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1️⃣0️⃣9️⃣ What is Prefix Sum?

Answer:

Prefix Sum is a technique where each element stores the cumulative sum of all previous elements, allowing fast range sum queries.

Formula:

Prefix[i] = Prefix[i-1] + Array[i]

Applications:

• Range sum queries

• Subarray problems

• Competitive programming

Benefit: Range sums can be calculated in O(1) after preprocessing.

1️⃣1️⃣0️⃣ What is Binary Lifting?

Answer:

Binary Lifting is an advanced algorithm used to efficiently answer ancestor-related queries in trees by precomputing ancestors at powers of two.

Applications:

• Lowest Common Ancestor (LCA)

• Tree Queries

• Competitive Programming

Time Complexity:

• Preprocessing: O(n log n)

• Query: O(log n)

Double Tap ❤️ For Part-12

🚀 Coding Interview Questions with Answers (Part 11)

1️⃣0️⃣1️⃣ What is Memoization?

Answer:

Memoization is a top-down Dynamic Programming technique where the results of previously solved subproblems are stored (cached). When the same subproblem appears again, the stored result is returned instead of recomputing it.

Advantages:

• Avoids repeated calculations

• Improves performance

• Reduces time complexity

Example: Fibonacci sequence using recursion with caching.

1️⃣0️⃣2️⃣ What is Tabulation?

Answer:

Tabulation is a bottom-up Dynamic Programming approach that solves smaller subproblems first and stores their results in a table. The final solution is built iteratively without recursion.

Advantages:

• No recursion overhead

• Avoids stack overflow

• Often faster than memoization

Example: Fibonacci sequence using an array.

1️⃣0️⃣3️⃣ What is Backtracking?

Answer:

Backtracking is an algorithmic technique that builds a solution step by step and abandons a path as soon as it determines that the path cannot lead to a valid solution.

Applications:

• N-Queens Problem

• Sudoku Solver

• Maze Solving

• Permutations and Combinations

Time Complexity: Depends on the problem, often exponential.

1️⃣0️⃣4️⃣ What is Branch and Bound?

Answer:

Branch and Bound is an optimization technique used to solve combinatorial problems by systematically exploring all possible solutions while eliminating branches that cannot produce a better result.

Applications:

• Travelling Salesman Problem

• Job Scheduling

• Knapsack Problem

Benefit: Reduces unnecessary computations compared to brute force.

1️⃣0️⃣5️⃣ What is Recursion?

Answer:

Recursion is a programming technique where a function calls itself to solve smaller instances of the same problem.

Every recursive function must have:

• Base Case: Stops recursion.

• Recursive Case: Calls itself with a smaller input.

Examples:

• Factorial

• Fibonacci

• Tree Traversal

1️⃣0️⃣6️⃣ What is Tail Recursion?

Answer:

Tail recursion is a special type of recursion where the recursive call is the last operation performed by the function.

Advantages:

• More memory efficient

• Can be optimized into iteration by some compilers

• Reduces stack usage

1️⃣0️⃣7️⃣ What is the Sliding Window Technique?

Answer:

Sliding Window is an algorithmic technique used to solve problems involving arrays or strings by maintaining a window of elements and moving it across the data.

Applications:

• Maximum sum subarray

• Longest substring without repeating characters

• Minimum window substring

Benefit: Often reduces time complexity from O(n²) to O(n).

1️⃣0️⃣8️⃣ What is the Two Pointers Technique?

Answer:

The Two Pointers technique uses two indices that move through an array or string to solve problems efficiently.

Applications:

• Two Sum (sorted array)

• Remove duplicates

• Reverse an array

• Check palindrome

Benefit: Frequently reduces time complexity from O(n²) to O(n).

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If I wanted to get my opportunity to interview at Google or Amazon for SDE roles in the next 6-8 months…

Here’s exactly how I’d approach it (I’ve taught this to 100s of students and followed it myself to land interviews at 3+ FAANGs):

► Step 1: Learn to Code (from scratch, even if you’re from non-CS background)

I helped my sister go from zero coding knowledge (she studied Biology and Electrical Engineering) to landing a job at Microsoft.

