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Data Structures: Difference between revisions
→Red-Black
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===AVL=== | ===AVL=== | ||
===Red-Black=== | ===Red-Black=== | ||
[[Wikipedia: Red–black tree]]<br> | |||
[https://www.geeksforgeeks.org/red-black-tree-set-1-introduction-2/ Geeks for geeks introduction]<br> | |||
[https://www.geeksforgeeks.org/red-black-tree-set-2-insert/ Geeks for geeks insertion]<br> | |||
[https://www.geeksforgeeks.org/red-black-tree-set-3-delete-2/ Geeks for geeks deletion]<br> | |||
A red-black tree follows the following rules | |||
# Each node is either red or black. | |||
# The root is black. This rule is sometimes omitted. Since the root can always be changed from red to black, but not necessarily vice versa, this rule has little effect on analysis. | |||
# All leaves (NIL) are black. | |||
# If a node is red, then both its children are black. | |||
# Every path from a given node to any of its descendant NIL nodes contains the same number of black nodes. | |||
====Intuition==== | |||
Consider any tree with a left and right child. | |||
From rule 4, we see that at most n/2 nodes are red. At least half will be black. | |||
Red nodes or levels are those interspersed between black levels. | |||
If the left child has <math>m</math> levels then at most the right child can have <math>2m</math> levels. | |||
Intuitively, this is more relaxed than AVL trees so they will have fewer operations for insert/delete but will be less balanced.<br> | |||
Red-black trees are used in in C++ (ordered_map, ordered_set) and Java (TreeMap, TreeSet). | |||
====Complexity=== | |||
<math>2\log (n+1)</math> height.<br> | |||
<math>O(\log n)</math> insert, delete | |||
===2-3=== | ===2-3=== | ||
===Treap=== | ===Treap=== | ||