Data Structures and Algorithms: Complete Roadmap

Data Structures and Algorithms: Complete Roadmap

Data Structures and Algorithms (DSA) is the single most important skill for cracking technical interviews at top tech companies. Google, Amazon, Microsoft, Meta—they all test DSA extensively.

But learning DSA can feel overwhelming. Where do you start? How deep do you go? How many problems are enough?

This comprehensive roadmap answers all these questions. It provides a structured path from absolute beginner to interview-ready, with specific topics, practice problems, and timelines.

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Why DSA Matters

For Interviews

Beyond Interviews

• Write more efficient code
• Solve complex problems systematically
• Understand how systems work under the hood
• Foundation for system design
• Competitive programming and hackathons

The Good News

DSA is learnable. It's pattern recognition and practice. Anyone can get good at it with the right approach and consistent effort.

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Understanding the Landscape

The Four Pillars

The Learning Path

Basics → Linear DS → Non-Linear DS → Algorithms → Patterns → Practice → Mastery

Time Investment

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Phase 1: Programming Fundamentals (Week 1-2)

Before DSA, ensure your programming basics are solid.

Prerequisites

Pick One Language (Recommended: C++, Java, or Python)

Master These Basics:

• Variables, data types
• Conditionals (if-else)
• Loops (for, while)
• Functions
• Arrays (1D and 2D)
• Strings
• Basic input/output

Practice Problems (5-10 Each)

• Print patterns
• Sum of numbers
• Factorial
• Prime numbers
• GCD/LCM
• Swap numbers
• Reverse a number
• Palindrome check

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Phase 2: Time and Space Complexity (Week 3)

Understanding complexity is crucial before diving into DSA.

Big O Notation

Comparison

O(1) < O(log n) < O(n) < O(n log n) < O(n²) < O(2ⁿ) < O(n!)

Space Complexity

Same notation, but for memory usage.

Practice

For every problem you solve:

1. What's the time complexity?
2. What's the space complexity?
3. Can it be improved?

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Phase 3: Arrays and Strings (Week 4-6)

Arrays and strings form the foundation of most DSA problems.

Array Topics

1. Basic Operations

   • Traversal
   • Insertion and deletion
   • Searching
   • Reversal

2. Techniques to Learn

   • Two pointers
   • Sliding window
   • Prefix sums
   • Kadane's algorithm

3. Key Problems

   • Two Sum
   • Best Time to Buy and Sell Stock
   • Maximum Subarray
   • Merge Sorted Arrays
   • Move Zeroes
   • Rotate Array
   • Container With Most Water

String Topics

1. Operations

   • Traversal
   • Comparison
   • Substring
   • Concatenation

2. Techniques

   • Two pointers for palindrome
   • Sliding window for substrings
   • Hashmaps for character counting

3. Key Problems

   • Valid Palindrome
   • Valid Anagram
   • Longest Substring Without Repeating Characters
   • String Compression
   • Implement strStr()
   • Group Anagrams

Practice Target

• 30-40 array problems
• 15-20 string problems
• Mix of easy and medium

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Phase 4: Hashing (Week 7-8)

Hash maps are your best friend for optimization.

Hash Map / Hash Set

When to Use:

• Need O(1) lookup
• Counting frequencies
• Finding duplicates
• Two Sum variants

Implementation:

• HashMap in Java
• dict in Python
• unordered_map in C++

Key Problems

• Two Sum (classic)
• Contains Duplicate
• Longest Consecutive Sequence
• Group Anagrams
• Subarray Sum Equals K
• Top K Frequent Elements
• Valid Sudoku

Practice Target

• 15-20 problems
• Focus on recognizing when hash maps help

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Phase 5: Linked Lists (Week 9-10)

Linked lists test pointer manipulation skills.

Types

1. Singly Linked List
2. Doubly Linked List
3. Circular Linked List

Operations to Master

• Traversal
• Insertion (start, end, middle)
• Deletion
• Reversal
• Finding middle element
• Detecting cycles

Key Problems

• Reverse Linked List ⭐
• Detect Cycle (Floyd's Algorithm) ⭐
• Merge Two Sorted Lists ⭐
• Remove Nth Node From End
• Find Middle of Linked List
• Intersection of Two Lists
• LRU Cache (Medium-Hard)
• Reorder List

Tips

• Use dummy head for edge cases
• Fast and slow pointers for many problems
• Draw diagrams before coding

Practice Target

• 15-20 problems
• Master the reverse operation perfectly

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Phase 6: Stacks and Queues (Week 11-12)

LIFO and FIFO structures with specific use cases.