We started with:
- A simple programming language (C++, Java, Python — pick one)
- FreeCodeCamp on YouTube for beginner-friendly lectures
- Key rule: Don’t just watch. Code along with the video line by line.

Time required: 30–40 days to get good with loops, conditions, syntax.

► Step 2: Start with DSA before jumping to development

Why?
- 90% of tech interviews in top companies focus on Data Structures & Algorithms
- You’ll need time to master it, so start early.

Start with:
- Arrays → Linked List → Stacks → Queues
- You can follow the DSA videos on my channel.
- Practice while learning is a must.

► Step 3: Follow a smart topic order

Once you’re done with basics, follow this path:

1. Searching & Sorting
2. Recursion & Backtracking
3. Greedy
4. Sliding Window & Two Pointers
5. Trees & Graphs
6. Dynamic Programming
7. Tries, Heaps, and Union Find

Make revision notes as you go — note down how you solved each question, what tricks worked, and how you optimized it.

► Step 4: Start giving contests (don’t wait till you’re “ready”)

Most students wait to “finish DSA” before attempting contests.
That’s a huge mistake.

Contests teach you:
- Time management under pressure
- Handling edge cases
- Thinking fast

Platforms: LeetCode Weekly/ Biweekly, Codeforces, AtCoder, etc.
And after every contest, do upsolving — solve the questions you couldn’t during the contest.

► Step 5: Revise smart

Create a “Revision Sheet” with 100 key problems you’ve solved and want to reattempt.

Every 2-3 weeks, pick problems randomly and solve again without seeing solutions.

This trains your recall + improves your clarity.

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9️⃣8️⃣ What is Divide and Conquer?

Answer:

Divide and Conquer is an algorithm design technique that solves a problem by: 

1. Dividing it into smaller subproblems. 

2. Solving each subproblem recursively. 

3. Combining their solutions to solve the original problem. 

Examples: 

• Merge Sort 

• Quick Sort 

• Binary Search 

9️⃣9️⃣ What is a Greedy Algorithm?

Answer:

A Greedy Algorithm builds a solution step by step by always choosing the locally optimal option at each stage, hoping it leads to the global optimum.

Examples: 

• Kruskal's Algorithm 

• Prim's Algorithm 

• Dijkstra's Algorithm 

• Huffman Coding 

Advantages: 

• Fast and easy to implement 

Limitation: 

• Does not always produce the optimal solution.

1️⃣0️⃣0️⃣ What is Dynamic Programming?

Answer:

Dynamic Programming (DP) is an optimization technique used to solve problems by breaking them into smaller overlapping subproblems and storing their solutions to avoid repeated computations.

Two Approaches: 

• Memoization (Top-Down): Uses recursion with caching. 

• Tabulation (Bottom-Up): Solves subproblems iteratively using a table. 

Applications: 

• Fibonacci Sequence 

• Longest Common Subsequence 

• Knapsack Problem 

• Coin Change Problem 

• Matrix Chain Multiplication 

Benefits: 

• Reduces time complexity 

• Avoids redundant calculations 

• Improves performance for complex recursive problems 

🔥 Double Tap ❤️ For Part-11

🚀 Coding Interview Questions with Answers (Part 10)

9️⃣1️⃣ What is Quick Sort?

Answer:

Quick Sort is a Divide and Conquer sorting algorithm that selects a pivot element and partitions the array so that elements smaller than the pivot are placed on its left and larger elements on its right. The process is then repeated recursively for the left and right subarrays.

Time Complexity:

• Best Case: O(n log n)

• Average Case: O(n log n)

• Worst Case: O(n²) (when the pivot selection is poor)

Advantages:

• Fast in practice

• In-place sorting (requires little extra memory)

• Widely used for large datasets

9️⃣2️⃣ What is Bubble Sort?

Answer:

Bubble Sort repeatedly compares adjacent elements and swaps them if they are in the wrong order. This process continues until the array is sorted.

Time Complexity:

• Best Case: O(n) (optimized version)

• Average Case: O(n²)

• Worst Case: O(n²)

Advantages:

• Easy to understand and implement.

Disadvantages:

• Inefficient for large datasets.

9️⃣3️⃣ What is Insertion Sort?

Answer:

Insertion Sort builds the sorted array one element at a time by inserting each new element into its correct position.

