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Leetcode Strategy

The Ultimate 7-Step Strategy to Solve DSA Problems

A robust approach to solving Data Structures and Algorithms (DSA) problems requires careful planning, implementation, and optimization. Here's a detailed, time-bound guide with examples to help you excel:

Step 1: Deep Problem Understanding (5–10 minutes)

What to Do:

  • Read the Problem Statement: Read the problem 2–3 times to grasp inputs, outputs, and constraints clearly.
  • Highlight Key Points: Identify key details like edge cases, constraints, and requirements.
  • Ask Questions:
    • What is the input?
    • What is the output?
    • Are there specific constraints (e.g., maximum array size, time limits)?
    • Are negative numbers, empty inputs, or duplicate values allowed?

Example:

Problem: Find the longest increasing subsequence in an array.

  • Input: [10, 9, 2, 5, 3, 7, 101, 18]
  • Output: Length of the subsequence: 4 (Subsequence: [2, 3, 7, 101])
  • Constraints: Array size ≤ 2500, elements ≤ 10^4.

Checklist to Write Down:

  1. Input format (e.g., array of integers).
  2. Output requirements (e.g., length of subsequence).
  3. Edge cases (e.g., empty array, single element).

Step 2: Devising a Strategy (10–15 minutes)

What to Do:

  • Identify the Problem Type:
    • Is it an optimization problem (Dynamic Programming)?
    • Is traversal required (Graph algorithms)?
    • Is sorting helpful (Greedy approach)?
  • Choose the Right Data Structure:
    • For quick lookups: HashMap/HashSet.
    • For sequences: Dynamic Arrays (e.g., Vectors).
    • For hierarchical problems: Trees or Graphs.
    • For priority-based problems: Heaps.
  • Write Down Possible Approaches:
    • Start with a brute-force approach.
    • Explore optimized algorithms (e.g., divide-and-conquer, binary search).

Example:

For the longest increasing subsequence:

  1. Brute-force: Generate all subsequences (O(2^N)).
  2. Optimized DP: Use dp[i] to store the LIS ending at i (O(N²)).
  3. Optimal Solution: Binary search + DP with a list (O(N log N)).

Step 3: Breaking Down the Problem (10–15 minutes)

What to Do:

  • Divide the solution into smaller, manageable subtasks.
  • List the steps sequentially, ensuring they align with your strategy.
  • Write pseudo-code for clarity.

What to Write While Breaking Down:

  1. Steps to preprocess the input (e.g., sort the array).
  2. Logic for iterative or recursive calls.
  3. Handling of edge cases.

Example (Pseudo-code for LIS):

  1. Create an empty list subsequence.
  2. Iterate through the array:
    • If current element > last element of subsequence, append it.
    • Else, replace the element in subsequence using binary search.
  3. Return the length of subsequence.

Step 4: Writing Pseudocode (10–15 minutes)

What to Do:

  • Translate the breakdown into structured pseudocode.
  • Ensure each line maps directly to a coding construct.
  • Write modular code to handle tasks like sorting, searching, etc.

Example Pseudocode for LIS:

Initialize subsequence = []
For each num in array:
    If num > last element of subsequence:
        Append num to subsequence
    Else:
        Replace the smallest element in subsequence > num
Return length of subsequence

Step 5: Coding and Debugging (20–30 minutes)

Coding:

  • Stick to the pseudocode and implement it in your chosen language.
  • Start with basic functionality and test incrementally.

Debugging:

  • Common Errors: Index out-of-bound errors, incorrect loop conditions, incorrect edge case handling.
  • Debugging Tips:
    • Print intermediate outputs to check logic flow.
    • Use IDEs with debugging tools to trace the code line by line.

Example Debugging for LIS:

  • Test with: [10, 9, 2, 5, 3, 7, 101, 18] → Expected Output: 4.
  • Edge Cases:
    • Empty array → Expected Output: 0.
    • Single element → Expected Output: 1.

Step 6: Iterative Optimization (15–20 minutes)

What to Do:

  • Analyze the current solution's complexity (time and space).
  • Identify bottlenecks using profiling tools or test cases.
  • Transition to a more efficient approach (e.g., O(N log N) from O(N²)).

Optimizing the Example:

  • From O(N²) DP, use Binary Search + DP for O(N log N).
  • Replace linear traversal with binary search for placement.

Step 7: Process Review (5–10 minutes)

What to Do:

  • Reflect on the approach and note learnings.
  • Write down similar problems you've solved to build pattern recognition.

Example Review Notes:

  • The problem is similar to "Longest Increasing Path in a Matrix".
  • Techniques learned: Binary search, use of DP arrays, edge case handling.

Time Allocation Summary:

Step Time Investment
Problem Understanding 5–10 minutes
Devising a Strategy 10–15 minutes
Breaking Down the Problem 10–15 minutes
Writing Pseudocode 10–15 minutes
Coding and Debugging 20–30 minutes
Iterative Optimization 15–20 minutes
Process Review 5–10 minutes

Key Insights for Similar Problems

  1. Identify Problem Categories:
    • Subarray problems → Use sliding window or prefix sums.
    • Graph traversal → Use BFS/DFS.
    • Optimization → Use DP or greedy algorithms.
  2. Explore Edge Cases:
    • Test for corner cases and constraints, e.g., array size of 1, negative numbers.
  3. Develop Pattern Recognition:
    • Solve 3–5 problems of a similar type to build intuition.
    • Example: Solve "LIS", "Longest Common Subsequence", and "Longest Palindromic Subsequence".

By following this structured, time-managed approach, you can tackle any DSA problem efficiently and build long-term expertise. 🚀