Direction: A binary search tree is constructed by inserting the following numbers in order.60, 25, 72, 15, 30, 68, 101, 13, 18, 47, 70, 34The number of nodes in the left subtree is:Correct answer is '7'. Can you explain this answer?

Question

Answer

Solution:

To find the number of nodes in the left subtree, we need to first construct the binary search tree using the given numbers.

Steps to construct the binary search tree:

1. Start with the first number 60 as the root of the tree.
2. Insert 25 as the left child of 60.
3. Insert 72 as the right child of 60.
4. Insert 15 as the left child of 25.
5. Insert 30 as the right child of 25.
6. Insert 68 as the left child of 72.
7. Insert 101 as the right child of 72.
8. Insert 13 as the left child of 15.
9. Insert 18 as the right child of 15.
10. Insert 47 as the right child of 30.
11. Insert 70 as the right child of 68.
12. Insert 34 as the left child of 30.

The binary search tree would look like this:

```
60
/ \
25 72
/ \ \
15 30 101
/ \ \
13 18 47
\
34
```

To find the number of nodes in the left subtree, we need to count the number of nodes that are on the left side of the root node (60).

Nodes in the left subtree:

1. Root of the left subtree: 25
2. Left child of 25: 15
3. Left child of 15: 13
4. Right child of 15: 18
5. Right child of 25: 30
6. Right child of 30: 47
7. Left child of 47: 34

Therefore, the number of nodes in the left subtree is 7.

Answer: 7.

Answer

Given, numbers to be inserted are:

60, 25, 72, 15, 30, 68, 101, 13, 18, 47, 70, 34

Algorithm for the construction of a binary tree:

If root is NULL

then create root node

return

If root exists then

compare the data with node.data

while until insertion position is located

If data is greater than node

data goto right subtree

else

goto left subtree

end while

insert data

end if

According to the given numbers and the algorithm, we construct a binary tree i.e.,

So, the number of nodes in the left subtree is 7 i.e., 13, 15, 18, 25, 30, 34, 47.

Hence, the correct answer is 7.

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