Learn By Patterns

1️⃣ Step 1: Check Constraints 📌

🔹 Small n (≤ 20)

• Brute force is valid
• Backtracking / Recursion
• Exponential allowed:
  • 2^n, n!
• Try all possible Permutations & Combinations

🔹 Medium n (10³ → 10⁶)

• ❌ No brute force
• Use:
  • Linear Time → O(n) / O(n log n)
• Patterns
  • Greedy
  • Two pointers
  • Heap
  • Dynamic Programming

🔹 Large n (≥ 10⁷)

• ❌ No linear solutions
• Use:
  • O(log n) only
  • Binary search
  • Math formulas
  • O(1) tricks

2️⃣ Step 2: Analyze Input Format

🌳 Tree / BST

• DFS:
  • All paths
  • Recursive traversal
  • Pre/In/Post order
• BFS:
  • level-by-level
  • shortest path in unweighted tree
• Focus:
  • tree properties, parent-child relationships

🌐 Graph (nodes + edges)

• BFS → shortest path
• DFS → connected components
• Union-Find:
  • “connected components”
  • “number of groups”
• Topological sort:
  • for Dependencies

🧩 2D Grid / Matrix

• DFS/BFS:
  • Islands problems
• Union-Find:
  • Connected regions
• DP:
  • Path problems
• Consider: 4-directional or 8-directional movement

📊 Sorted Array

• Two pointers technique - 1. Pattern - Two Pointers
• Binary search
• Greedy

🔤 String

• Two pointers:
  • Palindrome
• Sliding window:
  • Substrings
• Trie:
  • Word problems
• Stack:
  • parentheses/brackets

🔗 Linked List

• Two pointers → Fast/Slow pointers
• Dummy node techniques
• Cycle detection

3️⃣ Step 3: Analyze Output Format

📚 List of Lists (combinations, subsets, paths)

• Backtracking is almost always the answer
• Generate all possibilities
• Use recursion with choice/no-choice pattern

🔢 Single Number Output (max/min profit, cost, ways, jumps):

• Dynamic Programming for optimization
• Greedy for local optimal choices
• Mathematical approach for counting

🔄 Modified Array / String (in-place operations):

• Two Pointers for in-place modifications

📈 Ordered List (sorted sequence, valid task order):

• Sorting with custom comparators
• Topological sort
• Heap

4️⃣ Step 4: Keyword → Pattern Mapping 🔑

🧠 Dynamic Programming

• “number of ways”
• “Maximum/minimum” + “sum/profit/cost”
• “Can you reach”
• “Longest/shortest subsequence”
• “Optimal” or “best”

👉 Two Pointers

• “palindrome”
• “sorted array”
• “target sum”
• “remove duplicates”

⛰ Heap

• “k largest/smallest”
• “top k”
• “median”
• “priority”

📚 Stack

• “Parentheses” or “brackets”
• “valid expression”
• “Nested structure”
• “Undo operations”

📉 Monotonic Stack

• “Next greater element”
• “Next smaller element”

🗺 HashMap

• “Count frequency”
• “Find duplicates”
• “Anagram”

🌲 Trie

• “Word search”
• “Word prefixes”

⚡ Greedy

• “Minimum operations”

🔗 Union Find

• “Connected components”
• “Number of groups”

🔍 Binary Search

• “kth element”
• “Search in sorted”
• “Minimize maximum”
• “First/last occurrence”

🔢 Bit Manipulation

• “XOR” operations
• ""Single number” problems
• “power of 2”

📐 Math / Geometry

• “GCD / LCM”
• “prime numbers”
• “Angle calculations”
• “Coordinate”

🎮 Game Theory

• “Optimal strategy”
• “Win/lose scenarios”
• “Minimax”

🪟 Sliding Window

• “Substring” with conditions
• Subarray” with fixed/variable size
• “Maximum/minimum window”
• “Contains all”

5️⃣ How to Use This

• Step-by-step:

  1. Constraints
  2. Input
  3. Output
  4. Keywords

• Practice strategy:

  • Solve 5–10 problems per pattern
  • Practice only classification
  • Maintain personal keyword notes