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Data structures and algorithms roadmap: A comprehensive guide

Muhammad Abu Huraira

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What are data structures?What are algorithms?Why learn data structures and algorithms?When are you ready to learn about data structures and algorithms? Understanding data structures 1. Arrays Operations and time complexity 2. Linked lists Types of linked lists Singly linked list Doubly linked list Circular linked list Operations and time complexity 3. Stacks Operations and time complexity 4. Queues Operations and time complexity 5. Trees Types of trees Binary tree Binary search tree (BST)AVL tree (Balanced BST)Heap (Min-heap, max-heap)Operations and time complexity Trie Operations and time complexity 6. Graphs Types of graphs Directed graph (Digraph)Undirected graph Weighted graph Acyclic graph Graph representation Exploring algorithms 1. Searching algorithms Linear search Binary search 2. Sorting algorithms Bubble sort Merge sort 3. Graph algorithms Depth-first search (DFS)Breadth-first search (BFS)4. Dynamic programming A 6-step roadmap to building DSA proficiency Building a strong foundation

No matter which programming language you learn, data structures and algorithms (DSA) form the backbone of computer science. Understanding these concepts is crucial for efficient problem-solving and writing optimized code.

This comprehensive DSA roadmap will guide you through the essential topics and provide a detailed approach toward their mastery.

What are data structures?#

Data structures are ways to organize and store data in a computer to be accessed and modified efficiently.

What are algorithms?#

Algorithms are step-by-step procedures or formulas for solving problems. They perform operations on data structures to solve computational problems.

Why learn data structures and algorithms?#

Data structures and algorithms are a non-negotiable to learning to code. The better you understand them, the better you can:

Write efficient code that runs faster and uses fewer resources
Crack coding interviews at top tech companies
Have a deeper understanding of how the software works (and strong problem-solving skills to match

Data Structures for Coding Interviews in Python

Data structures are amongst the most fundamental concepts of Computer Science. The data structure chosen can make or break an entire computer program. Consequently, they are also largely categorized as a vital benchmark of computer science knowledge when it comes to industry interviews. This course contains a detailed review of all the common data structures and provides implementation level details in Python to allow readers to become well equipped. Now with more code solutions, lessons, and illustrations than ever, this is the course for you!

30hrs

Beginner

65 Challenges

24 Quizzes

When are you ready to learn about data structures and algorithms? #

Once you have a good understanding of a programming language and knowledge of time and space complexities, you're ready to start learning about data structures.

Choose a programming language to learn the basics:

Variables: Learn how to declare and use variables to store data.
Operators: Understand arithmetic, logical, and comparison operators.
Conditional statements: Explore how to execute different blocks of code based on specific conditions.
Loops: Learn about loops that allow performing certain operations repeatedly. Most programming languages offer multiple types of loop statements.
Functions/Methods: Understand how to define and call functions or methods for code reusability.
Scoping: Learn about variable scopes like local, global, and block scopes.

Next, learn about time and space complexities:

Time complexity: Measure how long it takes for an algorithm to be executed, focusing on worst-case scenarios (Big (O) notation), best-case scenarios (Omega notation), and average complexity (Theta notation).
Space complexity: Analyze the amount of memory space an algorithm requires, optimizing memory usage and avoiding excessive memory consumption.

Understanding data structures#

There are various data structures, but today, we'll discuss the following:

Arrays
Linked lists
Stacks
Queues
Trees
Graphs

1. Arrays#

Arrays are one of the simplest data structures, consisting of a collection of elements stored in contiguous memory locations. They provide constant-time access to elements based on their indexes, making them ideal for scenarios where random access is frequent. Arrays are widely used for implementing lists, matrices, and dynamic arrays.

Operations and time complexity#

Access: $O(1)$
Search: $O(n)$
Insertion/Deletion (at end): $O(1)$
Insertion/Deletion (in middle): $O(n)$

2. Linked lists#

Linked lists are dynamic data structures where elements, called nodes, are linked using pointers. Unlike arrays, linked lists allow for efficient insertion and deletion operations at any position. However, they have slower access times than arrays since a traversal is necessary to reach specific elements.

Types of linked lists#

Below are the different types of linked lists: Singly linked lists, doubly linked lists, and circular linked lists.

Singly linked list#

A singly linked list is a data structure that consists of a sequence of elements called nodes. Each node contains two parts:

Data: The value or information stored in the node
Next: A reference (or link) to the next node in the sequence

In a singly linked list, nodes are linked linearly, where each node points to the next node in the sequence. The last node’s next pointer points to a special sentinal value, often termed NULL, indicating the end of the list.

