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In a binary tree with n nodes, every node has an odd number of descendants. Every node is considered to be its own descendant. What is the number of nodes in the tree that has exactly one child?
  • a)
    0
  • b)
    1
  • c)
    (n − 1)/2
  • d)
    n - 1
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a binary tree with n nodes, every node has an odd number of descend...
It is mentioned that each node has odd number of descendants, including node itself, so all nodes must have even number of descendants - 0, 2, 4 and so on, which means each node should have either 0 or 2 children. So, there will be no node with 1 child. Hence, 0 is answer.
Following are a few examples.

Such a binary tree is full binary tree (a binary tree where every node has 0 or 2 children).
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Community Answer
In a binary tree with n nodes, every node has an odd number of descend...

Explanation:

Node with exactly one child:
- In a binary tree, a node with exactly one child is called a "leaf node" or a "child node".
- Given that every node has an odd number of descendants, it implies that each node will have either 1 or 3 or 5... descendants.
- Since a leaf node has only one child, it means that it will have exactly 1 descendant (the child itself).
- Therefore, in a binary tree where every node has an odd number of descendants, there cannot be any node with exactly one child.

Conclusion:
- The number of nodes in the tree that has exactly one child is 0.
- Hence, the correct answer is option 'A'.
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