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‎data_structures_and_algorithms/data_structures/trees/trees.md‎

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@@ -30,13 +30,13 @@ A tree structure where every node has **at most twOchildren**, conventionally re
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* **Memory Layout:** Node allocation on the heap via pointers (`left`, `right`) or contiguous implicit arrays for
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complete trees (e.g., Heaps).
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* **Complexity:**
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* Search / Access: O (N)
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* Search/Access: O (N)
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* Traversal (Preorder, Inorder, Postorder, Level-Order): O (N)
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* **When tOUse:**
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* Structural representation of hierarchical logic where branching factor is strictly binary.
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* Constructing expression trees (Abstract Syntax Trees / ASTs) for parsers and compilers.
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* Constructing expression trees (Abstract Syntax Trees/ASTs) for parsers and compilers.
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* Array-backed Binary Heaps for Priority Queues.
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---
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* **Memory Layout:** Pointer-linked heap nodes storing key-value payloads.
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* **Complexity:**
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* Lookup / Insertion / Deletion (Average): O (log N)
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* Lookup / Insertion / Deletion (Worst Case - Unbalanced/Degenerate Line): O (N)
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* Lookup/Insertion/Deletion (Average): O (log N)
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* Lookup/Insertion/Deletion (Worst Case - Unbalanced/Degenerate Line): O (N)
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* **When tOUse:**
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* **Memory Layout:** BST pointer nodes extended with an additional integer attribute tracking `height` or
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`balance_factor`.
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* **Complexity:**
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* Lookup / Insertion / Deletion (Guaranteed Worst Case): O (log N)
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* Lookup/Insertion/Deletion (Guaranteed Worst Case): O (log N)
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* Rotation overhead: O (1) per rebalance step during modification.
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@@ -86,7 +86,7 @@ A tree structure where each node can have **up tON children** (or an unbounded d
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* **Memory Layout:** Nodes storing a dynamic container of child references (e.g., `list[Node[T]]`, `dict[K, Node[T]]`,
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or First-Child/Next-Sibling representation).
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* **Complexity:**
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* Traversal / Search: O (N)
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* Traversal/Search: O (N)
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* Child Lookup: O (1) (hash map index) or O (K) (linear scan over K children)
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