Time Complexity:

• Best Case: O(n)

• Average Case: O(n²)

• Worst Case: O(n²)

Advantages:

• Simple implementation

• Efficient for small or nearly sorted datasets

• Stable sorting algorithm

9️⃣4️⃣ What is Selection Sort?

Answer:

Selection Sort repeatedly finds the smallest element from the unsorted portion of the array and places it at the beginning.

Time Complexity:

• Best Case: O(n²)

• Average Case: O(n²)

• Worst Case: O(n²)

Advantages:

• Simple to implement

• Performs fewer swaps compared to Bubble Sort

9️⃣5️⃣ What is Heap Sort?

Answer:

Heap Sort is a comparison-based sorting algorithm that uses a Binary Heap data structure.

Steps:

1. Build a Max Heap.

2. Swap the root with the last element.

3. Reduce the heap size.

4. Heapify the remaining elements.

5. Repeat until the array is sorted.

Time Complexity:

• Best Case: O(n log n)

• Average Case: O(n log n)

• Worst Case: O(n log n)

Advantages:

• Guaranteed O(n log n) performance

• In-place sorting algorithm

9️⃣6️⃣ What is Counting Sort?

Answer:

Counting Sort is a non-comparison-based sorting algorithm that counts the occurrences of each element and uses these counts to determine their correct positions.

Time Complexity: O(n + k)

Where:

• n = Number of elements

• k = Range of input values

Advantages:

• Extremely fast for small ranges

• Stable sorting algorithm

Limitation:

• Not suitable when the range of values is very large.

9️⃣7️⃣ What is Radix Sort?

Answer:

Radix Sort sorts numbers digit by digit, starting from either the least significant digit (LSD) or the most significant digit (MSD).

It commonly uses Counting Sort as the intermediate sorting algorithm.

Time Complexity: O(n × d)

Where:

• n = Number of elements

• d = Number of digits

Advantages:

• Very efficient for sorting integers and strings with fixed lengths.

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• Works on sorted and unsorted data.

• Examines elements sequentially.

• Time Complexity: O(n)

Binary Search

• Requires sorted data.

• Divides the search space into halves.

• Time Complexity: O(log n)

Binary Search is much faster than Linear Search for large sorted datasets.

1️⃣0️⃣0️⃣ What is Merge Sort?

Answer:

Merge Sort is a Divide and Conquer sorting algorithm that recursively divides an array into smaller halves, sorts them, and then merges the sorted halves.

Steps:

1. Divide the array into two halves.

2. Recursively sort each half.

3. Merge the sorted halves into one sorted array.

Time Complexity:

• Best Case: O(n log n)

• Average Case: O(n log n)

• Worst Case: O(n log n)

Advantages:

• Stable sorting algorithm

• Efficient for large datasets

• Guarantees consistent performance

🔥 Double Tap ❤️ For Part-10

🚀 Coding Interview Questions with Answers (Part 9)

9️⃣1️⃣ What is an Algorithm?

Answer:

An algorithm is a finite, step-by-step set of instructions designed to solve a specific problem or perform a task efficiently.

Characteristics of a Good Algorithm:

• Well-defined inputs and outputs

• Unambiguous steps

• Finite number of steps

• Efficient in terms of time and memory

• Produces the correct result

Example: Sorting a list of numbers or finding the shortest path in a graph.

9️⃣2️⃣ What is Time Complexity?

Answer:

Time complexity measures the amount of time an algorithm takes to execute as the input size ("n") increases.

It helps compare the efficiency of different algorithms without depending on hardware or programming language.

Common Time Complexities:

• O(1): Constant time

• O(log n): Logarithmic time

• O(n): Linear time

• O(n log n): Linearithmic time

• O(n²): Quadratic time

• O(2ⁿ): Exponential time

• O(n!): Factorial time

9️⃣3️⃣ What is Space Complexity?

Answer:

Space complexity measures the amount of memory an algorithm requires during execution relative to the input size.

It includes:

• Input storage

• Auxiliary (temporary) memory

• Recursive call stack

Efficient algorithms aim to optimize both time and space complexity.

9️⃣4️⃣ What is Big O Notation?

Answer:

Big O notation describes the upper bound (worst-case) time or space complexity of an algorithm.

