MY DSA PROGRESS

A comprehensive Data Structures and Algorithms learning repository with organized solutions, implementations, and practice problems across multiple DSA topics.

---

📚 Table of Contents

1. Loops
2. Patterns
3. Functions
4. Arrays
5. 2D Arrays
6. Strings
7. Sorting
8. Bit Manipulation
9. ArrayList
10. OOPs
11. Recursion
12. Divide and Conquer
13. Backtracking
14. Linked Lists
15. Stacks
16. Queues
17. Greedy Approach
18. Binary Trees
19. Heaps
20. Hashing
21. Maths for DSA
22. Binary Search Trees
23. Tries
24. Graphs
25. Dynamic Programming
26. Segment Trees
27. Codeforces Problems
28. Practice Questions

---

1. LOOPS

#	Problem	File	Description
1	Loop Fundamentals	1.LOOPS	Basic loop constructs and iterations

Notes:

• Foundation for all iterative algorithms
• Essential for understanding time complexity

---

2. PATTERNS

Patterns 1 & Patterns 2

#	Topic	Description
1	Number Patterns	Pyramid and triangle patterns
2	Star Patterns	Various star arrangements
3	Hollow Patterns	Box and hollow rectangle patterns
4	Diamond Patterns	Diamond shaped outputs

Key Concepts:

• Nested loops for 2D pattern generation
• Understanding row and column relationships
• Print statement optimization

---

3. FUNCTIONS

#	Concept	Description
1	Function Declaration	Basic function syntax
2	Parameters & Return	Passing arguments and returning values
3	Method Overloading	Multiple functions with same name
4	Scope & Variables	Local and global scope

---

4. ARRAYS

#	Problem	Approach	Time	Space
1	Array Basics	Direct access using indices	O(1)	O(1)
2	Linear Search	Traverse and find	O(n)	O(1)
3	Binary Search	Divide and conquer on sorted array	O(log n)	O(1)
4	Prefix Sum	Array preprocessing	O(n)	O(n)
5	Subarray Problems	Range queries optimization	O(n)	O(n)

Key Algorithms:

• Array traversal patterns
• Two-pointer technique
• Sliding window approach

---

5. 2D_ARRAY

#	Problem	Key Technique	Difficulty
1	Matrix Search	2D traversal	Easy
2	Matrix Rotation	In-place rotation	Medium
3	Diagonal Sum	Pattern recognition	Easy
4	Row-wise & Column-wise Search	Optimization	Medium

Approaches:

• Nested loops for 2D traversal
• Starting from corners for optimized search
• Spiral matrix traversal patterns

---

6. STRING

#	Problem	Algorithm	Complexity
1	String Basics	Character array operations	O(n)
2	Palindrome Check	Two pointer	O(n)
3	Anagram	Sorting/Hashing	O(n log n) / O(n)
4	String Compression	Character frequency	O(n)
5	Pattern Matching	KMP/Naive	O(n+m)

Key Concepts:

• Immutability of strings
• Character frequency counting
• String manipulation techniques

---

7. SORTING

Algorithm	File	Time Complexity	Space	Stable
Bubble Sort	7.Sorting/	O(n²)	O(1)	Yes
Selection Sort	7.Sorting/	O(n²)	O(1)	No
Insertion Sort	7.Sorting/	O(n²)	O(1)	Yes
Merge Sort	7.Sorting/	O(n log n)	O(n)	Yes
Quick Sort	7.Sorting/	O(n log n) avg	O(log n)	No
Counting Sort	7.Sorting/	O(n+k)	O(k)	Yes
Radix Sort	7.Sorting/	O(nk)	O(n+k)	Yes

Important Notes:

• Merge sort guaranteed O(n log n), stable
• Quick sort fastest average case, in-place
• For small arrays, insertion sort often fastest in practice
• Counting sort for limited range of integers

---

8. BIT MANIPULATION

#	Problem	Technique	Use Case
1	Check Bit	(n >> i) & 1	Verify if bit set
2	Set Bit	n | (1 << i)	Set i-th bit to 1
3	Unset Bit	n & ~(1 << i)	Set i-th bit to 0
4	Toggle Bit	n ^ (1 << i)	Flip i-th bit
5	Count Bits	Brian Kernighan's Algorithm	Count set bits
6	Power of 2	(n & (n-1)) == 0	Check if power of 2
7	XOR Properties	a ^ a = 0, a ^ 0 = a	Swap without temp