Doubly linked list#

A doubly linked list is a data structure similar to a singly linked list but with an additional link to the previous node. Each node contains three parts:

Data: The value or information stored in the node
Next: A reference (or link) to the next node in the sequence
Previous: A reference (or link) to the previous node in the sequence

This allows traversal of the list in both forward and backward directions. The first node’s previous link and the last node’s next link are typically NULL.

class Node:
    def __init__(self, data=None):
        self.data = data
        self.next = None
class CircularLinkedList:
    def __init__(self):
        self.head = None
    def is_empty(self):
        return self.head is None
    def append(self, data):
        new_node = Node(data)
        if self.is_empty():
            self.head = new_node
            new_node.next = self.head
            return
        current = self.head
        while current.next != self.head:
            current = current.next
        current.next = new_node
        new_node.next = self.head
    def prepend(self, data):
        new_node = Node(data)
        if self.is_empty():
            self.head = new_node
            new_node.next = self.head
            return
        current = self.head
        while current.next != self.head:
            current = current.next
        current.next = new_node
        new_node.next = self.head
        self.head = new_node
    def delete(self, key):
        if self.is_empty():
            return
        current = self.head
        prev = None
        while True:
            if current.data == key:
                if prev:
                    prev.next = current.next
                else:
                    while current.next != self.head:
                        current = current.next
                    current.next = self.head.next
                    self.head = self.head.next
                return
            prev = current
            current = current.next
            if current == self.head:
                break
    def print_list(self):
        if self.is_empty():
            print("List is empty")
            return
        current = self.head
        while True:
            print(current.data, end=" -> ")
            current = current.next
            if current == self.head:
                break
        print("HEAD")
# Example usage
def main():
    cll = CircularLinkedList()
    print("Initial list:")
    cll.print_list()
    print("\nAppending 1 to the list:")
    cll.append(1)
    cll.print_list()
    print("\nAppending 2 to the list:")
    cll.append(2)
    cll.print_list()
    print("\nPrepending 0 to the list:")
    cll.prepend(0)
    cll.print_list()
    print("\nDeleting 1 from the list:")
    cll.delete(1)
    cll.print_list()
if __name__ == "__main__":
    main()

Operations and time complexity#

A stack is usually implemented using a linked list, where operations have the following time complexities:

Push (Add an element to the top): $O(1)$
Pop (Remove an element from the top): $O(1)$
Peek (Get the top element without removing): $O(1)$
isEmpty (Check if stack is empty): $O(1)$

4. Queues#

Queues adhere to the First In, First Out (FIFO) order, where elements are added at the rear and removed from the front. They are useful for scenarios such as task scheduling, message passing, and managing requests.

Operations and time complexity#

Enqueue (Add element to rear): $O(1)$
Dequeue (Remove element from front): $O(1)$
Front (Get front element without removing): $O(1)$
isEmpty (Check if queue is empty): $O(1)$

To learn more about stack and queue, read our blog How to use stacks and queues.

5. Trees#

Trees are hierarchical data structures consisting of nodes connected by edges. They have a root node at the top and child nodes branching out. Trees are versatile and used in various applications, such as representing hierarchical data (file systems, organizational charts) and implementing search algorithms (binary search trees).

Types of trees#

Below are the different types of trees: Binary trees, binary search trees, AVL trees, heaps, and tries.

Binary tree#

A binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child.

Structure:
- Each node contains a value, a reference to the left child, and a reference to the right child.
- The tree starts with a root node, and each node may have zero, one, or two children.
Advantages:
- It has a simple structure.
- It helps to represent the hierarchical relationships between data elements.

Binary search tree (BST)#

A binary search tree (BST) is a binary tree in which each node has a value greater than all the values in its left subtree and less than all the values in its right subtree.

