GATE CS 2015 Set 3 — Question 21
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Question
Consider a binary tree that has 200 leaf nodes. Then, the number of nodes in that have exactly two children are _______.
Correct answer
199 to 199
Solution
In any binary tree, let:
Also, the number of edges .
From the sum of degrees (or counting edges from parents), .
Equating the two expressions for :
Given leaf nodes:
.
So, the number of nodes with exactly two children is 199.
- be the number of leaf nodes (nodes with 0 children).
- be the number of nodes with exactly 1 child.
- be the number of nodes with exactly 2 children.
- be the total number of nodes.
- be the total number of edges.
Also, the number of edges .
From the sum of degrees (or counting edges from parents), .
Equating the two expressions for :
Given leaf nodes:
.
So, the number of nodes with exactly two children is 199.
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