Key Insights:

• XOR used for finding single element in pairs
• Bit masking for efficient storage
• Bitwise operations faster than arithmetic

---

9. ARRAYLIST

16.arraylist/pairsum2.java

Problem: Pair Sum in Rotated Sorted Array

Input: [11, 15, 6, 8, 9, 10], target = 16
Output: Find pair that sums to target

Aspect	Details
Algorithm	Two Pointer on Rotated Array
Approach	Find pivot point → Use circular two pointers
Time Complexity	O(n)
Space Complexity	O(1)
Key Insight	In rotated sorted array, find breaking point then apply two pointer

Code Explanation:

• Find index j where arr[j] > arr[j+1] (breaking point)
• Right Pointer (RP) = j, Left Pointer (LP) = j+1
• Use modulo arithmetic to wrap around
• Move LP forward if sum too small, RP backward if sum too large

Key Formula:

LP = (LP + 1) % n  // Move forward with wrapping
RP = (n + RP - 1) % n  // Move backward with wrapping

---

10. OOPS

10.OOPs/abstraction.java

Concept	Implementation	Purpose
Encapsulation	Private fields, Public getters/setters	Hide internal details
Inheritance	extends keyword	Code reusability
Polymorphism	Method overriding	Runtime behavior change
Abstraction	Abstract classes & interfaces	Define contracts

Key Topics:

• Classes and Objects
• Access Modifiers (public, private, protected)
• Constructors and Destructors
• Static vs Instance members
• Abstract methods and classes
• Interfaces and implementations

---

11. RECURSION

12.Reccursion-1

Basic Recursion Concepts:

Problem	Pattern	Approach
Factorial	Mathematical	Base case: n==0, return 1
Fibonacci	Overlapping subproblems	Memoization for optimization
Power	Divide & Conquer	f(n) = f(n/2) * f(n/2)
Sum of Array	Linear Recursion	Sum = first + sum(rest)

13.Reccursion-2

13.Reccursion-2/tilingProblem.java

Problem: Tiling a 2×n Board with 1×2 Tiles

For n=4:
Possible tilings = 5

Recurrence: f(n) = f(n-1) + f(n-2)

Aspect	Details
Problem	How many ways to tile 2×n board with 1×2 tiles?
Recurrence	f(n) = f(n-1) + f(n-2)
Base Cases	f(0)=1, f(1)=1
Time Complexity	O(2^n) - Exponential
Optimization	Use DP - O(n)
Space Complexity	O(n) with DP

Intuition:

• At position n, we can place either:
  • One vertical tile (1×2) → remaining n-1
  • Two horizontal tiles (1×1 each rotated) → remaining n-2
• Total = f(n-1) + f(n-2)

Example:

n=1: 1 way (one vertical)
n=2: 2 ways (two vertical OR two horizontal)
n=3: 3 ways
n=4: 5 ways

---

12. DIVIDE AND CONQUER

Algorithm	Problem	Complexity	Strategy
Merge Sort	Sorting	O(n log n)	Split + Merge
Quick Sort	Sorting	O(n log n) avg	Partition + Recurse
Binary Search	Search Sorted	O(log n)	Split space in half
Strassen	Matrix Mult	O(n^2.81)	Smart multiplication

---

13. BACKTRACKING

Problem	Approach	Time	Space
N-Queens	Place queens safely	O(N!)	O(N)
Sudoku	Fill valid digits	Exponential	O(1)
Permutations	Generate all	O(N!)	O(N)
Combinations	Generate subsets	O(2^N)	O(N)
Maze	Find path	Exponential	O(N²)

Key Pattern:

1. Choose → Explore → Unchoose (Backtrack)
2. Maintain constraints/visited state
3. Early termination on invalid state

---

14. LINKED LISTS

17.LinkedList-1/LinkedList.java

Basic Linked List Operations:

