DATA STRUCTURES AND ALGORITHMS
Advanced Data Structures and Algorithms
Data structures and algorithms are fundamental concepts in computer science that help in organizing and managing data efficiently. This session introduces basic data structures and the importance of algorithms in developing efficient solutions to computational problems.
Objectives of This Session
– Explore more advanced data structures like Trees, Graphs, and Hash Tables.
– Understand key algorithms such as Depth-First Search (DFS), Breadth-First Search (BFS), and Hashing techniques.
– Analyze the efficiency and application of these structures and algorithms.
1. Advanced Data Structures
Trees:
– Description: A hierarchical structure consisting of nodes, with a single node known as the root, and zero or more subtrees.
– Types: Binary Trees, Binary Search Trees, AVL Trees, Red-Black Trees.
– Application: Used in databases, to manage sorted lists of data, as part of decision-making algorithms.
Graphs:
– Description: A collection of nodes (or vertices) and edges connecting some or all of them.
– Types: Directed and Undirected Graphs.
– Application: Used in networking, problem-solving, and to model complex relationships.
Hash Tables:
– Description: A data structure that implements an associative array, a structure that can map keys to values.
– Technique: Hashing, where the informational content of a key is used to determine a unique value called its hash code.
– Application: Used for quick data retrieval.
2. Essential Algorithms
Depth-First Search (DFS):
– Purpose: An algorithm for traversing or searching tree or graph data structures. It starts at the root and explores as far as possible along each branch before backtracking.
– Implementation:
void dfs(int v, vector<bool>& visited, vector<int> adj[]) {
visited[v] = true;
cout << v << ” “;
for (int u : adj[v]) {
if (!visited[u]) {
dfs(u, visited, adj);
}
}
}
Breadth-First Search (BFS):
– Purpose: An algorithm for searching a tree or graph that starts from the root and explores all neighbors at the present depth prior to moving on to nodes at the next depth level.
– Implementation:
void bfs(int s, vector<bool>& visited, vector<int> adj[]) {
queue<int> queue;
visited[s] = true;
queue.push(s);
while (!queue.empty()) {
int v = queue.front();
cout << v << ” “;
queue.pop();
for (int u : adj[v]) {
if (!visited[u]) {
visited[u] = true;
queue.push(u);
}
}
}
}
Hashing:
Purpose:
An algorithm used to uniquely identify a specific object from a group of similar objects.
Example:
Simple hash function for an integer array.
int hashFunction(int key, int tableSize) {
return key % tableSize;
}
3. Analyzing Complexity
– Discuss how to evaluate the time and space complexity of different algorithms and why it matters.
– Example analyses for DFS and BFS (both can be O(V + E), where V is vertices and E is edges).
4. Practical Exercises
Task:
Implement a simple hash table in C++.
Challenge:
Use BFS and DFS in a graph created by the students to understand traversal differences.
6. Getting Started with Learning
Resources:
– [Code With Harry for learning DSA] (https://bit.ly/3Ut425d )
– [W3 Schools for learning DSA] (https://www.w3schools.com/dsa/index.php)
Conclusion
This session enhanced your understanding of complex data structures and algorithms, focusing on their practical applications and the importance of algorithmic efficiency. These concepts are critical for solving real-world problems and optimizing performance in software development.
