GATE CS 2025 Set 2 — Question 13
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Programming & Data Structures → Trees → Binary Tree Properties
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Question
Consider a binary tree in which every node has either zero or two children.
Let be the number of nodes in .Which ONE of the following is the number of nodes in that have exactly two children?
Let be the number of nodes in .Which ONE of the following is the number of nodes in that have exactly two children?
Correct answer
(B) (n-1)/(2)
Solution
Let be the number of internal nodes (nodes with 2 children) and be the number of leaf nodes (nodes with 0 children).
In a binary tree where every node has either 0 or 2 children (a full or strict binary tree), the relationship between the number of leaf nodes and internal nodes is given by:The total number of nodes is the sum of leaf nodes and internal nodes:Substituting into the equation for :We need to find the number of nodes with exactly two children, which is . Rearranging the equation to solve for :Thus, the number of nodes with exactly two children is .
In a binary tree where every node has either 0 or 2 children (a full or strict binary tree), the relationship between the number of leaf nodes and internal nodes is given by:The total number of nodes is the sum of leaf nodes and internal nodes:Substituting into the equation for :We need to find the number of nodes with exactly two children, which is . Rearranging the equation to solve for :Thus, the number of nodes with exactly two children is .
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