Operation	Code	Time	Space
Add First	Insert at head	O(1)	O(1)
Add Last	Insert at tail	O(1)	O(1)
Print LL	Traverse all nodes	O(n)	O(1)
Remove First	Delete from head	O(1)	O(1)
Search	Linear search	O(n)	O(1)
Reverse	Reverse pointers	O(n)	O(1)

18.LinkedList-2/LinkedList.java

Advanced Operations:

Operation	Complexity	Notes
addAtIndex(int idx)	O(n)	Insert at specific position
removeStart()	O(1)	Delete from beginning
removeEnd()	O(n)	Delete from end
removeAtIndex(int idx)	O(n)	Delete at specific index

18.LinkedList-2/mergeSortInLL.java

Problem: Merge Sort on Linked List

Input: 3 -> 2 -> 5 -> 1 -> null
Output: 1 -> 2 -> 3 -> 5 -> null

Aspect	Details
Algorithm	Merge Sort using slow & fast pointers
Get Middle	Slow pointer moves 1 step, fast moves 2 steps
Divide	Split list into two halves recursively
Merge	Merge two sorted lists
Time Complexity	O(n log n)
Space Complexity	O(log n) - Recursion stack

Key Steps:

1. Find middle using slow/fast pointers
2. Recursively sort left and right halves
3. Merge two sorted halves in-order

Advantages over Array Merge Sort:

• No extra O(n) space for merging (in-place merge)
• Works efficiently for linked structures

---

15. STACKS

19.Stack-1/stackBasic.java

Stack Using ArrayList:

Stack Operations:
- isEmpty(): O(1)
- peek(): O(1)
- push(data): O(1) amortized
- pop(): O(1) amortized

Method	Implementation	Purpose
isEmpty()	list.size() == 0	Check if empty
peek()	list.get(size-1)	View top element
push()	list.add()	Add to top
pop()	list.remove(size-1)	Remove from top

19.Stack-1/stackLL.java

Stack Using Linked List:

Advantage	Benefit
No pre-allocation	Dynamic sizing
Better for sparse	No wasted space
Intrinsic	Operations are O(1)

Implementation Details:

• Head acts as top of stack
• Push: Insert at head O(1)
• Pop: Remove from head O(1)
• Peek: Access head data O(1)

Stack Applications

Application	Use Case	Example
Expression Evaluation	Infix to Postfix	Calculator
Backtracking	Undo/Redo	Text Editor
Function Calls	Call Stack	Program Execution
DFS	Graph Traversal	Topological Sort
Balanced Parentheses	Validation	Compiler

---

16. QUEUES

Operation	Complexity	Implementation
Enqueue	O(1)	Add to rear
Dequeue	O(1)	Remove from front
Peek	O(1)	View front
isEmpty	O(1)	Check size

Types of Queues:

Type	Properties	Use Case
Simple Queue	FIFO	Standard queue operations
Circular Queue	Efficient space	Fixed buffer
Deque	FIFO from both ends	Sliding window
Priority Queue	Min/Max heap	Task scheduling

Applications:

• BFS graph traversal
• Job scheduling
• Print queue management
• Round-robin CPU scheduling

---

17. GREEDY APPROACH

22.Greedy Approch/lexographicallySmallest.java

Problem: Lexicographically Smallest String of Length n with Sum k

Aspect	Details
Problem	Generate smallest string of length n where char sum = k
Approach	Greedy: Fill from end with largest chars possible
Algorithm	Start with 'a's, from right add (z's) as needed
Time Complexity	O(n)
Space Complexity	O(n) for result array

Key Insight:

• To get lexicographically smallest: prefer 'a' at front
• Fill from end with larger characters
• Each position i needs character such that: char_value + remaining_sum ≥ k

Algorithm:

1. Initialize all characters as 'a'
2. Start from right (index n-1)
3. For each position, calculate available sum
4. Insert largest character that fits
5. Update remaining sum

Example:

n=5, k=15
Start: aaaaa
From right, need sum=15:
- pos 4: can use 'z'(26)? No, adjust
- Fill strategically to get smallest string
Result: aabbb (1+1+2+2+2=8) or similar

Greedy Strategy Applications:

• Activity Selection
• Huffman Coding
• Fractional Knapsack
• Coin Change
• Job Sequencing