Stack

When to Use:

• Matching parentheses
• Undo operations
• Expression evaluation
• Monotonic stack problems

Key Problems:

• Valid Parentheses ⭐
• Min Stack
• Daily Temperatures
• Next Greater Element
• Evaluate Reverse Polish Notation
• Largest Rectangle in Histogram

Queue

When to Use:

• First-come-first-served
• BFS traversal
• Sliding window maximum

Key Problems:

• Implement Queue using Stacks
• Sliding Window Maximum
• Design Circular Queue

Practice Target

• 15-20 problems (stack heavy)
• Master monotonic stack pattern

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Phase 7: Trees (Week 13-16)

Trees are heavily tested—spend adequate time here.

Binary Tree Basics

Traversals (Must Know):

• Inorder (Left, Root, Right)
• Preorder (Root, Left, Right)
• Postorder (Left, Right, Root)
• Level Order (BFS)

Implementation: Both recursive and iterative

Binary Search Tree (BST)

• Insert
• Delete
• Search
• Validate BST
• Inorder successor/predecessor

Key Tree Problems

Easy:

• Maximum Depth of Binary Tree
• Same Tree
• Invert Binary Tree
• Symmetric Tree
• Diameter of Binary Tree

Medium:

• Binary Tree Level Order Traversal ⭐
• Validate Binary Search Tree ⭐
• Construct Tree from Preorder and Inorder
• Lowest Common Ancestor
• Path Sum
• Serialize and Deserialize Binary Tree

Hard:

• Binary Tree Maximum Path Sum
• Word Ladder

Advanced Trees (For Later)

• AVL Trees (understand concept)
• Segment Trees (range queries)
• Trie (string problems)

Trie Problems

• Implement Trie
• Word Search II
• Design Add and Search Words Data Structure

Practice Target

• 30-40 tree problems
• Master all traversals by heart

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Phase 8: Heaps / Priority Queues (Week 17-18)

For problems requiring min/max extraction.

Core Concepts

• Min Heap vs Max Heap
• Heapify operation
• Insert and Extract operations
• Building heap from array

When to Use

• Kth largest/smallest element
• Merge K sorted lists
• Stream-related problems
• Scheduling problems

Key Problems

• Kth Largest Element ⭐
• Merge K Sorted Lists ⭐
• Find Median from Data Stream
• Top K Frequent Elements
• Task Scheduler
• Sort Characters By Frequency

Practice Target

• 10-15 problems
• Know when heap vs sorting is better

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Phase 9: Graphs (Week 19-22)

Graphs are complex but frequently tested.

Representations

• Adjacency Matrix
• Adjacency List (preferred)

Graph Traversals

BFS (Breadth-First Search):

• Level-by-level exploration
• Shortest path in unweighted graphs
• Using queue

DFS (Depth-First Search):

• Go deep before going wide
• Using recursion or stack
• Connected components

Key Algorithms

Key Problems

BFS/DFS:

• Number of Islands ⭐
• Clone Graph ⭐
• Course Schedule (Topological Sort) ⭐
• Pacific Atlantic Water Flow
• Word Ladder
• Surrounded Regions

Shortest Path:

• Network Delay Time
• Cheapest Flights Within K Stops

Union Find:

• Number of Connected Components
• Redundant Connection

Practice Target

• 25-30 graph problems
• Master BFS/DFS without thinking

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Phase 10: Dynamic Programming (Week 23-28)

DP is the hardest topic but frequently asked.

Core Concepts

1. Overlapping Subproblems - Same subproblems solved multiple times
2. Optimal Substructure - Optimal solution contains optimal subsolutions

Approaches

• Top-Down (Memoization): Recursion + cache
• Bottom-Up (Tabulation): Iterative with table

DP Patterns

Learning Path for DP

Week 1: 1D DP

• Fibonacci
• Climbing Stairs
• House Robber
• Maximum Subarray

Week 2: 2D DP

• Unique Paths
• Minimum Path Sum
• Longest Common Subsequence
• Edit Distance

Week 3: Knapsack Variants

• 0/1 Knapsack
• Coin Change
• Target Sum
• Partition Equal Subset Sum

Week 4-6: Practice and Patterns

• Word Break
• Longest Increasing Subsequence
• Regular Expression Matching
• Distinct Subsequences

Practice Target

• 40-50 DP problems
• Start with easy, gradually increase difficulty

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Phase 11: Greedy Algorithms (Week 29-30)

Make locally optimal choices hoping for global optimum.

