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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Object Oriented Programming System (OOPs) is a programming model built on the perception of “objects” that contains data and methods. The major purpose of Object Oriented Programming is to increase the maintainability and flexibility of programs. Object …
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Write a simple C++ program to simulate the insertion program.
### Insertion The following is pseudo-code for insertion. #### Insertion in AVL Tree ```plaintext if (root is null) { create a new tree with the item at the root return true } // end if else if item is equal to the root { return false } // end else if else if item is less than root { recursively insert the item at the left subtree if the height of the left subtree has increased { decrement balance if balance is zero { reset increase to false } if balance is less than -1 { reset increase to false } } } ``` This pseudocode is part of a larger algorithm used to insert elements into an AVL tree, which is a type of self-balancing binary search tree. The primary operations performed in this pseudocode include: 1. **Checking if the root is null:** - If it is, a new tree is created with the item as the root, and the function returns `true`. 2. **Comparing the item to the root:** - If the item is equal to the root, the function returns `false`, indicating the item already exists in the tree. 3. **Recursive insertion for items less than the root:** - If the item is less than the root, it is recursively inserted into the left subtree. - If the height of the left subtree increases as a result of the insertion, the balance factor is adjusted accordingly. - If necessary, adjustments are made to maintain the AVL tree property, namely, that the balance factor remains between -1 and 1. If the balance factor goes out of this range, further balancing operations (not shown in the provided pseudocode) would be necessary. These steps ensure that the AVL tree remains balanced after each insertion, providing efficient performance for search, insertion, and deletion operations.
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Transcribed Image Text:### Insertion The following is pseudo-code for insertion. #### Insertion in AVL Tree ```plaintext if (root is null) { create a new tree with the item at the root return true } // end if else if item is equal to the root { return false } // end else if else if item is less than root { recursively insert the item at the left subtree if the height of the left subtree has increased { decrement balance if balance is zero { reset increase to false } if balance is less than -1 { reset increase to false } } } ``` This pseudocode is part of a larger algorithm used to insert elements into an AVL tree, which is a type of self-balancing binary search tree. The primary operations performed in this pseudocode include: 1. **Checking if the root is null:** - If it is, a new tree is created with the item as the root, and the function returns `true`. 2. **Comparing the item to the root:** - If the item is equal to the root, the function returns `false`, indicating the item already exists in the tree. 3. **Recursive insertion for items less than the root:** - If the item is less than the root, it is recursively inserted into the left subtree. - If the height of the left subtree increases as a result of the insertion, the balance factor is adjusted accordingly. - If necessary, adjustments are made to maintain the AVL tree property, namely, that the balance factor remains between -1 and 1. If the balance factor goes out of this range, further balancing operations (not shown in the provided pseudocode) would be necessary. These steps ensure that the AVL tree remains balanced after each insertion, providing efficient performance for search, insertion, and deletion operations.
### Insertion in AVL Tree #### Algorithm Steps 1. **Determine Position for Insertion:** - **If the item is greater than the root:** - Recursively insert the item into the right subtree. - If the height of the right subtree has increased: - Decrement the balance. - If the balance is zero: - Reset `increase` to `false`. - If the balance is less than -1: - Reset `increase` to `false`. - Perform a re-balance. ```plaintext if item is greater than root { recursively insert the item at the right subtree if the height of the right subtree has increased { decrement balance if (balance is zero) { reset increase to false if (balance is less than -1) { reset increase to false perform a re-balance } // end if balance } // end if } // end if } // end else if ``` In an AVL tree, insertion follows defined steps to ensure the tree remains balanced after every insertion. When inserting: - If the new item is greater than the root, it will be inserted into the right subtree. - After the item is inserted, the height of the right subtree may increase. - If this causes the height of a subtree to change, the balance factor is adjusted. Depending on the balance factor, the tree may need re-balancing to ensure efficient look-up times in the tree. Understanding and following these steps is crucial for maintaining the balanced nature of an AVL tree, which is an essential aspect of many search operations in computer science.
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Transcribed Image Text:### Insertion in AVL Tree #### Algorithm Steps 1. **Determine Position for Insertion:** - **If the item is greater than the root:** - Recursively insert the item into the right subtree. - If the height of the right subtree has increased: - Decrement the balance. - If the balance is zero: - Reset `increase` to `false`. - If the balance is less than -1: - Reset `increase` to `false`. - Perform a re-balance. ```plaintext if item is greater than root { recursively insert the item at the right subtree if the height of the right subtree has increased { decrement balance if (balance is zero) { reset increase to false if (balance is less than -1) { reset increase to false perform a re-balance } // end if balance } // end if } // end if } // end else if ``` In an AVL tree, insertion follows defined steps to ensure the tree remains balanced after every insertion. When inserting: - If the new item is greater than the root, it will be inserted into the right subtree. - After the item is inserted, the height of the right subtree may increase. - If this causes the height of a subtree to change, the balance factor is adjusted. Depending on the balance factor, the tree may need re-balancing to ensure efficient look-up times in the tree. Understanding and following these steps is crucial for maintaining the balanced nature of an AVL tree, which is an essential aspect of many search operations in computer science.
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