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In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the node's value, and all values in the right subtree are greater?
- a)Min-Heap Property
- b)Max-Heap Property
- c)AVL Property
- d)Binary Tree Property
Correct answer is option 'D'. Can you explain this answer?
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In a binary search tree, which property ensures that all values in the...
In a binary search tree (BST), the left subtree of a node contains only values smaller than the node's value, and the right subtree contains only values greater than the node's value. This property enables efficient searching, insertion, and deletion operations in a BST.
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In a binary search tree, which property ensures that all values in the...
Binary Search Tree (BST)
A binary search tree (BST) is a type of binary tree where each node has a key (value) and satisfies the following properties:
1. The left subtree of a node contains only values that are smaller than the node's value.
2. The right subtree of a node contains only values that are greater than the node's value.
3. Both the left and right subtrees are also binary search trees.
Property of a Binary Search Tree
- The property mentioned in the question ensures that all values in the left subtree of a node are smaller than the node's value, and all values in the right subtree are greater.
- This property is known as the Binary Tree Property or the Binary Search Property.
Explanation
To understand why the Binary Tree Property holds true, let's consider an example. Suppose we have the following BST:
```
8
/ \
3 10
/ \ \
1 6 14
/ \ /
4 7 13
```
If we look at the left subtree of the node with value 8, we can see that all the values (1, 3, 4, 6, and 7) are smaller than 8. Similarly, if we look at the right subtree of the node with value 8, we can see that all the values (10, 14, and 13) are greater than 8. This pattern holds true for each node in the tree.
Key Points
- The Binary Tree Property is essential in a binary search tree as it allows for efficient searching, insertion, and deletion operations.
- When searching for a value in a BST, we can compare the value with the current node and traverse either the left or right subtree based on the comparison result.
- Insertion and deletion operations also rely on the Binary Tree Property to maintain the correct ordering of values in the tree.
- Without the Binary Tree Property, the BST would lose its distinguishing feature and could degenerate into a simple binary tree where searching would require traversing the entire tree.
A binary search tree (BST) is a type of binary tree where each node has a key (value) and satisfies the following properties:
1. The left subtree of a node contains only values that are smaller than the node's value.
2. The right subtree of a node contains only values that are greater than the node's value.
3. Both the left and right subtrees are also binary search trees.
Property of a Binary Search Tree
- The property mentioned in the question ensures that all values in the left subtree of a node are smaller than the node's value, and all values in the right subtree are greater.
- This property is known as the Binary Tree Property or the Binary Search Property.
Explanation
To understand why the Binary Tree Property holds true, let's consider an example. Suppose we have the following BST:
```
8
/ \
3 10
/ \ \
1 6 14
/ \ /
4 7 13
```
If we look at the left subtree of the node with value 8, we can see that all the values (1, 3, 4, 6, and 7) are smaller than 8. Similarly, if we look at the right subtree of the node with value 8, we can see that all the values (10, 14, and 13) are greater than 8. This pattern holds true for each node in the tree.
Key Points
- The Binary Tree Property is essential in a binary search tree as it allows for efficient searching, insertion, and deletion operations.
- When searching for a value in a BST, we can compare the value with the current node and traverse either the left or right subtree based on the comparison result.
- Insertion and deletion operations also rely on the Binary Tree Property to maintain the correct ordering of values in the tree.
- Without the Binary Tree Property, the BST would lose its distinguishing feature and could degenerate into a simple binary tree where searching would require traversing the entire tree.
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In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the nodes value, and all values in the right subtree are greater?a)Min-Heap Propertyb)Max-Heap Propertyc)AVL Propertyd)Binary Tree PropertyCorrect answer is option 'D'. Can you explain this answer?
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In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the nodes value, and all values in the right subtree are greater?a)Min-Heap Propertyb)Max-Heap Propertyc)AVL Propertyd)Binary Tree PropertyCorrect answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the nodes value, and all values in the right subtree are greater?a)Min-Heap Propertyb)Max-Heap Propertyc)AVL Propertyd)Binary Tree PropertyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the nodes value, and all values in the right subtree are greater?a)Min-Heap Propertyb)Max-Heap Propertyc)AVL Propertyd)Binary Tree PropertyCorrect answer is option 'D'. Can you explain this answer?.
In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the nodes value, and all values in the right subtree are greater?a)Min-Heap Propertyb)Max-Heap Propertyc)AVL Propertyd)Binary Tree PropertyCorrect answer is option 'D'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the nodes value, and all values in the right subtree are greater?a)Min-Heap Propertyb)Max-Heap Propertyc)AVL Propertyd)Binary Tree PropertyCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a binary search tree, which property ensures that all values in the left subtree of a node are smaller than the nodes value, and all values in the right subtree are greater?a)Min-Heap Propertyb)Max-Heap Propertyc)AVL Propertyd)Binary Tree PropertyCorrect answer is option 'D'. Can you explain this answer?.
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