Added Trie Data structure in Advance DSA

dsa/Advance/trie.md

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+---
+id: 02-Trie
+title: Introduction to Trie
+sidebar_label: Trie
+tags:
+  - dsa
+  - data-structures
+  - binary-tree
+  - intermediate
+  - javascript
+  - python
+  - c++
+  - java
+  - programming
+  - tutorial
+sidebar_position: 2
+---
+
+# Trie Data Structure and Algorithms
+
+## Introduction
+
+A Trie, also known as a prefix tree, is a type of search tree that is used to store a dynamic set of strings. The name "Trie" comes from the word "retrieval" as they are used to retrieve a key in a dataset of strings. Tries are particularly useful for tasks involving a large set of strings, such as dictionary words or contact lists.
+
+## Basic Structure
+
+A Trie is a tree-like data structure where each node represents a single character of a string. The root node is associated with an empty string. Each subsequent node represents the next character of the inserted string. Nodes that share a common prefix share the same path from the root.
+
+### Example
+
+```
+          root
+         /  |  \
+        t   b   c
+       /|    \   \
+      h o     a   a
+     /   \     \   \
+    e     r     t   r
+
+/ \ \
+ r k t
+```
+
+In the example above, the Trie stores the words "the", "their", "there", "bat", "cat", and "cart".
+
+## Operations
+
+### Insertion
+
+To insert a word into a Trie, we start at the root node and follow the path corresponding to the characters in the word. If a node for a character does not exist, we create a new node. After inserting all characters, we mark the last node as the end of a word.
+
+### Search
+
+To search for a word in a Trie, we follow the path corresponding to the characters in the word starting from the root. If we can follow the path for all characters and reach a node marked as the end of a word, the word exists in the Trie.
+
+### Deletion
+
+To delete a word from a Trie, we first ensure the word exists. If it does, we remove the nodes corresponding to the word's characters, starting from the last character and moving towards the root. If removing a node would break the path for another word, we stop the deletion process for that node.
+
+### Prefix Search
+
+A Trie can efficiently find all words with a given prefix. By following the path corresponding to the prefix characters, we can reach a node where all the sub-nodes form words with the given prefix.
+
+## Applications
+
+- **Autocomplete**: Tries are used to provide suggestions in search engines and text editors.
+- **Spell Checker**: Tries store a large dictionary of words for quick lookup and suggestions.
+- **IP Routing**: In networking, Tries can be used to store routing tables.
+- **Genome Analysis**: Tries can store and search DNA sequences efficiently.
+
+## Advantages and Disadvantages
+
+### Advantages
+
+- **Fast Lookups**: O(n) complexity for search, insertion, and deletion where n is the length of the word.
+- **Prefix Search**: Efficiently find all words with a given prefix.
+- **Memory Efficiency**: Space optimization for storing keys with common prefixes.
+
+### Disadvantages
+
+- **Space Complexity**: Requires more memory compared to some other data structures, especially for a sparse dataset.
+- **Implementation Complexity**: More complex to implement than basic data structures like arrays or linked lists.
+
+## Complexity Analysis
+
+- **Insertion**: O(n), where n is the length of the word.
+- **Search**: O(n), where n is the length of the word.
+- **Deletion**: O(n), where n is the length of the word.
+- **Space Complexity**: O(ALPHABET*SIZE * n \_ m), where n is the number of keys and m is the average key length.
+
+## Example Implementation in Python
+
+```python
+class TrieNode:
+    def __init__(self):
+        self.children = {}
+        self.is_end_of_word = False
+
+class Trie:
+    def __init__(self):
+        self.root = TrieNode()
+
+    def insert(self, word):
+        node = self.root
+        for char in word:
+            if char not in node.children:
+                node.children[char] = TrieNode()
+            node = node.children[char]
+        node.is_end_of_word = True
+
+    def search(self, word):
+        node = self.root
+        for char in word:
+            if char not in node.children:
+                return False
+            node = node.children[char]
+        return node.is_end_of_word
+
+    def delete(self, word):
+        def _delete(node, word, depth):
+            if not node:
+                return False
+            if depth == len(word):
+                if node.is_end_of_word:
+                    node.is_end_of_word = False
+                return len(node.children) == 0
+            char = word[depth]
+            if char in node.children:
+                should_delete = _delete(node.children[char], word, depth + 1)
+                if should_delete:
+                    del node.children[char]
+                    return len(node.children) == 0
+            return False
+        _delete(self.root, word, 0)
+
+    def starts_with(self, prefix):
+        node = self.root
+        for char in prefix:
+            if char not in node.children:
+                return False
+            node = node.children[char]
+        return True
+```
+
+## References
+
+1.  GeeksforGeeks - Trie
+2.  Wikipedia - Trie
+3.  TutorialsPoint - Trie

