72Laboratories

Complete Data Structures & Algorithms Study Guide

Phase 1: Foundation (Weeks 1-4)

1. Learn a Programming Language

Time Required: 1-2 weeks Languages to Consider: Python, Java, C++, JavaScript

Key Concepts:

• Basic syntax and data types
• Control structures (if/else, loops)
• Functions and methods
• Object-oriented programming basics
• Input/output operations

Practice:

• Solve 10-15 basic coding problems
• Implement basic programs (calculator, simple games)

2. Arrays & Strings

Time Required: 1-2 weeks

Core Topics:

• Array declaration, initialization, and traversal
• Multi-dimensional arrays
• String manipulation and methods
• Character arrays vs strings

Essential Problems:

• Two Sum, Best Time to Buy/Sell Stock
• Reverse Array, Rotate Array
• Valid Anagram, Longest Substring Without Repeating Characters
• Palindrome Check, String Rotation

Practice Goal: 15-20 problems

3. Linked Lists

Time Required: 1 week

Core Topics:

• Singly, doubly, and circular linked lists
• Insertion, deletion, and traversal operations
• Pointer manipulation

Essential Problems:

• Reverse Linked List, Merge Two Sorted Lists
• Detect Cycle in Linked List
• Remove Nth Node from End
• Intersection of Two Linked Lists

Practice Goal: 10-15 problems

Phase 2: Core Data Structures (Weeks 5-8)

4. Stack & Queue

Time Required: 1 week

Core Topics:

• Stack: LIFO operations, applications
• Queue: FIFO operations, circular queue, priority queue
• Implementation using arrays and linked lists

Essential Problems:

• Valid Parentheses, Min Stack
• Implement Queue using Stacks
• Sliding Window Maximum
• Next Greater Element

Practice Goal: 12-15 problems

5. Hashing & Heap

Time Required: 1-2 weeks

Hashing:

• Hash tables, hash functions, collision resolution
• HashMaps, HashSets

Heap:

• Min heap, max heap operations
• Priority queues, heap sort

Essential Problems:

• Two Sum, Group Anagrams
• Top K Frequent Elements
• Merge K Sorted Lists
• Find Median from Data Stream

Practice Goal: 15-20 problems

Phase 3: Algorithmic Techniques (Weeks 9-14)

6. Recursion & Backtracking

Time Required: 2 weeks

Core Topics:

• Base cases and recursive relations
• Tree recursion, memoization basics
• Backtracking template and pruning

Essential Problems:

• Factorial, Fibonacci, Tower of Hanoi
• Generate Parentheses, Letter Combinations
• N-Queens, Sudoku Solver
• Word Search, Permutations

Practice Goal: 20-25 problems

7. Searching & Sorting

Time Required: 1-2 weeks

Searching:

• Linear search, binary search and variations
• Search in rotated arrays

Sorting:

• Bubble, selection, insertion, merge, quick, heap sort
• Time/space complexity analysis

Essential Problems:

• Binary Search, Search Insert Position
• Find First/Last Position in Sorted Array
• Search in Rotated Sorted Array
• Merge Intervals, Sort Colors

Practice Goal: 15-20 problems

8. Mathematical Algorithms

Time Required: 1 week

Core Topics:

• Prime numbers, GCD, LCM
• Modular arithmetic, fast exponentiation
• Combinatorics basics

Essential Problems:

• Sieve of Eratosthenes
• Power of Two, Happy Number
• Excel Sheet Column Number
• Pascal’s Triangle

Practice Goal: 10-15 problems

9. Bitwise Operations & Tricks

Time Required: 1 week

Core Topics:

• AND, OR, XOR, NOT operations
• Bit manipulation tricks
• Applications in optimization

Essential Problems:

• Single Number, Number of 1 Bits
• Power of Two, Reverse Bits
• Sum of Two Integers
• Maximum XOR of Two Numbers

Practice Goal: 10-12 problems

10. Greedy Algorithms

Time Required: 1 week

Core Topics:

• Greedy choice property
• Activity selection, interval scheduling
• Huffman coding concept

Essential Problems:

• Activity Selection, Fractional Knapsack
• Jump Game, Gas Station
• Minimum Number of Arrows
• Task Scheduler

Practice Goal: 12-15 problems

Phase 4: Advanced Topics (Weeks 15-22)

11. Dynamic Programming

Time Required: 3 weeks

Core Topics:

• Overlapping subproblems, optimal substructure
• Memoization vs tabulation
• 1D and 2D DP patterns

Essential Problems:

• Fibonacci, Climbing Stairs
• Coin Change, Longest Increasing Subsequence
• 0/1 Knapsack, Edit Distance
• Longest Common Subsequence
• House Robber, Best Time to Buy/Sell Stock

Practice Goal: 30-40 problems

12. Advanced DP Techniques

Time Required: 1 week

Core Topics:

• State compression, bitmask DP
• DP on trees, digit DP basics

Essential Problems:

• Traveling Salesman (small input)
• Minimum Cost to Cut a Stick
• Stone Game variations

Practice Goal: 8-10 problems

13. Graph Algorithms

Time Required: 2 weeks

Core Topics:

• Graph representation (adjacency list/matrix)
• BFS, DFS traversals
• Shortest path algorithms (Dijkstra, Bellman-Ford)
• Minimum spanning tree (Kruskal, Prim)

Essential Problems:

• Number of Islands, Clone Graph
• Course Schedule (Topological Sort)
• Network Delay Time
• Minimum Spanning Tree
• Word Ladder

Practice Goal: 20-25 problems

14. Advanced Graph Algorithms

Time Required: 1 week

Core Topics:

• Union-Find (Disjoint Set)
• Strongly connected components
• Maximum flow basics

Essential Problems:

• Number of Provinces
• Redundant Connection
• Critical Connections in Network

Practice Goal: 8-10 problems

Phase 5: Specialized Topics (Weeks 23-28)

15. DSU & MST

Time Required: 1 week

Focus on:

• Union-Find optimizations (path compression, union by rank)
• Applications in network connectivity

Practice Goal: 8-10 problems

16. Network Flow Algorithms

Time Required: 1 week

Core Topics:

• Max flow min cut theorem
• Ford-Fulkerson, Edmonds-Karp algorithms

Practice Goal: 5-8 problems

17. String Algorithms

Time Required: 1 week

Core Topics:

• Pattern matching (KMP, Rabin-Karp)
• Trie data structure
• Longest common substring

Essential Problems:

• Implement Trie, Word Search II
• Longest Palindromic Substring
• Find All Anagrams in String

Practice Goal: 10-12 problems

18. Computational Geometry

Time Required: 1 week

Core Topics:

• Basic geometric operations
• Convex hull, line intersection
• Closest pair of points

Practice Goal: 5-8 problems

19. Segment Trees & Fenwick Trees

Time Required: 1 week

Core Topics:

• Range query and update operations
• Lazy propagation basics

Essential Problems:

• Range Sum Query, Range Minimum Query
• Count of Smaller Numbers After Self

Practice Goal: 8-10 problems

20. Sparse Table & Binary Lifting

Time Required: 1 week

Core Topics:

• Range minimum/maximum queries
• Lowest common ancestor problems

Practice Goal: 5-8 problems

Phase 6: Contest & Advanced Topics (Weeks 29-32)

21. Advanced Tree Algorithms

Time Required: 1 week

Core Topics:

• Heavy-light decomposition
• Centroid decomposition basics

Practice Goal: 5-7 problems

22. Tries & Suffix Trees

Time Required: 1 week

Core Topics:

• Advanced trie applications
• Suffix array basics

Practice Goal: 8-10 problems

23. Game Theory & Nim Game

Time Required: 1 week

Core Topics:

• Minimax algorithm
• Nim game and variations
• Sprague-Grundy theorem basics

Practice Goal: 5-8 problems

24. Approximation & Randomized Algorithms

Time Required: 1 week

Core Topics:

• Monte Carlo methods
• Randomized quicksort
• Approximation ratios

Practice Goal: 3-5 problems

Study Schedule & Tips

Weekly Schedule

• Monday-Wednesday: Learn theory and basic implementations
• Thursday-Friday: Solve practice problems
• Saturday: Review and solve harder problems
• Sunday: Rest or light revision

Practice Platforms

1. LeetCode: For interview preparation
2. HackerRank: For implementation practice
3. Codeforces: For competitive programming
4. GeeksforGeeks: For theory and examples

Assessment Milestones

• Week 8: Should solve easy problems in 15-20 minutes
• Week 16: Should solve medium problems in 30-45 minutes
• Week 24: Should approach hard problems systematically
• Week 32: Ready for technical interviews and contests

Key Success Factors

1. Consistency: Study 2-3 hours daily
2. Practice: Solve problems immediately after learning concepts
3. Review: Revisit difficult problems after a week
4. Implementation: Code everything from scratch
5. Analysis: Always analyze time and space complexity
6. Mock Interviews: Practice explaining solutions aloud

Final Preparation Phase

• Weeks 33-36: Focus on company-specific problems
• Mock interviews: 2-3 per week
• System design: Basic concepts for senior roles
• Revision: Quick review of all major topics

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Resources

• Books: “Introduction to Algorithms” by CLRS, “Algorithm Design Manual” by Skiena
• Online Courses: Coursera Algorithm Specialization, MIT OpenCourseWare
• YouTube Channels: Abdul Bari, Tushar Roy, Back to Back SWE
• Practice: Daily coding problem, Blind 75 list

Total Duration: 8-9 months of consistent study Expected Outcome: Ready for technical interviews at top companies