It shows how the algorithm's performance grows as the input size increases.

Examples:

• Accessing an array element → O(1)

• Linear Search → O(n)

• Binary Search → O(log n)

• Merge Sort → O(n log n)

9️⃣5️⃣ What is Big Theta (Θ) Notation?

Answer:

Big Theta (Θ) notation describes the exact or tight bound of an algorithm's complexity.

It indicates that the algorithm performs within both the upper and lower bounds for large input sizes.

Example:

Merge Sort has a time complexity of Θ(n log n) because it consistently performs at that rate in the best, average, and worst cases.

9️⃣6️⃣ What is Big Omega (Ω) Notation?

Answer:

Big Omega (Ω) notation describes the lower bound (best-case) time complexity of an algorithm.

It represents the minimum amount of time an algorithm will take under the best possible conditions.

Example:

Linear Search has a best-case complexity of Ω(1) when the target element is found at the first position.

9️⃣7️⃣ What is Binary Search?

Answer:

Binary Search is a searching algorithm that finds an element in a sorted array by repeatedly dividing the search range in half.

Steps:

1. Find the middle element.

2. Compare it with the target.

3. Search the left or right half accordingly.

4. Repeat until the element is found or the search space becomes empty.

Time Complexity: O(log n)

Requirement: The array must be sorted.

9️⃣8️⃣ What is Linear Search?

Answer:

Linear Search checks each element one by one until the target element is found or the end of the collection is reached.

Advantages:

• Works on both sorted and unsorted data.

• Easy to implement.

Time Complexity: O(n)

9️⃣9️⃣ What is the Difference Between Linear Search and Binary Search?

Answer:

Linear Search

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Each recursive call adds a new stack frame containing: 

• Function parameters 

• Local variables 

• Return address 

If recursion is too deep, it can lead to a Stack Overflow error.

8️⃣0️⃣ What is the Time Complexity of Common Data Structures?

Answer:

Data Structure | Search | Insert | Delete

Array | O(n) | O(n) | O(n)

Linked List | O(n) | O(1) | O(1)

Stack | O(n) | O(1) | O(1)

Queue | O(n) | O(1) | O(1)

Hash Table | O(1) | O(1) | O(1)

Binary Search Tree | O(log n) | O(log n) | O(log n)

Heap | O(n) | O(log n) | O(log n) 

*Average case. Worst-case performance may be higher depending on the implementation.

🔥 Double Tap ❤️ For Part-9

🚀 Coding Interview Questions with Answers (Part 8)

7️⃣1️⃣ What is a Sparse Matrix?

Answer:

A sparse matrix is a matrix in which most of the elements are 0. Instead of storing every element, only the non-zero elements are stored to save memory.

Applications:

• Machine Learning

• Graph representations

• Scientific computing

• Image processing

Advantages:

• Saves memory

• Improves computational efficiency

7️⃣2️⃣ What is a Dynamic Array?

Answer:

A dynamic array is an array that can automatically resize itself when more elements are added.

Unlike a fixed-size array, it allocates additional memory when its capacity is reached.

Examples:

• ArrayList in Java

• vector in C++

• list (dynamic array implementation) in Python

Advantages:

• Flexible size

• Fast random access

• Easy insertion at the end

7️⃣3️⃣ What is Load Factor?

Answer:

Load factor is the ratio of the number of stored elements to the total number of buckets in a hash table.

Formula:

Load Factor = Number of Elements / Number of Buckets

A high load factor increases the likelihood of collisions, while a low load factor improves performance but uses more memory.

7️⃣4️⃣ What is Collision Resolution?

Answer:

Collision resolution refers to the techniques used to handle situations where multiple keys are mapped to the same location in a hash table.

Common Methods:

• Separate Chaining

• Linear Probing

• Quadratic Probing

• Double Hashing

The goal is to maintain efficient search, insertion, and deletion operations.

7️⃣5️⃣ What is the Difference Between Linear Probing and Chaining?

Answer:

Linear Probing

• Stores collided elements in the next available slot.

• Uses open addressing.

• Requires less memory.

• Performance decreases as the table becomes full.

Separate Chaining

• Stores collided elements in a linked list at the same bucket.

• Easier to handle many collisions.