---

18. BINARY TREES

23.Binary Trees/BinaryTreeB.java

Tree Traversals:

Traversal	Pattern	Use Case	Order
Preorder	Root-Left-Right	Copy tree, Prefix expression	Node before children
Inorder	Left-Root-Right	BST sorting, Infix expression	Node between children
Postorder	Left-Right-Root	Delete tree, Postfix expression	Children before node
Level Order	BFS	Level-wise processing	Layer by layer

Time Complexity: O(n) for all traversals Space Complexity: O(h) where h = height (recursion stack)

23.Binary Trees/CheckUnivaluated.java

Problem: Check if Tree Contains Duplicate Values

Input: Tree with nodes: 1, 2, 3, 4, 5, 6, 8
Output: false (all unique)

Aspect	Details
Algorithm	DFS with ArrayList tracking
Approach	Visit each node, check if value seen before
Time Complexity	O(n)
Space Complexity	O(n) for ArrayList + O(h) for recursion
Returns	true if duplicate found, false if all unique

Logic:

1. If node exists in list → duplicate found (return true)
2. Else → add to list
3. Check left subtree recursively
4. Check right subtree recursively
5. If either subtree has duplicate → return true

23.Binary Trees/LowestCommonAncestor.java

Problem: Find Lowest Common Ancestor (LCA)

Input: Tree, n1=4, n2=5
       1
      / \
     2   3
    / \
   4   5
   
Output: 2 (LCA of 4 and 5)

Aspect	Details
Algorithm	Find paths to both nodes, compare
getPath()	DFS to find path from root to node
LCA Finding	Compare paths, last common node = LCA
Time Complexity	O(n) for path finding + O(h) for comparison
Space Complexity	O(h) for paths and recursion

Approach:

1. Find path from root to n1
2. Find path from root to n2
3. Compare paths until divergence
4. Last common node before divergence = LCA

23.Binary Trees/MinDistanceBetweenTwoNodes.java

Problem: Minimum Distance Between Two Nodes

Distance = distance(n1 to LCA) + distance(LCA to n2)

Aspect	Details
Algorithm	Find LCA + calculate distances
LCA2()	Optimized LCA finding
dist()	Calculate distance from node to target
Time Complexity	O(n)
Space Complexity	O(h) recursion depth
Key Formula	Total Distance = dist(LCA to n1) + dist(LCA to n2)

Optimized LCA (LCA2):

• If node is null or matches n1 or n2 → return node
• Check left and right subtrees
• If both subtrees have values → current is LCA
• If only one → return that one

23.Binary Trees/transformingToSumTree.java

Problem: Transform Binary Tree to Sum Tree

Original:      1              Transform:        15
              / \                              /  \
             2   3                           5    5
              \                               \
               4                              9
                \                              \
                 5                             5

Each node = sum of all elements in its subtree

Aspect	Details
Algorithm	Post-order traversal with accumulation
Approach	Visit children first, then update node
Time Complexity	O(n) - visit each node once
Space Complexity	O(h) - recursion stack
Key Insight	Store old value before updating

Algorithm:

1. Recursively transform left subtree
2. Recursively transform right subtree
3. Store old node value
4. Update node = leftSum + rightSum
5. Return old value + updated node value

Return Value Logic:

• Returns total sum including current node's original value
• Used by parent node in recursion

---

19. HEAPS

Heap Type	Property	Use Case	Extraction
Min Heap	Parent ≤ Children	Find minimum	Smallest first
Max Heap	Parent ≥ Children	Find maximum	Largest first
Priority Queue	Custom priority	Task scheduling	Highest priority

Operations:

Operation	Time Complexity	Space
Insert	O(log n)	O(1)
Delete Min/Max	O(log n)	O(1)
Heapify	O(n)	O(1)
Get Min/Max	O(1)	O(1)

Applications:

• Dijkstra's Algorithm
• Huffman Coding
• Heap Sort
• K-th Largest Element
• Median in Stream

---

20. HASHING

Structure	Average	Worst	Use
Hash Table	O(1)	O(n)	General lookup
HashMap	O(1)	O(n)	Key-value pairs
HashSet	O(1)	O(n)	Unique elements
LinkedHashMap	O(1)	O(n)	Insertion order

Collision Handling:

Technique	Method	Pros	Cons
Chaining	Linked list at each bucket	Simple	Extra space
Open Addressing	Linear/Quadratic probing	Space efficient	Clustering
Double Hashing	Two hash functions	Better distribution	Complex

Applications:

• Duplicate detection
• Frequency counting
• Two-sum problems
• Anagram grouping
• Cache implementation

---

21. MATHS FOR DSA

Topic	Application	Complexity
GCD/LCM	Fraction simplification	O(log min(a,b))
Prime Numbers	Sieve of Eratosthenes	O(n log log n)
Modular Arithmetic	Large number handling	O(1) per operation
Combinatorics	Permutation/Combination	O(n) to O(2^n)
Number Theory	Divisors, Factors	O(√n)

Key Formulas:

nCr = n! / (r! × (n-r)!)
nPr = n! / (n-r)!
Euler's Theorem: a^φ(n) ≡ 1 (mod n)
Fermat's Little Theorem: a^(p-1) ≡ 1 (mod p) for prime p

---

22. BINARY SEARCH TREES

27.binary Search Trees/BSTBasics.java

BST Property: Left < Root < Right

Operation	Algorithm	Time	Space
Search	Divide search space in half	O(log n) avg, O(n) worst	O(log n)
Insert	Find position, add node	O(log n) avg, O(n) worst	O(log n)
Delete	Handle 3 cases	O(log n) avg, O(n) worst	O(log n)

Delete Cases:

Case 1: Leaf node
   → Simply remove

Case 2: One child
   → Replace with child

Case 3: Two children
   → Replace with inorder successor (leftmost in right subtree)
   → Delete inorder successor

printInRange(int k1, int k2):

• Prints all values in range [k1, k2]
• Time: O(m) where m = nodes in range
• Space: O(h) recursion depth
• Strategy: Skip left if value > k2, skip right if value < k1

27.binary Search Trees/MergeBST.java

Problem: Merge Two BSTs

BST1:    2        BST2:     1
        / \                / \
       1   3              0   5

Merged (sorted): 0, 1, 1, 2, 3, 5

Step	Operation	Complexity
Inorder Traversal	Get sorted array from each BST	O(m) + O(n)
Merge Arrays	Merge two sorted arrays	O(m + n)
Build BST	Create balanced BST from sorted	O(m + n)

Time Complexity: O(m + n) Space Complexity: O(m + n) for arrays

27.binary Search Trees/ConvertToBST.java

Problem: Convert Binary Tree to Balanced BST

Phase	Operation	Purpose
Get Sorted	Inorder traversal to ArrayList	Extract elements in order
Build Balanced	Recursive middle selection	Create balanced structure
Connect Nodes	Recursively build left/right	O(n) total connections

balanceBST Recursion:

For array [0,1,2,3,4]:
- mid = 2, root = 2
- left = build(0,1)
- right = build(3,4)
- Balanced tree created

Advantages:

• O(log n) search guaranteed
• Prevents degenerate trees
• Optimal height = O(log n)

---

23. TRIES

Operation	Complexity	Use Case
Insert	O(m) - length of word	Add word to dictionary
Search	O(m)	Find exact word
StartsWith	O(m)	Prefix matching
Delete	O(m)	Remove word

Structure:

• Root node (empty)
• 26 children per node (for lowercase letters)
• isEndOfWord flag

Applications:

• Autocomplete
• Spell checker
• IP routing
• Phone directory
• Search engines

---

24. GRAPHS

29. Graph/a_GraphBasics.java

Graph Representation:

Method	Space	Edge Lookup	Use When
Adjacency Matrix	O(V²)	O(1)	Dense graphs
Adjacency List	O(V+E)	O(degree)	Sparse graphs
Edge List	O(E)	O(E)	Iteration heavy

Edge Structure:

class Edge {
    int src;      // Source vertex
    int dest;     // Destination vertex
    int wt;       // Weight
}

29. Graph/c_connected_component.java

Problem: Find Connected Components

Graph with 2 components:
Component 1: {0, 1, 2, 3}
Component 2: {4}

Aspect	Details
Algorithm	DFS/BFS from each unvisited node
Time Complexity	O(V + E)
Space Complexity	O(V) for visited array + O(E) for graph
Purpose	Identify disconnected subgraphs

