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A binary tree T has 20 leaves. The number of nodes in T having two children is
- a)18
- b)19
- c)17
- d)Any number between 10 and 20
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A binary tree T has 20 leaves. The number of nodes in T having two chi...
Sum of all degrees = 2 * |E|. Here considering tree as a k-ary tree :
Sum of degrees of leaves + Sum of degrees for Internal Node except root + Root's degree = 2 * (No. of nodes - 1). Putting values of above terms,
L + (I-1)*(k+1) + k = 2 * (L + I - 1)
L + k*I - k + I -1 + k = 2*L + 2I - 2
L + K*I + I - 1 = 2*L + 2*I - 2
K*I + 1 - I = L
(K-1)*I + 1 = L
Given k = 2, L=20
==> (2-1)*I + 1 = 20
==> I = 19
==> T has 19 internal nodes which are having two children.
L + (I-1)*(k+1) + k = 2 * (L + I - 1)
L + k*I - k + I -1 + k = 2*L + 2I - 2
L + K*I + I - 1 = 2*L + 2*I - 2
K*I + 1 - I = L
(K-1)*I + 1 = L
Given k = 2, L=20
==> (2-1)*I + 1 = 20
==> I = 19
==> T has 19 internal nodes which are having two children.
Most Upvoted Answer
A binary tree T has 20 leaves. The number of nodes in T having two chi...
Explanation:
Therefore, the correct answer is option B (19).
A binary tree is a tree data structure where each node has at most two children, which are referred to as the left child and the right child.
A leaf node is a node that does not have any children.
Let's assume that there are "x" nodes in the binary tree that have two children.
The total number of nodes in the binary tree would be (x + 20) because there are 20 leaf nodes.
In a binary tree, the total number of edges is one less than the total number of nodes. Therefore, the total number of edges in this binary tree would be (x + 20 - 1) = (x + 19).
If we consider each node in the binary tree (except for the leaf nodes), it would have either one child or two children. Therefore, the total number of edges in the binary tree would be twice the number of nodes that have two children and once the number of nodes that have one child.
We can write an equation based on the above observation as follows: (2x + y = x + 19), where "y" is the number of nodes that have one child.
Simplifying the above equation, we get x = 19 - y.
Since each non-leaf node in the binary tree has either one child or two children, the total number of non-leaf nodes in the binary tree would be (x + y).
Substituting the value of x from the above equation, we get the total number of non-leaf nodes as (19 - y + y) = 19.
Therefore, the correct answer is option B (19).
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Community Answer
A binary tree T has 20 leaves. The number of nodes in T having two chi...
If you keep 20 leaves and allot one parent to 2 leaves we get 10 parents (10 nodes with 2 children). Then if we allot one parent to each 2 of 10 nodes, We get 5 parents (5 nodes with 2 children).Then in that 5 nodes, 4 nodes (remember 1 node left here)will have 2 parents (2 nodes with 2 children )and for that 2 nodes 1 parent is assigned (1 node with 2 children) . For this one node and 1 node left before we assign one parent (1 node with 2 children) Total nodes with 2 children are. 10+5+2+1+1=19 nodes
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A binary tree T has 20 leaves. The number of nodes in T having two children isa)18b)19c)17d)Any number between 10 and 20Correct answer is option 'B'. Can you explain this answer?
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