• Requires additional memory for linked lists.

7️⃣6️⃣ What is Tree Traversal?

Answer:

Tree traversal is the process of visiting every node in a tree exactly once in a specific order.

Common Types:

• Preorder

• Inorder

• Postorder

• Level-order

Tree traversal is used for searching, printing, and processing tree data.

7️⃣7️⃣ What is the Difference Between Preorder, Inorder, and Postorder Traversal?

Answer:

• Preorder: Root → Left → Right

• Inorder: Left → Root → Right

• Postorder: Left → Right → Root

Applications:

• Preorder: Copying a tree

• Inorder: Produces sorted output in a Binary Search Tree

• Postorder: Deleting or freeing a tree

7️⃣8️⃣ What is Level-Order Traversal?

Answer:

Level-order traversal visits the nodes of a tree level by level, starting from the root.

It uses a Queue and is also known as Breadth-First Traversal (BFS) for trees.

Applications:

• Printing trees level by level

• Finding the shortest path in unweighted trees

• Binary tree serialization

7️⃣9️⃣ What is the Recursion Stack?

Answer:

The recursion stack is the memory area used by the system to keep track of active recursive function calls.

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🚀 Coding Interview Questions with Answers (Part 7)

6️⃣1️⃣ What is Graph Traversal?
Answer:
Graph traversal is the process of visiting every vertex (node) in a graph in a systematic way.
The two most common graph traversal algorithms are:
• Breadth-First Search (BFS)
• Depth-First Search (DFS)

Applications:
• Finding paths in a graph
• Network routing
• Social network analysis
• Web crawling

6️⃣2️⃣ What is the Difference Between BFS and DFS?
Answer:
Breadth-First Search (BFS)
• Visits nodes level by level.
• Uses a Queue data structure.
• Finds the shortest path in an unweighted graph.
• Requires more memory for large graphs.

Depth-First Search (DFS)
• Explores one path completely before backtracking.
• Uses a Stack (or recursion).
• Does not always find the shortest path.
• Typically uses less memory than BFS.

6️⃣3️⃣ What is a Trie?
Answer:
A Trie (Prefix Tree) is a tree-like data structure used to store and search strings efficiently.
Applications:
• Autocomplete
• Spell checking
• Dictionary lookup
• Search engines
Time Complexity:
• Search: O(L)
• Insert: O(L)
Where L is the length of the word.

6️⃣4️⃣ What is a Segment Tree?
Answer:
A Segment Tree is a binary tree used to perform efficient range queries and updates on an array.
Applications:
• Range Sum Query
• Minimum/Maximum Query
• Competitive Programming
Time Complexity:
• Build: O(n)
• Query: O(log n)
• Update: O(log n)

6️⃣5️⃣ What is a Fenwick Tree (Binary Indexed Tree)?
Answer:
A Fenwick Tree is a data structure used to efficiently calculate prefix sums and update elements in an array.
Advantages:
• Less memory than Segment Tree
• Easier implementation
• Fast updates and queries
Time Complexity:
• Update: O(log n)
• Query: O(log n)

6️⃣6️⃣ What is a Disjoint Set (Union-Find)?
Answer:
A Disjoint Set, also known as Union-Find, is a data structure used to maintain a collection of non-overlapping sets.
It supports two operations:
• Find: Determines which set an element belongs to.
• Union: Merges two sets into one.
Applications:
• Kruskal's Minimum Spanning Tree Algorithm
• Cycle Detection
• Network Connectivity

6️⃣7️⃣ What is an Adjacency Matrix?
Answer:
An Adjacency Matrix is a 2D array used to represent a graph.
• Rows and columns represent vertices.
• A value of 1 (or the edge weight) indicates a connection.
• A value of 0 indicates no connection.
Advantages: Fast edge lookup (O(1))
Disadvantages: Uses O(V²) memory, making it inefficient for sparse graphs.

6️⃣8️⃣ What is an Adjacency List?
Answer:
An Adjacency List represents a graph by storing a list of neighboring vertices for each vertex.
Advantages: Requires O(V + E) memory. Efficient for sparse graphs.
Disadvantages: Edge lookup is slower than an adjacency matrix.

