
In a complete n-ary tree, each internal node has n children or no children. This means that each internal node can have at most n children.
Formula:
The total number of nodes in a complete n-ary tree can be calculated using the formula:
Total nodes (T) = I + L
Calculating the total number of nodes:
Given that I = 10 and L = 41, we can calculate the total number of nodes:
T = I + L
T = 10 + 41
T = 51
Calculating the number of edges:
In a tree, the number of edges (E) is always one less than the number of nodes (T). So, in this case, E = T - 1.
E = T - 1
E = 51 - 1
E = 50
Calculating the number of edges in terms of n:
In an n-ary tree, the number of edges is related to the number of internal nodes (I) and the number of children each node has (n) by the formula:
E = (n - 1) * I
Substituting the given values, we have:
50 = (n - 1) * 10
Simplifying the equation:
50 = 10n - 10
60 = 10n
n = 6
Therefore, the value of n is 6.
Conclusion:
The value of n, the number of children each node has in the complete n-ary tree, is 6. Therefore, the correct answer is option 'D'.
- L = 41 (number of leaves)
- I = 10 (number of internal nodes)
To find:
The value of n, the number of children each node has in the complete n-ary tree.
Explanation:
In a complete n-ary tree, each internal node has n children or no children. This means that each internal node can have at most n children.
Formula:
The total number of nodes in a complete n-ary tree can be calculated using the formula:
Total nodes (T) = I + L
Calculating the total number of nodes:
Given that I = 10 and L = 41, we can calculate the total number of nodes:
T = I + L
T = 10 + 41
T = 51
Calculating the number of edges:
In a tree, the number of edges (E) is always one less than the number of nodes (T). So, in this case, E = T - 1.
E = T - 1
E = 51 - 1
E = 50
Calculating the number of edges in terms of n:
In an n-ary tree, the number of edges is related to the number of internal nodes (I) and the number of children each node has (n) by the formula:
E = (n - 1) * I
Substituting the given values, we have:
50 = (n - 1) * 10
Simplifying the equation:
50 = 10n - 10
60 = 10n
n = 6
Therefore, the value of n is 6.
Conclusion:
The value of n, the number of children each node has in the complete n-ary tree, is 6. Therefore, the correct answer is option 'D'.
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A complete n-ary tree is a tree in which each node has n children or no children. Let I be the number of internal nodes and L be the number of leaves in a complete n-ary tree. If L = 41, and I = 10, what is the value of n?a)6b)3c)4d)5Correct answer is option 'D'. Can you explain this answer?
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