Structure:
- It’s same to a binary tree but with the added property of ordered nodes.
- It ensures that for any node, the values in the left subtree are less than the node, and those in the right subtree are greater than the node.
Advantages:
- It’s efficient in search, insertion, and deletion operations, provided that the binary search tree is balanced.
- It maintains order, which allows for an easy range of queries.

class TreeNode:
    def __init__(self, key):
        self.left = None
        self.right = None
        self.val = key
class BST:
    def __init__(self):
        self.root = None
    def insert(self, key):
        if not self.root:
            self.root = TreeNode(key)
        else:
            self._insert_recursive(self.root, key)
    def _insert_recursive(self, node, key):
        if key < node.val:
            if not node.left:
                node.left = TreeNode(key)
            else:
                self._insert_recursive(node.left, key)
        else:
            if not node.right:
                node.right = TreeNode(key)
            else:
                self._insert_recursive(node.right, key)
    def search(self, key):
        return self._search_recursive(self.root, key)
    def _search_recursive(self, node, key):
        if not node or node.val == key:
            return node
        if key < node.val:
            return self._search_recursive(node.left, key)
        else:
            return self._search_recursive(node.right, key)
    
    def print_inorder(self):
        self._print_inorder_recursive(self.root)
        print()
    def _print_inorder_recursive(self, node):
        if node:
            self._print_inorder_recursive(node.left)
            print(node.val, end=" ")
            self._print_inorder_recursive(node.right)
# Example usage
def main():
    bst = BST()
    print("Initial BST (in-order traversal):")
    bst.print_inorder()
    print("\nInserting 50 into the BST:")
    bst.insert(50)
    bst.print_inorder()
    print("\nInserting 30 into the BST:")
    bst.insert(30)
    bst.print_inorder()
    print("\nInserting 20 into the BST:")
    bst.insert(20)
    bst.print_inorder()
    print("\nInserting 40 into the BST:")
    bst.insert(40)
    bst.print_inorder()
    print("\nInserting 70 into the BST:")
    bst.insert(70)
    bst.print_inorder()
    print("\nInserting 60 into the BST:")
    bst.insert(60)
    bst.print_inorder()
    print("\nInserting 80 into the BST:")
    bst.insert(80)
    bst.print_inorder()
    search_key = 60
    result = bst.search(search_key)
    if result:
        print(f"\nFound node with value {result.val}")
    else:
        print("\nKey not found")
if __name__ == "__main__":
    main()

AVL tree (Balanced BST)#

An AVL tree is a self-balancing binary search tree where the difference in heights between the left and right subtrees of any node is at most one.

Structure:
- It’s same to a binary search tree but with an additional balance property.
- While some implementations store the balance factor in each node, it can also be computed dynamically as needed. A node’s balance factor is the difference in height between its left and right subtrees.
Advantages:
- It ensures balanced height, leading to $O(log (n))$ time complexity for search, insertion, and deletion operations.
- It prevents worst-case scenarios found in unbalanced BSTs.

Heap (Min-heap, max-heap)#

A heap is a special tree-based data structure that satisfies the heap property. There are two types of heaps: Min-heap and max-heap.

Structure:
- It is typically implemented as a binary tree.
- It is often stored in an array for efficient access and manipulation.
Advantages:
- It is used in efficient implementation of priority queues.
- It provides quick access to the minimum or maximum element.

Min-heap: In a min-heap, the value of each node is greater than or equal to the value of its parent. The minimum value is always located at the root node.

Operations and time complexity#

Insertion: $O(log(n))$
Deletion (Root element): $O(log(n))$
Peek (Find minimum in a min-heap or maximum in a max-heap): $O(1)$

Trie#

A trie is a tree-like data structure used to store a dynamic set of strings, where the keys are usually strings.

Structure:
- Each node represents a single character of a string.
- The root represents the empty string, and each path from the root to a leaf represents a string in the set.
Advantages:
- It is efficient for prefix-based searches, such as autocomplete and spell checking.
- It provides $O(m)$ time complexity for search and inserts operations, where $m$ is the length of the key.

Operations and time complexity#

Insert (Insert a word in trie): $O(m)$ , where $m$ is the length of the word
Search(Search a word in trie): $O(m)$
Delete (Delete a word from trie): $O(m)$
Prefix search (If any word in the trie starts with the given prefix): $O(m)$

6. Graphs#

Graphs are nonlinear data structures with vertices (nodes) connected by edges. They are used to model relationships, networks, and complex systems. Graphs can be directed (edges have a direction) or undirected (edges have no direction).

Types of graphs#

Below are the different types of graphs: Directed graphs, undirected graphs, weighted graphs, cyclic graphs, and acyclic graphs.

Directed graph (Digraph)#

A directed graph (digraph) is one in which the edges have a direction. Each edge goes from one vertex to another (or the same vertex).

Structure:
- It consists of vertices (nodes) and directed edges (arcs).
- Each edge is represented as an ordered pair (u, v), indicating a direction from vertex u to vertex v.
Advantages:
- It is suitable for representing relationships with direction, such as web links, one-way streets, or precedence relationships.