When Greedy Works

• Problem has greedy choice property
• Optimal substructure exists
• Local choice leads to global optimal

Key Problems

• Activity Selection
• Jump Game
• Gas Station
• Maximum Subarray (Kadane's)
• Partition Labels
• Task Scheduler
• Queue Reconstruction by Height

Practice Target

• 15-20 problems
• Learn to identify when greedy applies

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Phase 12: Backtracking (Week 31-32)

Explore all possibilities systematically.

Pattern

def backtrack(state):
    if is_solution(state):
        add_to_result(state)
        return

    for choice in choices:
        make_choice(choice)
        backtrack(new_state)
        undo_choice(choice)  # Backtrack

Key Problems

• Subsets ⭐
• Permutations ⭐
• Combination Sum ⭐
• N-Queens
• Word Search
• Letter Combinations of Phone Number
• Palindrome Partitioning

Practice Target

• 15-20 problems
• Understand the template thoroughly

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Interview Preparation Strategy

The Numbers Game

Quality Over Quantity

Don't just solve—understand:

1. Solve without looking at solution first
2. If stuck, see hints before full solution
3. Understand the approach, not just code
4. Re-solve without looking after 1-2 days
5. Track patterns you're weak in

The Revision Strategy

Spaced Repetition:

• Day 1: Solve problem
• Day 3: Re-solve (no looking)
• Day 7: Re-solve again
• Day 14: Final check

Weekly Review:

• Review all problems from the week
• Note common patterns
• Identify weaknesses

Mock Interviews

Once you've solved 150+ problems:

• Pramp (free peer mock interviews)
• Interviewing.io
• Practice with friends
• Time yourself (45 min per problem max)

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Practice Resources

Online Judges

Problem Lists

1. LeetCode Blind 75 - Essential interview problems
2. NeetCode 150 - Curated modern list
3. Striver's SDE Sheet - Comprehensive Indian resource
4. LeetCode Top 100 Liked - Popular problems

Books

Video Resources

• Abdul Bari (YouTube) - Algorithm explanations
• Striver (YouTube) - SDE sheet walkthroughs
• NeetCode (YouTube) - LeetCode solutions
• William Fiset (YouTube) - Algorithm visualizations

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Common Mistakes to Avoid

In Learning

In Interviews

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Realistic Timelines

3-Month Plan (Intensive)

Month 1:

• Arrays, Strings, Hashing
• Linked Lists, Stacks, Queues
• 60 problems

Month 2:

• Trees, Heaps
• Basic Graphs (BFS/DFS)
• 60 problems

Month 3:

• Dynamic Programming
• Advanced topics + revision
• 80 problems + mock interviews

6-Month Plan (Balanced)

Month 1-2: Foundations + Linear DS Month 3-4: Trees + Graphs Month 5-6: DP + Revision + Mocks

1-Year Plan (Thorough)

For those starting from scratch or aiming for top companies with deep preparation.

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Your Weekly Study Plan Template

Weekly Structure

Daily Structure (3 Hours)

0:00 - 0:30: Review yesterday's problems
0:30 - 1:30: New problem (attempt without help)
1:30 - 2:30: Second problem or study solution path
2:30 - 3:00: Notes and pattern documentation

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Key Takeaways

1. Pick one language and stick with it
2. Follow a structured roadmap—don't jump around randomly
3. Understand complexity for every solution
4. Master the patterns—many problems are variations
5. Practice consistently—2-3 hours daily beats weekend marathons
6. Think before coding—in interviews, approach matters
7. Track your progress—patterns you're weak in, problems solved
8. Take mock interviews—simulate real pressure
9. Quality over quantity—understand 100 problems deeply > solving 300 superficially
10. Stay patient—DSA mastery takes months, not weeks

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Frequently Asked Questions

How many problems should I solve?

For service companies: 100-150. For product companies: 200-300. For FAANG: 300+. But quality matters more.

Should I learn C++ just for DSA?

Not necessary. Python or Java work fine. C++ has slight advantages in competitive programming but makes no difference for interviews.

How important is competitive programming?

Helpful but not required for interviews. CP is more speed-focused; interviews care more about communication and problem-solving approach.

What if I'm not from a CS background?

You can still learn DSA. It may take longer, but the roadmap is the same. Start from basics and be patient.

How do I know when I'm ready for interviews?

When you can solve most LeetCode mediums in 30-40 minutes and explain your approach clearly. Mock interviews help assess readiness.

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Ready to master DSA? Explore more resources on Sproutern for coding tutorials, interview prep, and career guidance.