Hello and welcome! In today's lesson, we will delve into the practical application of the Breadth-First Search (BFS) algorithm to solve intriguing algorithmic problems. We'll focus on a popular problem - finding the shortest path from the given source to the given destination in an unweighted, connected, and undirected graph. This problem frequently surfaces in various domains, such as spatial networks, social networks, computing, and logistics.

Our problem involves developing a minimum-cost route planner by using the BFS algorithm for a logistics company. The company operates in a bustling urban environment where there are multiple pickup and drop-off points, represented as nodes in a graph. The paths between these points, represented as edges in the graph, are bidirectional. Therefore, you can traverse them both ways. In other words, the graph is undirected.

Your task is to find the shortest path from a source node to a destination node in this graph.

One possible approach to this problem is to use the so-called brute-force approach, where you calculate all the possible paths from the source to the destination and then determine the shortest path among them. While this strategy might sound like it solves the problem, in reality, it can be very inefficient, especially when the number of nodes and edges is large. Storing all possible paths could lead to overflowing memory and sluggish time complexity. In fact, the time complexity for this algorithm is exponential, meaning it wouldn't perform well for even medium-sized graphs.

A much more efficient way to address this problem is by using the Breadth-First Search (BFS) algorithm. BFS is perfect for finding the shortest path in an unweighted graph because it explores all nodes at the current 'depth' before moving on to nodes at the next 'depth level'.