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‎Advanced_DataStructure/Problems/problem1.md‎

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# Problem 1: Implement Trie (Prefix Tree)
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## Problem Statement
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Implement a trie with insert, search, and startsWith methods.
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## Input Format
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- Operations: insert(word), search(word), startsWith(prefix).
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## Output Format
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- True/False for search and startsWith.
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## Constraints
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- 1 <= word.length, prefix.length <= 2000
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## Example
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**Input:** insert("apple"), search("apple")
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**Output:** True

‎Advanced_DataStructure/Problems/problem10.md‎

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# Problem 10: Bloom Filter
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## Problem Statement
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Implement a Bloom Filter for probabilistic set membership testing.
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## Input Format
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- Operations: add(item), contains(item).
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## Output Format
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- Boolean for contains (may have false positives).
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## Constraints
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- 1 <= items <= 10^6
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## Example
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**Input:** add("hello"), contains("hello")
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**Output:** True

‎Advanced_DataStructure/Problems/problem11.md‎

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# Problem 11: Order Statistics Tree
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## Problem Statement
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Implement a BST that supports select(k) — find kth smallest — and rank(x) in O(log n).
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## Input Format
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- Operations: insert, select(k), rank(x).
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## Output Format
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- Integer.
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## Constraints
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- 1 <= n <= 10^5
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## Example
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**Input:** insert(3,1,4,5,2), select(3)
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**Output:** 3

‎Advanced_DataStructure/Problems/problem12.md‎

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# Problem 12: Interval Tree
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## Problem Statement
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Build an interval tree to efficiently find all intervals overlapping a given interval.
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## Input Format
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- A list of intervals and a query interval.
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## Output Format
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- List of overlapping intervals.
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## Constraints
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- 1 <= n <= 10^5
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## Example
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**Input:** intervals=[(15,20),(10,30),(17,19)], query=(14,16)
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**Output:** [(15,20),(10,30)]

‎Advanced_DataStructure/Problems/problem13.md‎

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# Problem 13: Sparse Table
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## Problem Statement
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Build a Sparse Table for O(1) range minimum queries after O(N log N) preprocessing.
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## Input Format
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- An array, range queries.
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## Output Format
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- Minimum in range.
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## Constraints
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- 1 <= n <= 10^5
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## Example
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**Input:** arr=[7,2,3,0,5,10,3,12,18], query(0,4)
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**Output:** 0

‎Advanced_DataStructure/Problems/problem14.md‎

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# Problem 14: Suffix Array
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## Problem Statement
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Build the suffix array for a given string.
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## Input Format
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- A string `s`.
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## Output Format
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- A list of indices representing the suffix array.
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## Constraints
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- 1 <= len(s) <= 10^5
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## Example
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**Input:** s = "banana"
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**Output:** [5,3,1,0,4,2]

‎Advanced_DataStructure/Problems/problem15.md‎

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# Problem 15: Treap
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## Problem Statement
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Implement a Treap (tree + heap) with random priorities for balanced BST operations.
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## Input Format
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- Operations: insert, delete, search.
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## Output Format
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- Boolean for search.
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## Constraints
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- 1 <= n <= 10^5
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## Example
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**Input:** insert(5), insert(3), insert(7), search(3)
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**Output:** True

‎Advanced_DataStructure/Problems/problem16.md‎

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# Problem 16: Splay Tree
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## Problem Statement
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Implement a Splay Tree that moves accessed nodes to the root.
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## Input Format
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- Operations: insert, search, delete.
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## Output Format
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- Boolean for search.
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## Constraints
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- 1 <= n <= 10^5
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## Example
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**Input:** insert(10), insert(20), search(10)
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**Output:** True

‎Advanced_DataStructure/Problems/problem17.md‎

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# Problem 17: B-Tree Operations
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## Problem Statement
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Implement basic B-Tree insertion and search operations.
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## Input Format
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- Operations: insert, search, minimum order t.
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## Output Format
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- Boolean for search.
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## Constraints
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- 2 <= t <= 100
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## Example
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**Input:** insert(10,20,5,6,12), search(6)
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**Output:** True

‎Advanced_DataStructure/Problems/problem18.md‎

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# Problem 18: AVL Tree
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## Problem Statement
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Implement an AVL tree with self-balancing insertion and deletion.
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## Input Format
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- Operations: insert, delete, search.
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## Output Format
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- Boolean for search.
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## Constraints
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- 1 <= n <= 10^5
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## Example
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**Input:** insert(10,20,30), search(20)
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**Output:** True

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