Weighted graph#

A weighted graph is a graph in which each edge has a numerical value (weight) associated with it. The weight can represent distance, cost, or any other quantitative measure.

Structure:
- It consists of vertices and weighted edges.
- Each edge is represented as a tuple (u, v, w) where w is the weight of the edge between vertices u and v.
Advantages:
- It is useful for optimization problems, such as the shortest path or minimum spanning tree.
- It can represent more complex relationships compared to unweighted graphs.

Graph representation#

Graphs are usually represented as either an adjacency list or an adjacency matrix to solve graph-related problems.

Adjacency list: It’s a collection of lists where each list corresponds to a node and contains its neighbors. In the case of weighted graphs, the weight is stored along with the corresponding nodes.
Adjacency matrix: It’s a 2D array where each cell, $matrix[i][j]$ , represents the edge between nodes $i$ and $j$ . The value of $matrix[i][j]$ equals $1$ (or the weight in the case of a weighted graph) if there’s an edge between nodes $i$ and $j$ , and $0$ otherwise.

1. Searching algorithms#

Searching algorithms are fundamental in computer science and practical applications. They allow us to efficiently locate specific elements within a data structure. Some key reasons for their importance include:

Data retrieval: Quick data retrieval is crucial in applications such as databases, search engines, and file systems.
Optimization: Efficient searching algorithms can significantly reduce the time complexity of operations, enhancing the performance of software applications.
Foundation for other algorithms: Many advanced algorithms, such as certain dynamic programming solutions and graph algorithms, rely on efficient searching techniques as a core component.
Real-world applications: Searching algorithms are ubiquitous in everyday technology, from finding a contact in your phonebook to searching for a product in an online store.

Linear search#

Linear search iteratively checks each element in a list until the target element is found or the end of the list is reached. It is simple but less efficient for large datasets. The time complexity of the linear search is $O(n)$ , where $n$ is the number of elements in the list. In the worst case, every element must be checked, making it impractical for large datasets.

Binary search#

Binary search is an efficient algorithm for finding a target value within a sorted list. It repeatedly divides the search interval in half by comparing the target value to the middle element. The search is complete if the target is equal to the middle element. If the target is less than the middle element, the search continues on the left subarray. If the target is greater, it continues on the right subarray. This process continues until the target is found or the search interval is empty. Binary search has a worst-case time complexity of $O(log(n))$ , making it significantly faster than linear search for large datasets, provided the list is sorted.

2. Sorting algorithms#

Sorting algorithms arrange elements in a specific order (usually ascending or descending), which is essential for many applications. Their importance includes:

Efficiency: Many algorithms, like binary search, require sorted data to function correctly and efficiently.
Data analysis: Sorted data is easier to analyze and visualize, which is important for tasks like statistical analysis and reporting.
Simplifying problem-solving: Some complex problems become easier to solve when data is sorted, such as finding duplicates or detecting patterns.
Improving other algorithms: Sorting is often a preprocessing step for other algorithms, improving their performance and reliability. For example, sorting before searching or merging intervals.
Everyday use: Sorting is commonly used in practical applications, such as organizing emails, files, or playlist tracks.

Bubble sort#

Bubble sort is a simple sorting algorithm that repeatedly steps through the list, comparing adjacent elements and swapping them if they are in the wrong order. This process is repeated for each element in the list. Each pass through the list ensures the next largest element moves to its correct position. The algorithm continues until no swaps are needed, indicating the list is sorted. Although easy to understand, bubble sort is inefficient for large lists with a time complexity of $O(n^2)$ .

Merge sort#

Merge sort is an efficient, stable sorting algorithm that uses the divide-and-conquer strategy. It recursively breaks down a list into two equal halves until each sublist contains only one element. Since a single-element list is inherently sorted, the algorithm then begins the process of merging these sublists back together. During the merging phase, it compares the smallest elements of each sublist and combines them in sorted order. This process continues recursively until all sublists are merged into one sorted list. Merge sort is particularly efficient with a time complexity of $O(n log (n))$ and is well-suited for sorting large datasets.

def merge_sort(arr):
    if len(arr) > 1:
        mid = len(arr) // 2
        left_half = arr[:mid]
        right_half = arr[mid:]
        merge_sort(left_half)
        merge_sort(right_half)
        i = j = k = 0
        while i < len(left_half) and j < len(right_half):
            if left_half[i] < right_half[j]:
                arr[k] = left_half[i]
                i += 1
            else:
                arr[k] = right_half[j]
                j += 1
            k += 1
        while i < len(left_half):
            arr[k] = left_half[i]
            i += 1
            k += 1
        while j < len(right_half):
            arr[k] = right_half[j]
            j += 1
            k += 1
    return arr
# Example usage
arr = [64, 34, 25, 12, 22, 11, 90]
print("Array before sorting:", arr)
sorted_arr = merge_sort(arr)
print("Sorted array:", sorted_arr)