Applications:

• Network analysis
• Social networks (friends groups)
• Image processing (blob detection)

Graph Algorithms:

Algorithm	Time	Space	Purpose
BFS	O(V+E)	O(V)	Shortest path (unweighted)
DFS	O(V+E)	O(V)	Connectivity, cycles
Dijkstra	O((V+E)logV)	O(V)	Shortest path (weighted, positive)
Bellman-Ford	O(VE)	O(V)	Shortest path (negative edges)
Floyd-Warshall	O(V³)	O(V²)	All-pairs shortest path
Kruskal	O(E log E)	O(V)	Minimum spanning tree
Prim	O(V²) or O((V+E)logV)	O(V)	Minimum spanning tree
Topological Sort	O(V+E)	O(V)	Directed acyclic graphs

---

25. DYNAMIC PROGRAMMING

DP Strategy: Optimal Substructure + Overlapping Subproblems

Approach	Method	When to Use
Top-Down	Recursion + Memoization	Natural recursive structure
Bottom-Up	Iteration + Tabulation	Want to avoid recursion

Classic Problems:

Problem	Subproblems	Time	Space
Fibonacci	f(n) = f(n-1) + f(n-2)	O(n)	O(n)
0/1 Knapsack	Include/exclude items	O(nW)	O(nW)
LCS	Match characters	O(mn)	O(mn)
Edit Distance	Insert/delete/replace	O(mn)	O(mn)
Coin Change	Min coins to make amount	O(nA)	O(n)
Longest Increasing Subsequence	Include/skip elements	O(n²) or O(n log n)	O(n)

Memoization Techniques:

• HashMap for irregular states
• Array for indexed states
• 2D arrays for two-parameter problems

---

26. SEGMENT TREES

31.Segment Trees/a_basics.java

Problem: Range Sum Query with Updates

Operation	Complexity	Implementation
Build Tree	O(n)	Initialize segment tree
Query	O(log n)	Get sum in range
Update	O(log n)	Update single element

Segment Tree Structure:

Array: [1, 2, 3, 4]
Tree (array indices): Position 0 = root, 2i+1 = left, 2i+2 = right

    10 (sum of all)
    /  \
   3    7
  / \  / \
 1  2  3  4

buildST() - Build Tree:

- Recursive division of range
- Base case: si == sj (single element)
- Combine left and right sums
- Time: O(n)

getSumUtil() - Query:

- If range outside query → return 0
- If range inside query → return tree[i]
- Else partial overlap → split and combine
- Time: O(log n)

updateSTUtil() - Update:

- Update affected tree nodes on path to root
- Difference propagation
- Time: O(log n)

31.Segment Trees/b_MinMaxST.java

Problem: Range Min/Max Query

Operation	Modification
Min Query	Use Math.min() instead of sum
Max Query	Use Math.max() instead of sum
Combine	min(left, right) or max(left, right)

Applications:

• Sparse table preprocessing
• 2D range queries
• Finding kth element in range

---

27. CODEFORCES PROBLEMS

Problem	Type	Difficulty	Algorithm
TBD	-	-	-

Note: Add your Codeforces solutions with problem codes and links

---

28. PRACTICE QUESTIONS

Source	Level	Topics Covered
LeetCode	Mixed	All DSA topics
InterviewBit	Mixed	DSA + Interview prep
HackerRank	Beginner-Advanced	All topics
GeeksforGeeks	All	Theory + Practice

---

📊 Quick Reference Matrix

Complexity Cheat Sheet

Operation	Best	Average	Worst	Space
Array Access	O(1)	O(1)	O(1)	O(n)
Array Search (unsorted)	O(1)	O(n)	O(n)	O(1)
Binary Search	O(1)	O(log n)	O(log n)	O(1)
Linear Search	O(1)	O(n)	O(n)	O(1)
Bubble Sort	O(n)	O(n²)	O(n²)	O(1)
Merge Sort	O(n log n)	O(n log n)	O(n log n)	O(n)
Quick Sort	O(n log n)	O(n log n)	O(n²)	O(log n)
Hash Insert	O(1)	O(1)	O(n)	O(n)
BST Insert	O(log n)	O(log n)	O(n)	O(log n)
Linked List Insert	O(1)	O(n)	O(n)	O(1)
Stack Push/Pop	O(1)	O(1)	O(1)	O(n)
Queue Enqueue/Dequeue	O(1)	O(1)	O(1)	O(n)

