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A binary search tree is generated by inserting the following integers in order:
50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24
How many nodes are there in the left sub-tree and the right sub-tree of the root, respectively?
- a)(4, 7)
- b)(7, 4)
- c)(8, 3)
- d)(3, 8)
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A binary search tree is generated by inserting the following integers ...
Binary Tree - Tree in which each node has at most two child nodes.
Binary search tree - A binary tree in which the left child contains only nodes with values less than the parent node, and the right child contains only nodes with values greater than or equal to the parent. Binary search tree is used for efficient searching. The binary search tree for the above problem is given below.
Binary search tree - A binary tree in which the left child contains only nodes with values less than the parent node, and the right child contains only nodes with values greater than or equal to the parent. Binary search tree is used for efficient searching. The binary search tree for the above problem is given below.
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Community Answer
A binary search tree is generated by inserting the following integers ...
Explanation:
To find the number of nodes in the left sub-tree and the right sub-tree of the root, we need to construct the binary search tree from the given integers.
Constructing the Binary Search Tree:
1. Start with an empty binary search tree.
2. Insert the integers in the given order: 50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24.
The binary search tree will be constructed as follows:
```
50
/ \
15 62
/ \ / \
5 20 58 91
/ / /
3 37 60
\
24
```
Counting Nodes:
To count the number of nodes in the left sub-tree and the right sub-tree of the root, we can traverse the tree in a depth-first manner and count the nodes.
Counting Nodes in Left Sub-tree:
Starting from the root node (50), we can count the nodes in the left sub-tree as follows:
1. Move to the left child (15).
2. Move to the left child (5).
3. Move to the left child (3).
4. There are no more left children. Move to the right child (8).
5. There are no more left children. Move to the right child (20).
6. There are no more left children. Move back to the previous node (5).
7. There are no more left children. Move back to the previous node (15).
8. There are no more left children. Move back to the previous node (50).
We have counted 4 nodes in the left sub-tree: 3, 5, 8, and 20.
Counting Nodes in Right Sub-tree:
Starting from the root node (50), we can count the nodes in the right sub-tree as follows:
1. Move to the right child (62).
2. Move to the left child (58).
3. There are no more left children. Move back to the previous node (62).
4. Move to the right child (91).
5. There are no more left children. Move back to the previous node (62).
6. There are no more left children. Move back to the previous node (50).
We have counted 7 nodes in the right sub-tree: 58, 60, 91, 37, 24.
Therefore, the number of nodes in the left sub-tree is 4 and the number of nodes in the right sub-tree is 7. Hence, the correct answer is option B: (7, 4).
To find the number of nodes in the left sub-tree and the right sub-tree of the root, we need to construct the binary search tree from the given integers.
Constructing the Binary Search Tree:
1. Start with an empty binary search tree.
2. Insert the integers in the given order: 50, 15, 62, 5, 20, 58, 91, 3, 8, 37, 60, 24.
The binary search tree will be constructed as follows:
```
50
/ \
15 62
/ \ / \
5 20 58 91
/ / /
3 37 60
\
24
```
Counting Nodes:
To count the number of nodes in the left sub-tree and the right sub-tree of the root, we can traverse the tree in a depth-first manner and count the nodes.
Counting Nodes in Left Sub-tree:
Starting from the root node (50), we can count the nodes in the left sub-tree as follows:
1. Move to the left child (15).
2. Move to the left child (5).
3. Move to the left child (3).
4. There are no more left children. Move to the right child (8).
5. There are no more left children. Move to the right child (20).
6. There are no more left children. Move back to the previous node (5).
7. There are no more left children. Move back to the previous node (15).
8. There are no more left children. Move back to the previous node (50).
We have counted 4 nodes in the left sub-tree: 3, 5, 8, and 20.
Counting Nodes in Right Sub-tree:
Starting from the root node (50), we can count the nodes in the right sub-tree as follows:
1. Move to the right child (62).
2. Move to the left child (58).
3. There are no more left children. Move back to the previous node (62).
4. Move to the right child (91).
5. There are no more left children. Move back to the previous node (62).
6. There are no more left children. Move back to the previous node (50).
We have counted 7 nodes in the right sub-tree: 58, 60, 91, 37, 24.
Therefore, the number of nodes in the left sub-tree is 4 and the number of nodes in the right sub-tree is 7. Hence, the correct answer is option B: (7, 4).
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