This week we'll start getting technical, introducing you to the central data structure in the course: Graphs. You'll learn the basics and then have a chance to dive in a little deeper into the code, getting ready to start building that Google Maps-like application.

This week you'll get the backbone of your map search engine up and running. In previous courses, including the previous courses in this specialization, you've probably been given most of the classes you needed to complete the assignments. But learning how to design classes from scratch is a key skill that you will need as you become a more sophisticated Java programmer. This week we'll give you the tools you need to create a robust and elegant class design for your map search engine. We'll introduce a similar problem and show you how it can be represented as a graph. Then we'll introduce two core search algorithms: depth-first search and breadth-first search. Finally, we'll turn our graph problem into a set of Java classes. Your task on the programming assignment this week will be to do the same thing, but in the context on the map search engine!

In the past two weeks, you've developed a strong understanding of how to design classes to represent a graph and how to use a graph to represent a map. In this week, you'll add a key feature of map data to our graph representation -- distances -- by adding weights to your edges to produce a "weighted graph". Although this might seem like a small change, the algorithms that work for unweighted graphs may prove ineffective for weighted graphs. To address this problem, you'll explore more advanced shortest path algorithms. First, you'll see how to find the shortest path on a weighted graph, then you'll see how to find it more quickly. In the project, you'll apply these ideas to create the core of any good mapping application: finding the shortest route from one location to another.

In this week, we'll go beyond the problem of finding a path between two points, and focus on problems requiring overall path planning. For example, if you wanted to go on errands and visit 6 different locations before returning home, what is the optimal route? This problem is actually a really well known problem in computer science known as the Travelling Salesperson Problem (TSP). Attempting to solve the problem will lead us to explore complexity theory, what it means to be NP-Hard, and how to solve "hard" problems using heuristics and approximation algorithms. We'll end the week by showing how reformulating a problem can have a huge impact: making something which was effectively unsolvable before, now solvable!

You made it to the last week of our course! We're glad you're still with us. As a reward, there's no new content to learn this week. Instead you'll get the opportunity to extend your project in a direction of your own choosing. We hope you've got some neat ideas for personalizing your map application, and we look forward to seeing them in the peer review gallery. Submitting to the peer review gallery is optional (though the extension is required), but we hope you'll choose to participate.