Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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### Understanding Binary Search Trees (BST) #### Example Problem: Given the BST (Binary Search Tree) tree below, fill in the values in the table. #### Visual Diagram: The diagram shows a BST with nodes represented by circular shapes with numerical values assigned to them. The tree starts with the root node 0034 and branches out through a hierarchy of nodes. - The root node is 0034. - Nodes descend from the root with connections established by lines indicating left (lesser value) and right (greater value): - The left subtree of the root contains nodes: 0005, 0045, etc. - The right subtree of the root contains nodes: 0067, 0098, etc. #### Nodes in the BST: - **Root Node**: 0034 - **Subtrees and Descendants**: - Left Subtree of 0034: 0005, 0017, 0021, 0002, 0050, 0040, 0045, 0043, 0055, 0049, etc. - Right Subtree of 0034: 0067, 0098, 0076, 0071, 0092, 0087, 0078, 0084, etc. #### Properties and Values Table: This table is designed to be completed using the provided BST diagram. Below are the properties that need to be determined: | Property | Value | |-------------------------------------------|------------------------| | Height of tree | | | Height of node 45 | | | Depth of node 17 | | | Node 76 degree | | | Tree degree | | | Name the nodes in left subtree of node 98 | | | Order of tree | | | Internal path length | | | External path length | | #### Explanation of Each Property: - **Height of Tree**: The maximum depth or distance from the root node to the furthest leaf node. - **Height of Node 45**: The distance from node 0045 to its furthest leaf node. - **Depth of Node 17**: The distance from the root node 0034 to node 0017. - **Node 76 Degree**: The number of children linked to node 0076. - **Tree Degree**: The maximum number of
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Transcribed Image Text:### Understanding Binary Search Trees (BST) #### Example Problem: Given the BST (Binary Search Tree) tree below, fill in the values in the table. #### Visual Diagram: The diagram shows a BST with nodes represented by circular shapes with numerical values assigned to them. The tree starts with the root node 0034 and branches out through a hierarchy of nodes. - The root node is 0034. - Nodes descend from the root with connections established by lines indicating left (lesser value) and right (greater value): - The left subtree of the root contains nodes: 0005, 0045, etc. - The right subtree of the root contains nodes: 0067, 0098, etc. #### Nodes in the BST: - **Root Node**: 0034 - **Subtrees and Descendants**: - Left Subtree of 0034: 0005, 0017, 0021, 0002, 0050, 0040, 0045, 0043, 0055, 0049, etc. - Right Subtree of 0034: 0067, 0098, 0076, 0071, 0092, 0087, 0078, 0084, etc. #### Properties and Values Table: This table is designed to be completed using the provided BST diagram. Below are the properties that need to be determined: | Property | Value | |-------------------------------------------|------------------------| | Height of tree | | | Height of node 45 | | | Depth of node 17 | | | Node 76 degree | | | Tree degree | | | Name the nodes in left subtree of node 98 | | | Order of tree | | | Internal path length | | | External path length | | #### Explanation of Each Property: - **Height of Tree**: The maximum depth or distance from the root node to the furthest leaf node. - **Height of Node 45**: The distance from node 0045 to its furthest leaf node. - **Depth of Node 17**: The distance from the root node 0034 to node 0017. - **Node 76 Degree**: The number of children linked to node 0076. - **Tree Degree**: The maximum number of
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