3. Graph algorithms#

Graph algorithms are essential for solving problems related to networks and relationships. Their significance includes:

Network analysis: They help analyze and optimize networks, such as social networks, computer networks, transportation systems, and utility grids.
Connectivity: Determining connectivity and identifying components within a graph is crucial for understanding the structure and robustness of networks.
Optimization: Graph algorithms are used in optimization problems, such as finding the minimum spanning tree or maximum flow in a network.
Modeling real-world problems: Many real-world problems can be modeled as graphs, making graph algorithms a powerful tool for finding solutions in diverse fields like biology, sociology, linguistics, and more.

Depth-first search (DFS)#

Depth-first search (DFS) is a graph traversal algorithm that explores the vertices of a graph as deeply as possible along each branch before backtracking. Here’s a more detailed explanation:

Starting point: DFS begins at a chosen starting vertex and explores as far as possible along each branch before backtracking. It uses a stack data structure, either explicitly or through recursion, to keep track of the vertices to be explored.
Exploration process: From the starting vertex, DFS visits an adjacent unvisited vertex, marks it as visited, and then recursively applies the same process to this new vertex. If no adjacent unvisited vertices are found, it backtracks to the previous vertex to continue the search.
Backtracking: If a vertex has no unvisited adjacent vertices, DFS backtracks to the most recent vertex that still has unexplored neighbors. This process continues until all vertices connected to the starting vertex are visited.

DFS is used for traversing trees, finding connected components in undirected graphs, and solving maze problems by exploring all paths and backtracking when necessary. It has a time complexity of $O(V + E)$ when using adjacency lists, where $V$ is the number of vertices, and $E$ is the number of edges. DFS is efficient for problems requiring full path exploration or connectivity checks.

Breadth-first search (BFS)#

Breadth-first search (BFS) is a graph traversal algorithm that explores vertices level by level, starting from the root node or any specified node. Here’s a more detailed explanation:

Level-wise exploration: BFS explores all vertices at the present "depth" (or level) before moving on to vertices at the next level. It uses a queue data structure to maintain the order of exploration, starting with the root node and then exploring its neighbors, followed by their neighbors, and so on.
Process:
1. Begin with the root node and enqueue it.
2. Dequeue a vertex, mark it as visited, and enqueue all its adjacent vertices that have not yet been visited.
3. Continue this process until all vertices reachable from the initial node have been visited.

from collections import deque
class Graph:
    def __init__(self):
        self.graph = {}
    def add_edge(self, u, v):
        if u not in self.graph:
            self.graph[u] = []
        self.graph[u].append(v)
    def print_graph(self):
        for node, neighbors in self.graph.items():
            print(f"{node}: {', '.join(map(str, neighbors))}")
    def bfs(self, start):
        visited = set()
        queue = deque([start])
        visited.add(start)
        while queue:
            v = queue.popleft()
            print(v, end=' ')
            for neighbor in self.graph.get(v, []):
                if neighbor not in visited:
                    queue.append(neighbor)
                    visited.add(neighbor)
# Example usage
g = Graph()
g.add_edge(0, 1)
g.add_edge(0, 2)
g.add_edge(1, 2)
g.add_edge(2, 0)
g.add_edge(2, 3)
g.add_edge(3, 3)
print("Graph representation:")
g.print_graph()
print("\nBFS starting from vertex 2:")
g.bfs(2)

4. Dynamic programming#

Dynamic programming is a powerful optimization technique used to improve the efficiency of recursive algorithms by storing the results of overlapping subproblems and reusing them when needed, rather than recalculating them. This approach is particularly effective for problems that exhibit optimal substructure and overlapping subproblems. Optimal substructure means that the optimal solution to the problem can be constructed from optimal solutions to its subproblems.

To learn more about dynamic programming, read our blog: From recursion to dynamic programming.

The illustration below calculates each fibonacci number by summing the two preceding numbers. This results in a tree of recursive calls, where many subproblems are solved multiple times.

$fib(4)$ calls $fib(3)$ and $fib(2)$
$fib(3)$ calls $fib(2)$ and $fib(1)$ .
$fib(2)$ calls $fib(1)$ and $fib(0)$ .

