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🔤 Tries & Strings Mastery

Your complete roadmap to mastering Tries and String Algorithms —
covering everything from prefix-based structures (Tries, XOR problems) to advanced string matching and manipulation techniques like KMP, Z-function, and Rabin-Karp.

📚 Table of Contents

  1. Introduction
  2. Trie (Prefix Tree) Problems
  3. String Fundamentals & Hashing
  4. String Matching Algorithms
  5. String Manipulation & Parsing
  6. Concepts to Remember
  7. Study Plan (5 Weeks)
  8. Progress Tracker
  9. Final Goal
  10. Author Note

🧠 Introduction

This section focuses on two of the most powerful topics in modern problem-solving:

  • Tries (Prefix Trees) — used for searching, prefix-matching, and XOR problems.
  • String Algorithms — pattern matching, hashing, palindrome analysis, and parsing.

Mastering these builds the foundation for problems in autocomplete systems, text editors, search engines, and pattern recognition.

🌲 Trie (Prefix Tree) Problems

# Problem Concept Status
1 Implement Trie - II (Prefix Tree) Insert, search, erase, prefix counting ☐
2 Longest String with All Prefixes Maintain prefix chain validity ☐
3 Number of Distinct Substrings in a String Use Trie to store unique substrings ☐
4 Bit Prerequisites for Trie Problems Learn bit manipulation for XOR-Trie ☐
5 Maximum XOR With an Element From Array Query bitwise Trie efficiently ☐
6 Maximum XOR of Two Numbers in an Array Binary Trie pairwise XOR optimization ☐
7 Word Search II Backtracking + Trie hybrid for multi-word search ☐

🧠 Pattern: Tries help transform string/prefix or XOR problems into logarithmic-time lookups, enabling fast pattern and number queries.

✳️ String Fundamentals & Hashing

# Problem Concept Status
1 Minimum Number of Bracket Reversals Stack-based balancing logic ☐
2 Count and Say Recursively build the next term of sequence ☐
3 Hashing in Strings (Theory) Rolling hash and collision handling ☐
4 Rabin-Karp Algorithm Substring search using polynomial rolling hash ☐

🧩 Goal: Learn hashing and counting-based logic before advancing to string matching.

🔍 String Matching Algorithms

# Problem Concept Status
1 Z-Function Compute longest prefix-suffix matches in O(n) ☐
2 KMP Algorithm / LPS (pi) Array Prefix function for efficient matching ☐
3 Shortest Palindrome Build palindrome using reversed prefix + KMP ☐
4 Longest Happy Prefix Longest prefix also acting as suffix ☐
5 Count Palindromic Subsequences DP + string recurrence relationships ☐

🧠 Pattern: Both Z-function and KMP revolve around precomputing overlap information — essential for matching, prefix checking, and palindrome analysis.

✂️ String Manipulation & Parsing

# Problem Concept Status
1 Check if Two Strings are Anagram Frequency count or sorting ☐
2 Reverse Words / Palindrome Check Reverse order or compare mirror positions ☐
3 Largest Odd Number in a String Traverse from end for last odd digit ☐
4 Longest Common Prefix Compare characters of all strings ☐
5 Isomorphic String Maintain 1-to-1 mapping between characters ☐
6 Check if One String is Rotation of Another Check if s2 is substring of s1 + s1 ☐
7 Remove Outermost Parentheses Stack or counter to track nesting ☐
8 Sort Characters by Frequency Use hashmap + max-heap ☐
9 Maximum Nesting Depth of Parentheses Track max open count ☐
10 Roman Number ↔ Integer Conversion Bidirectional parsing with lookup map ☐
11 Implement Atoi (String to Integer) Manual parsing with overflow detection ☐
12 Count Number of Substrings Sliding window or prefix-sum based ☐
13 Longest Palindromic Substring Expand around center (no DP) ☐
14 Sum of Beauty of All Substrings Hashmap + frequency difference ☐
15 Reverse Every Word in a String Reverse words in-place using two pointers ☐

🧠 Pattern: Use stack, hashmaps, and two-pointers to manipulate substrings efficiently — without converting to extra data structures.

⚙️ Concepts to Remember

Concept Description
Trie (Prefix Tree) Efficient prefix storage for strings and bits
Rolling Hash Convert substrings to comparable integer values
Z / KMP Algorithms Precompute longest border for string patterning
Palindrome Techniques Reverse, expand, or check symmetry dynamically
Frequency Mapping Used for anagram and character grouping problems
Stack Parsing Evaluate or clean expressions with parentheses
Two-pointer Logic Simplifies reversal, substring, and counting logic

📆 Study Plan (5 Weeks)

Week Focus Key Topics
Week 1 Trie Basics Insert/Search/Erase, Longest Prefix, XOR Trie
Week 2 String Fundamentals Bracket reversal, Count and Say, Hashing
Week 3 String Matching Z-Function, KMP, Palindrome Prefix
Week 4 String Manipulation Anagram, Reverse, Prefix, Parentheses
Week 5 Parsing + Advanced Patterns Atoi, Longest Palindrome, Beauty of Substrings

🧩 Tip: For KMP/Z problems, dry run string examples manually to visualize prefix overlaps.

✅ Progress Tracker

Tries

  • Implement Trie - II (Prefix Tree)
  • Longest String with All Prefixes
  • Number of Distinct Substrings
  • Bit PreRequisites for Trie
  • Maximum XOR With an Element From Array
  • Word Search II
  • Maximum XOR of Two Numbers in Array

String Fundamentals & Hashing

  • Minimum Number of Bracket Reversals
  • Count and Say
  • Hashing in Strings (Theory)
  • Rabin-Karp Algorithm

String Matching

  • Z-Function
  • KMP Algorithm / LPS(pi) Array
  • Shortest Palindrome
  • Longest Happy Prefix
  • Count Palindromic Subsequences

String Manipulation & Parsing

  • Check if Two Strings are Anagram
  • Reverse Words / Palindrome Check
  • Largest Odd Number in a String
  • Longest Common Prefix
  • Isomorphic String
  • Check if One String is Rotation of Another
  • Remove Outermost Parentheses
  • Sort Characters by Frequency
  • Maximum Nesting Depth of Parentheses
  • Roman Number ↔ Integer Conversion
  • Implement Atoi
  • Count Number of Substrings
  • Longest Palindromic Substring
  • Sum of Beauty of All Substrings
  • Reverse Every Word in a String

🎯 Final Goal

By completing this roadmap, you will:

  • Master Tries and Prefix/XOR problems
  • Implement all major string matching algorithms (KMP, Z, Rabin-Karp)
  • Be fluent in string manipulation, parsing, and palindrome logic
  • Develop pattern recognition skills for competitive and interview problems

💬 Author Note

Strings and Tries teach one of the most powerful lessons in DSA —
how data can represent both words and numbers structurally.
Once you see patterns in prefixes, repetitions, and mirrors —
every string problem becomes intuitive.

Happy Coding 💻
#DSA #Trie #Strings #KMP #ZFunction #RabinKarp #Parsing #InterviewPrep