Gain insights into essential algorithms for effective problem-solving in Java. Delve into recursion, dynamic programming, and graph algorithms to enhance your coding and tackle complex problems confidently.

As a developer, mastering the concepts of algorithms and being proficient in implementing them is essential to improving problem-solving skills. This course aims to equip you with an in-depth understanding of algorithms and how they can be utilized for problem solving in Java.

Starting with the basics, you'll gain a foundational understanding of what algorithms are, with topics ranging from simple multiplication algorithms to analyzing algorithms. Then, you’ll delve into more advanced topics like recursion, backtracking, dynamic programming, and greedy algorithms. You'll also learn about basic graph algorithms, depth-first search, shortest paths, minimum spanning trees, and all-pairs shortest paths. 

By the end of this course, you'll have acquired a wide range of skills that will significantly enhance your ability to solve problems efficiently in Java. Through this course, not only will you improve your coding skills, but you will also gain confidence in tackling complex problems.

Mastering Algorithms for Problem Solving in Java

# Task
Write a Java program to determine whether an undirected graph can be directed to make it strongly connected. Recall that a directed graph is strongly connected if, for any two vertices $u$ and $v$, there is a path in the graph from $u$ to $v$ and a path in the graph from $v$ to $u$.

Your program should take as input an undirected graph represented as an adjacency list, and should return $true$ if it is possible to direct each edge of the graph so that the resulting directed graph is strongly connected and $false$ otherwise.


# Logic building
We can use the following algorithm to solve the problem:

**Algorithm**

1. Perform DFS on the undirected graph to compute the finishing times of each vertex.
2. Compute the transpose of the graph by reversing all the edges.
3. Perform DFS on the transposed graph to compute the strongly connected components (SCCs) in reverse order of finishing times.
4. If the transposed graph has more than one SCC, then it's not possible to direct each edge of the graph to make it strongly connected. Otherwise, it is possible.

Your program should define the following function:

```java
public static boolean isStronglyConnected(Map<Integer, List<Integer>> graph) {
    // implement the algorithm here
}
```
The graph parameter is a `Map<Integer, List<Integer>>` representing the undirected graph as an adjacency list. The function should return `true` if it is possible to direct each edge of the graph so that the resulting directed graph is strongly connected, and `false` otherwise.

We can assume that the vertices in the graph are numbered from 1 to $N$, where $N$ is the number of vertices.

We can use the following sample input and output to test your program:

**Sample input**
```
{1=[2, 3], 2=[1, 3], 3=[1, 2], 4=[5], 5=[4]}
```

**Sample Output**
```
True
```

**Explanation:**
The given undirected graph can be directed as follows to make it strongly connected: $1 -> 2 -> 3 -> 1$ and $4 -> 5 -> 4$. Note that there are other ways to direct the edges to make the graph strongly connected.


# Solution

The following coding workspace contains the solution to the problem described above.

Solution to the problem related to basic graph algorithms.

Getting Started

Introduction to Algorithm

Recursion

Backtracking

Dynamic Programming

Greedy Algorithms

Prove Your Skills: A Five-Chapter Assessment

Basic Graph Algorithms

Depth-First Search

Minimum Spanning Trees

Shortest Paths

All-Pairs Shortest Paths

Pushing Your Limits: A Comprehensive Assessment

Wrapping up

Solution: Basic Graph Algorithms

Task