🧭 Master Roadmap to Problem Identification

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πŸ”Ή 1. Recursion Problems (Foundation)​

Use recursion when a problem can be defined in terms of smaller self-similar subproblems with a clear base case.
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A. Mathematical Recurrence​

  1. Factorial of n
  2. Fibonacci numbers (naΓ―ve recursion)
  3. Power of n (x^n) using recursion
  4. Greatest Common Divisor (Euclidean algorithm)

B. Divide & Conquer​

  1. Binary Search
  2. Merge Sort
  3. Quick Sort
  4. Maximum/Minimum in an array
  5. Count inversions in an array

C. Recursion with Strings/Arrays​

  1. Reverse a string recursively
  2. Palindrome check recursively
  3. Print all subsequences of a string
  4. Print all permutations of a string

D. Tree/Graph Recursion​

  1. Tree traversals (inorder, preorder, postorder)
  2. Height/Depth of a binary tree
  3. Count nodes in a binary tree
  4. Lowest Common Ancestor (LCA) using recursion
  5. DFS on a graph

πŸ”Ή 2. Backtracking Problems (Branching + Choices + Undo)​

Backtracking = Recursion + exploring multiple choices + pruning/undo when a choice doesn’t work.
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A. Classic Backtracking​

  1. N-Queens problem
  2. Rat in a Maze (all paths)
  3. Knight’s Tour problem
  4. Sudoku solver
  5. Word Search in a grid

B. Subsets/Permutations/Combinations​

  1. Generate all subsets of a set
  2. Generate all permutations of a string/array
  3. Combination Sum (with/without duplicates)
  4. Phone keypad letter combinations
  5. Partition to K equal sum subsets

C. Constraint-Solving​

  1. Hamiltonian Path in a graph
  2. Coloring a graph
  3. Word break using backtracking
  4. Crossword fill problem

πŸ”Ή 3. Dynamic Programming Problems (Overlapping Subproblems + Optimal Substructure)​

DP is recursion optimized with memoization/tabulation. Usually involves optimization: min, max, count, true/false.
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A. 1D DP (Basic)​

  1. Fibonacci with memoization
  2. Climbing Stairs (ways to reach top)
  3. Min cost climbing stairs
  4. House Robber problem
  5. Jump Game (can reach end?)

B. Subset/Knapsack Problems​

  1. Subset Sum problem
  2. Partition Equal Subset Sum
  3. 0/1 Knapsack problem
  4. Unbounded Knapsack
  5. Coin Change (min coins / total ways)

C. String DP​

  1. Longest Common Subsequence (LCS)
  2. Longest Common Substring
  3. Edit Distance (Levenshtein)
  4. Palindrome Partitioning (min cuts)
  5. Regular Expression Matching

D. Grid/Matrix DP​

  1. Unique Paths in a grid
  2. Minimum Path Sum
  3. Maximal Square of 1s
  4. Cherry Pickup problem
  5. Gold Mine problem

E. Advanced DP​

  1. Longest Increasing Subsequence (LIS)
  2. Longest Bitonic Subsequence
  3. Matrix Chain Multiplication
  4. Egg Dropping problem
  5. Rod Cutting problem

πŸ“ Practice Strategy​

  • Stage 1 β†’ Recursion: Solve problems until recursion feels natural (focus on base/recursive cases).
  • Stage 2 β†’ Backtracking: Pick problems with multiple choices & constraints.
  • Stage 3 β†’ DP: Start with recursive solutions β†’ then optimize with memoization β†’ then tabulation.

⚑ By mastering these ordered problem lists, you’ll instantly know:

  • β€œThis is recursion” β†’ self-similar breakdown.
  • β€œThis is backtracking” β†’ choices + pruning.
  • β€œThis is DP” β†’ overlapping subproblems + optimization.

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