---

🎯 Learning Path Recommendations

Beginner Level

1. Loops, Patterns, Functions
2. Arrays, 2D Arrays
3. Strings, Basic Sorting
4. ArrayList Basics

Intermediate Level

5. Bit Manipulation
6. Sorting (All algorithms)
7. Linked Lists
8. Stacks & Queues
9. OOPs Concepts

Advanced Level

10. Recursion (Parts 1 & 2)
11. Divide and Conquer
12. Backtracking
13. Binary Trees
14. Heaps & Hashing
15. Greedy Approach
16. Binary Search Trees
17. Tries
18. Graphs

Expert Level

19. Dynamic Programming
20. Segment Trees
21. Advanced Graph Algorithms
22. Interview Problems

---

🚀 Performance Optimization Tips

Time Complexity Optimization:

• Use hashing for O(n) lookup instead of O(n²)
• Apply two-pointer technique on sorted arrays
• Use segment trees for repeated range queries
• Cache intermediate results (memoization)

Space Complexity Optimization:

• In-place algorithms (reverse, sort)
• Iterator patterns instead of loading all
• Rolling hash for string problems
• Stream processing for large data

---

📝 Common Patterns to Remember

Pattern	When to Use	Example
Two Pointers	Sorted array, target sum	Pair Sum
Sliding Window	Substring/subarray problems	Max window sum
Fast/Slow Pointers	Cycle detection, middle finding	Linked list middle
Recursion + Memoization	Overlapping subproblems	DP problems
BFS	Level-order, shortest path	Graph traversal
DFS	All combinations, paths	Backtracking
Prefix Sum	Range sum queries	Array queries
Divide & Conquer	Sorting, power	Merge sort, fast exponentiation

---

🔗 File Structure Summary

DATA STRUCTURES AND ALGORITHMS/
├── 1.LOOPS/                    → Basic iterations
├── 2.Patterns1/ & 4.Patterns2/ → Pattern printing
├── 3.functions/                → Function basics
├── 5.Array/                    → Array operations
├── 7.SORTING/                  → All sorting algorithms
├── 8.string/                   → String algorithms
├── 9.BitManipulation/          → Bit operations
├── 10.OOPs/                    → Object-oriented concepts
├── 12.Reccursion-1/            → Basic recursion
├── 13.Reccursion-2/            → Advanced recursion (Tiling, etc)
├── 16.arraylist/               → ArrayList operations (Pair Sum II)
├── 17.LinkedList-1/            → Basic LL (Add, Remove, Print)
├── 18.LinkedList-2/            → Advanced LL (Merge Sort)
├── 19.Stack-1/                 → Stack implementation
├── 20.Stack-2/                 → Stack applications
├── 21.Queue/                   → Queue operations
├── 22.Greedy Approch/          → Greedy algorithms
├── 23.Binary Trees/            → Tree problems (LCA, Sum Tree, etc)
├── 24.Heaps/                   → Heap data structure
├── 25.Hashing/                 → Hash tables & sets
├── 27.binary Search Trees/     → BST operations
├── 28. Tries/                  → Trie data structure
├── 29. Graph/                  → Graph algorithms
├── 30. DP/                     → Dynamic programming
├── 31.Segment Trees/           → Segment tree queries
└── Codeforces/ & Practice/     → Competitive problems

---

💡 Key Takeaways

1. Master Time & Space Tradeoffs - Choose the right algorithm for constraints
2. Understand Fundamentals - Strong basics make advanced topics easier
3. Practice Implementation - Coding problems repeatedly builds muscle memory
4. Analyze Complexity - Always calculate O(n) and O(space) before coding
5. Learn Patterns - Recognize problem patterns to apply known solutions
6. Debug Efficiently - Use test cases to validate logic
7. Optimize Gradually - Get working solution first, then optimize

---

Last Updated: December 2024

Happy Learning! Keep solving, keep improving! 🎓