6️⃣9️⃣ What is a Circular Linked List?
Answer:
A Circular Linked List is a linked list in which the last node points back to the first node instead of pointing to "NULL".
Applications:
• CPU Scheduling
• Multiplayer Games
• Circular Buffers
• Music Playlists
Benefit: Traversal can continue indefinitely without restarting.

7️⃣0️⃣ What is a Doubly Linked List?
Answer:
A Doubly Linked List is a linked list where each node contains:
• Data
• Pointer to the next node
• Pointer to the previous node
Advantages: Supports forward and backward traversal. Easier insertion and deletion compared to a singly linked list.
Disadvantages: Requires extra memory for the previous pointer. Slightly more complex to implement.

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🚀 Coding Interview Questions with Answers (Part 6)

5️⃣1️⃣ What is a Hash Table?
Answer:
A hash table (also called a hash map or dictionary) is a data structure that stores data as key-value pairs. It uses a hash function to calculate an index where the value is stored, enabling very fast lookup, insertion, and deletion.

Average Time Complexity:
• Search: O(1)
• Insert: O(1)
• Delete: O(1)

Applications:
• Caching
• Database indexing
• Dictionaries
• Symbol tables

5️⃣2️⃣ What is Hashing?
Answer:
Hashing is the process of converting a key into a fixed-size integer (called a hash value) using a hash function. This hash value determines where the data will be stored in a hash table.

Benefits:
• Fast data retrieval
• Efficient searching
• Reduced lookup time

5️⃣3️⃣ What are Collisions in Hashing?
Answer:
A collision occurs when two or more different keys produce the same hash value and are assigned to the same index in a hash table.

Common Collision Resolution Techniques:
• Separate Chaining
• Linear Probing
• Quadratic Probing
• Double Hashing

5️⃣4️⃣ What is a Binary Tree?
Answer:
A binary tree is a hierarchical data structure in which each node has at most two children, known as the left child and the right child.

Applications:
• Expression trees
• File systems
• Decision trees
• Hierarchical data representation

5️⃣5️⃣ What is a Binary Search Tree (BST)?
Answer:
A Binary Search Tree (BST) is a binary tree in which:
• All values in the left subtree are smaller than the root.
• All values in the right subtree are greater than the root.

This property allows efficient searching, insertion, and deletion.

Average Time Complexity:
• Search: O(log n)
• Insert: O(log n)
• Delete: O(log n)

5️⃣6️⃣ What is an AVL Tree?
Answer:
An AVL Tree is a self-balancing Binary Search Tree where the height difference (balance factor) between the left and right subtrees of any node is at most 1.
Whenever the tree becomes unbalanced, rotations are performed to restore balance.

Benefit: Maintains O(log n) search, insertion, and deletion time.

5️⃣7️⃣ What is a Heap?
Answer:
A heap is a complete binary tree that satisfies the heap property.

Types:
• Min Heap: The parent node is smaller than or equal to its children.
• Max Heap: The parent node is greater than or equal to its children.

Applications:
• Priority Queues
• Heap Sort
• Scheduling algorithms

5️⃣8️⃣ What is the Difference Between a Min Heap and a Max Heap?
Answer:
Min Heap
• Smallest element is at the root.
• Parent ≤ Children.
• Used when the minimum value is frequently required.

Max Heap
• Largest element is at the root.
• Parent ≥ Children.
• Used when the maximum value is frequently required.

5️⃣9️⃣ What is a Graph?
Answer:
A graph is a non-linear data structure consisting of vertices (nodes) and edges that connect those vertices.
Graphs can be:
• Directed or Undirected
• Weighted or Unweighted
• Cyclic or Acyclic

Applications:
• Social networks
• GPS navigation
• Computer networks
• Recommendation systems

6️⃣0️⃣ What are the Types of Graphs?
Answer:
Graphs are classified into several types based on their structure:
• Directed Graph: Edges have a direction.
• Undirected Graph: Edges have no direction.
• Weighted Graph: Edges have weights or costs.
• Unweighted Graph: All edges have equal weight.
• Cyclic Graph: Contains one or more cycles.
• Acyclic Graph: Does not contain any cycles.
• Connected Graph: Every node is reachable from every other node.
• Disconnected Graph: Some nodes cannot be reached from others.

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