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A binary search tree is generated by inserting in order the following integers:
50, 15, 62, 5, 20,58, 91, 3, 8, 37, 60, 24
The number of nodes in the left subtree and right subtree of the root respectively is
50, 15, 62, 5, 20,58, 91, 3, 8, 37, 60, 24
The number of nodes in the left subtree and right subtree of the root respectively is
- 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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A binary search tree is generated by inserting in order the following ...
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Explanation:
To determine the number of nodes in the left and right subtrees of the root, we need to construct the binary search tree (BST) using the given integers and count the number of nodes in each subtree.
Constructing the BST:
We start by inserting the first integer, 50, as the root of the BST. Then, we insert the remaining integers one by one according to the rules of a binary search tree:
- 15 is less than 50, so it becomes the left child of the root.
- 62 is greater than 50, so it becomes the right child of the root.
- 5 is less than 50 and less than 15, so it becomes the left child of 15.
- 20 is greater than 15 and less than 50, so it becomes the right child of 15.
- 58 is greater than 50 and less than 62, so it becomes the left child of 62.
- 91 is greater than 50 and greater than 62, so it becomes the right child of 62.
- 3 is less than 50, less than 15, and less than 5, so it becomes the left child of 5.
- 8 is greater than 5 and less than 15, so it becomes the right child of 5.
- 37 is greater than 15 and less than 50, so it becomes the right child of 20.
- 60 is greater than 50, greater than 58, and less than 62, so it becomes the right child of 58.
- 24 is greater than 15, less than 50, and less than 37, so it becomes the left child of 37.
Counting the nodes:
To determine the number of nodes in the left and right subtrees of the root, we count the nodes in each subtree.
- Left subtree of the root (15, 5, 3, 8): 4 nodes
- Right subtree of the root (62, 58, 91, 20, 37, 60, 24): 7 nodes
Therefore, the correct answer is option 'B' (7 nodes in the right subtree and 4 nodes in the left subtree).
To determine the number of nodes in the left and right subtrees of the root, we need to construct the binary search tree (BST) using the given integers and count the number of nodes in each subtree.
Constructing the BST:
We start by inserting the first integer, 50, as the root of the BST. Then, we insert the remaining integers one by one according to the rules of a binary search tree:
- 15 is less than 50, so it becomes the left child of the root.
- 62 is greater than 50, so it becomes the right child of the root.
- 5 is less than 50 and less than 15, so it becomes the left child of 15.
- 20 is greater than 15 and less than 50, so it becomes the right child of 15.
- 58 is greater than 50 and less than 62, so it becomes the left child of 62.
- 91 is greater than 50 and greater than 62, so it becomes the right child of 62.
- 3 is less than 50, less than 15, and less than 5, so it becomes the left child of 5.
- 8 is greater than 5 and less than 15, so it becomes the right child of 5.
- 37 is greater than 15 and less than 50, so it becomes the right child of 20.
- 60 is greater than 50, greater than 58, and less than 62, so it becomes the right child of 58.
- 24 is greater than 15, less than 50, and less than 37, so it becomes the left child of 37.
Counting the nodes:
To determine the number of nodes in the left and right subtrees of the root, we count the nodes in each subtree.
- Left subtree of the root (15, 5, 3, 8): 4 nodes
- Right subtree of the root (62, 58, 91, 20, 37, 60, 24): 7 nodes
Therefore, the correct answer is option 'B' (7 nodes in the right subtree and 4 nodes in the left subtree).
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