Note that $fib(2)$ , $fib(1)$ , and $fib(0)$ are recalculated multiple times. This redundancy leads to exponential time complexity, making it inefficient for large values of $n$ . Dynamic programming avoids redundant calculations by storing the results of subproblems and reusing them.

Dynamic programming is widely used in various applications such as computing the Fibonacci sequence, where each term is the sum of the two preceding ones; finding the longest common subsequence in sequences, which involves finding the longest sequence that can be derived from both original sequences without changing the order of characters. By breaking down these problems into simpler subproblems and storing their solutions, dynamic programming significantly reduces computation time and avoids redundant calculations.

To further increase your knowledge and skills in algorithms, we recommend the course “Algorithms for Coding Interviews.” This course is offered in three languages: Python, C++, and Java.

A 6-step roadmap to building DSA proficiency#

By following a structured roadmap and working on practical projects, you can build a strong foundation with data structures and algorithms.

Foundations: Start with basic data structures like arrays, linked lists, and stacks. Understand their properties, operations, and time complexities.
Trees and graphs: Learn about binary trees, binary search trees, heaps, and graph representations. Practice tree traversal algorithms (inorder, preorder, postorder) and graph algorithms (DFS, BFS).
Sorting and searching: Dive into sorting algorithms (bubble sort, merge sort, quick sort) and searching techniques (linear search, binary search). Compare their efficiencies and understand when to use each.
Dynamic programming: Master dynamic programming concepts by solving classic problems like the 0/1 knapsack problem, longest common subsequence, and optimal matrix chain multiplication.
Advanced topics: Explore advanced data structures (tries, segment trees, hash tables) and algorithmic techniques (divide and conquer, greedy algorithms, backtracking). Solve challenging problems and work on projects requiring algorithmic optimization.
Projects: Apply your knowledge by working on projects that require implementing data structures and algorithms, such as building a search engine, designing a recommendation system, or optimizing a sorting algorithm for large datasets.

Building a strong foundation#

Mastering data structures and algorithms is essential to your long-term success as a coder. It's a continuous learning process that requires dedication, practice, and problem-solving skills.

At Educative, we offer various hands-on courses that cover these programming building blocks in various languages. Check them out below:

Frequently Asked Questions

Why are data structures and algorithms important?

Understanding data structures and algorithms is crucial for problem-solving and optimization in computer science. They form the foundation for writing efficient and scalable code, vital for software development and technical interviews.

What are some basic data structures to learn first?

Begin with simple structures such as arrays, linked lists, stacks, and queues. Afterward, move to more advanced structures like trees, heaps, hash tables, and graphs.

What is the difference between BFS and DFS in graphs?

Breadth-first search (BFS) explores all neighbors level by level, while depth-first search (DFS) goes deep into a branch before backtracking. BFS is often used to find the shortest path, and DFS is used to explore all paths or components.

What is the difference between a stack and a queue?

A stack follows the last in, first out (LIFO) principle, meaning the last item added is the first to be removed. A queue follows the first in, first out (FIFO) principle, meaning the first item added is the first to be removed.

What is a graph, and what are its applications?

A graph is a data structure consisting of nodes (vertices) and edges connecting them. Graphs are widely used in networking, social networks, and solving shortest path problems, such as in navigation systems.

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Data structures and algorithms roadmap: A comprehensive guide

What are data structures?#

What are algorithms?#

Why learn data structures and algorithms?#

When are you ready to learn about data structures and algorithms? #

Understanding data structures#

1. Arrays#

Operations and time complexity#

2. Linked lists#

Types of linked lists#

Singly linked list#

Doubly linked list#

Circular linked list#

Operations and time complexity#

3. Stacks#

Operations and time complexity#

4. Queues#

Operations and time complexity#

5. Trees#

Types of trees#

Binary tree#

Binary search tree (BST)#

AVL tree (Balanced BST)#

Heap (Min-heap, max-heap)#

Operations and time complexity#

Trie#

Operations and time complexity#

6. Graphs#

Types of graphs#

Directed graph (Digraph)#

Undirected graph#

Weighted graph#

Acyclic graph#

Graph representation#

Exploring algorithms#

1. Searching algorithms#

Linear search#

Binary search#

2. Sorting algorithms#

Bubble sort#

Merge sort#

3. Graph algorithms#

Depth-first search (DFS)#

Breadth-first search (BFS)#

4. Dynamic programming#

A 6-step roadmap to building DSA proficiency#

Building a strong foundation#