AVL Trees Explained: How Rotations Keep BST Operations O(log n)
AVL trees are a type of self-balancing binary search tree (BST) that maintain logarithmic height through a balance rule. This rule ensures that the heights of the left and right subtrees of any node differ by no more than one. When this balance is disrupted by insertions or deletions, the tree self-corrects using rotations to restore balance and maintain efficient operation times.
- ▪An AVL tree adds a rule to a BST that keeps the tree balanced by ensuring the height difference between left and right subtrees is at most one.
- ▪When an insertion or deletion causes a node's balance factor to reach -2 or +2, the tree becomes unbalanced and requires a rotation to fix it.
- ▪There are four cases of imbalance in AVL trees, but they can be resolved using just two types of rotations: left and right.
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try { if(localStorage) { let currentUser = localStorage.getItem('current_user'); if (currentUser) { currentUser = JSON.parse(currentUser); if (currentUser.id === 3909129) { document.getElementById('article-show-container').classList.add('current-user-is-article-author'); } } } } catch (e) { console.error(e); } Prakhar Srivastava for codeintuition Posted on May 20 • Originally published at codeintuition.io AVL Trees Explained: How Rotations Keep BST Operations O(log n) #algorithms #leetcode #career #interview You learn binary search trees and walk away believing every operation is O(log n). It isn't. That guarantee only holds when the tree stays balanced, and a plain BST has no mechanism to enforce that.
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