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A Red-Black Tree is a type of self-balancing binary search tree in which each node contains an extra bit for denoting the color of the node, either red or black. Red-Black Trees maintain balance through a set of properties that ensure the tree remains approximately balanced during insertions and deletions, allowing operations such as search, insertion, and deletion to be performed in O(log n) time in the worst case. The key properties of a Red-Black Tree are as follows: 1. Every node is either red or black. 2. The root node is always black. 3. All leaves (NULL or NIL nodes) are black. 4. If a node is red, then both its children are black (no two red nodes can be adjacent). 5. Every path from a node to its descendant NULL nodes contains the same number of black nodes (this number is called the black-height). These properties help maintain the tree’s __________ ______ ________ ______ ___ ___ ___ ____ ________ ____.
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