#### Overview of this book

Begin your journey into the fascinating world of algorithms with this comprehensive course. Starting with an introduction to the basics, you will learn about pseudocode and flowcharts, the fundamental tools for representing algorithms. As you progress, you'll delve into the efficiency of algorithms, understanding how to evaluate and optimize them for better performance. The course will also cover various basic algorithm types, providing a solid foundation for further exploration. You will explore specific categories of algorithms, including search and sort algorithms, which are crucial for managing and retrieving data efficiently. You will also learn about graph algorithms, which are essential for solving problems related to networks and relationships. Additionally, the course will introduce you to the data structures commonly used in algorithms. Towards the end, the focus shifts to algorithm design techniques and their real-world applications. You will discover various strategies for creating efficient and effective algorithms and see how these techniques are applied in real-world scenarios. By the end of the course, you will have a thorough understanding of algorithmic principles and be equipped with the skills to apply them in your technical career.
Free Chapter
Chapter 1: Introduction to Algorithms
Chapter 2: Pseudocode and Flowcharts
Chapter 3: Algorithm Efficiency
Chapter 4: Basic Algorithm Types
Chapter 5: Search Algorithms
Chapter 6: Sort Algorithms
Chapter 7: Graph Algorithms
Chapter 8: Data Structures Used in Algorithms
Chapter 9: Algorithm Design Techniques
Chapter 10: Real World Applications of Algorithms
Conclusion
Where to continue?

# 7.6 Practice Problems

Let's dive into some practical problems that can help us understand these graph algorithms better.

## Problem 1: DFS in Maze Solving

Let's start with an easy problem of solving a maze using DFS. In this problem, we are given a grid (2D array), and we have to find a path from the start position to the goal position. We can move up, down, left, and right, but not diagonally.

Here's a simple Python implementation using DFS:

You can test this with a simple maze (list of lists where 0 signifies a path and 1 is a wall).

## Problem 2: Shortest Path in a Grid with BFS

A typical example of BFS is finding the shortest path in a grid (e.g., from the top-left corner to the bottom-right corner). This is because BFS is a level order traversal, and it visits all vertices at the same level before going deeper into the graph. Let's try to solve a problem using BFS. The problem statement is similar to the previous problem, but instead of DFS, we use BFS to find...