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GO Classes DPP | PYTHON & DSA |TREE

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1 1 vote

A binary tree has the following properties:

  • The number of nodes with exactly two children is $12$
     
  • The number of nodes with exactly one child is $5$
     

Which of the following statements is/are correct?

  1. The number of leaf nodes is $13$
     
  2. The total number of nodes in the tree is $30$
     
  3. The number of edges in the tree is $29$
     
  4. The height of the tree must be at least $6$

1 Answer

0 0 votes
Let

$\mathrm{n}_2=$ number of nodes with exactly two children $= 12$

$n_1=$ number of nodes with exactly one child $= 5$

$\mathrm{n}_0=$ number of leaf nodes

For any binary tree,

$$
\mathrm{n}_0=\mathrm{n}_2+1
$$

So,
$$
n_0=12+1=13
$$

Statement A is correct.

 

$\text { Total nodes }=\mathrm{n}_0+\mathrm{n}_1+\mathrm{n}_2$

$=13+5+12$

$ =30$

Statement B is correct.
 

In any tree,

edges $=$ nodes $-1$

So, edges $=30-1=29$

Statement C is correct.
 

The height is not atleast $6.$

D is false.
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