dsa/Advance/trie_practice_questions.md

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+---
+id: 02-Leetcode trie Practice Questions
+title: Leetcode trie Practice Questions
+sidebar_label: Leetcode trie Practice Questions
+tags:
+  - dsa
+  - data-structures
+  - binary-tree
+  - intermediate
+  - javascript
+  - python
+  - c++
+  - java
+  - programming
+  - tutorial
+sidebar_position: 2
+---
+
+## Questions
+
+### 1. Implement Trie (Prefix Tree)
+
+**Problem:** Implement a trie with `insert`, `search`, and `startsWith` methods.
+
+**Link:** [Implement Trie (Prefix Tree)](https://leetcode.com/problems/implement-trie-prefix-tree/)
+
+### 2. Add and Search Word - Data structure design
+
+**Problem:** Design a data structure that supports adding new words and finding if a string matches any previously added string.
+
+**Link:** [Add and Search Word - Data structure design](https://leetcode.com/problems/add-and-search-word-data-structure-design/)
+
+### 3. Longest Word in Dictionary
+
+**Problem:** Find the longest word in the dictionary that can be built one character at a time by other words in the dictionary.
+
+**Link:** [Longest Word in Dictionary](https://leetcode.com/problems/longest-word-in-dictionary/)
+
+### 4. Replace Words
+
+**Problem:** Implement a function to replace all words in a sentence with their root forms using a dictionary of roots.
+
+**Link:** [Replace Words](https://leetcode.com/problems/replace-words/)
+
+### 5. Stream of Characters
+
+**Problem:** Design a class to search for strings in a stream of characters.
+
+**Link:** [Stream of Characters](https://leetcode.com/problems/stream-of-characters/)
+
+### 6. Design Search Autocomplete System
+
+**Problem:** Implement a search autocomplete system that supports inputting characters and returning the top 3 historical hot sentences.
+
+**Link:** [Design Search Autocomplete System](https://leetcode.com/problems/design-search-autocomplete-system/)
+
+### 7. Prefix and Suffix Search
+
+**Problem:** Design a class that supports querying words with given prefix and suffix.
+
+**Link:** [Prefix and Suffix Search](https://leetcode.com/problems/prefix-and-suffix-search/)
+
+### 8. Word Search II
+
+**Problem:** Given a 2D board and a list of words, find all words that can be formed by letters of the board.
+
+**Link:** [Word Search II](https://leetcode.com/problems/word-search-ii/)
+
+### 9. Map Sum Pairs
+
+**Problem:** Implement a MapSum class with insert and sum methods, which sum all keys with a given prefix.
+
+**Link:** [Map Sum Pairs](https://leetcode.com/problems/map-sum-pairs/)
+
+### 10. Design Add and Search Words Data Structure
+
+**Problem:** Design a data structure that supports adding new words and finding if a string matches any previously added string, with support for wildcards.
+
+**Link:** [Design Add and Search Words Data Structure](https://leetcode.com/problems/design-add-and-search-words-data-structure/)
+
+### 11. Palindrome Pairs
+
+**Problem:** Given a list of unique words, find all pairs of distinct indices (i, j) such that the concatenation of words[i] and words[j] is a palindrome.
+
+**Link:** [Palindrome Pairs](https://leetcode.com/problems/palindrome-pairs/)
+
+### 12. Maximum XOR of Two Numbers in an Array
+
+**Problem:** Find the maximum XOR of two numbers in an array.
+
+**Link:** [Maximum XOR of Two Numbers in an Array](https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array/)
+
+### 13. Concatenated Words
+
+**Problem:** Find all concatenated words in a given dictionary of words.
+
+**Link:** [Concatenated Words](https://leetcode.com/problems/concatenated-words/)
+
+### 14. Design Phone Directory
+
+**Problem:** Design a phone directory that initially has all phone numbers available to be assigned and supports checking availability, getting a number, and releasing a number.
+
+**Link:** [Design Phone Directory](https://leetcode.com/problems/design-phone-directory/)
+
+### 15. Search Suggestions System
+
+**Problem:** Given an array of products and a search word, design a system that suggests at most 3 products as you type each character of the search word.
+
+**Link:** [Search Suggestions System](https://leetcode.com/problems/search-suggestions-system/)
+
+### 16. Word Filter
+
+**Problem:** Implement a WordFilter class that supports searching for words with a given prefix and suffix.
+
+**Link:** [Word Filter](https://leetcode.com/problems/word-filter/)
+
+### 17. Index Pairs of a String
+
+**Problem:** Given a string text and an array of words, return all index pairs [i, j] so that the substring text[i...j] is in the array of words.
+
+**Link:** [Index Pairs of a String](https://leetcode.com/problems/index-pairs-of-a-string/)
+
+### 18. Camelcase Matching
+
+**Problem:** Given a list of queries and a pattern, return a list of booleans where each boolean indicates whether the query matches the pattern.
+
+**Link:** [Camelcase Matching](https://leetcode.com/problems/camelcase-matching/)
+
+### 19. Prefix and Suffix Search
+
+**Problem:** Implement a class that supports querying words with a given prefix and suffix (similar to question 7 but can be a different version or extension).
+
+**Link:** [Prefix and Suffix Search](https://leetcode.com/problems/prefix-and-suffix-search/)
+
+### 20. Delete Duplicate Folders in System
+
+**Problem:** Given a system of folders, delete all duplicate folders and return the list of unique folders.
+
+**Link:** [Delete Duplicate Folders in System](https://leetcode.com/problems/delete-duplicate-folders-in-system/)