Choose the correct alternatives (more than one may be correct) and write the corresponding letters only:
A $2-3$ tree is such that
The number of internal nodes of a $2-3$ tree having $9$ leaves could be
Answer (a) 4, (d) 7
$4 \rightarrow$ When each leaf has $3$ childs. So $9/3 = 3$ Internal nodes, Then one internal node those internal nodes.
$7 \rightarrow$ When each leaf has $2$ childs & one leaf out of $4$ get $3$ childs. Ex $\rightarrow 8/4 = 2$ child per internal node. Then one of that internal node get extra third child. Then $2$ internal nodes to connect these $4$. Then $1$ internal node to connect this $2$. So $4+2+1 = 7$.
No other way is possible.
6 also possible ans
@srestha plz check bcoz it not satisfy this which is given in question All paths from root to the leaves have the same length.
Correct me if iam wrong : there are 5 possible structures with the given property..
In 2-3 Tree for 9 leaves, internal nodes can be 4 or 7
Ans should be 4 and 7