Graph Problems in Java

Among various subjects of computer science, one of the most important ones is graph issues that included data structures representing pairwise relations of things. A graph is a combination of nodes or vertices and the connection between them or the edges.

It means that depending on the nature of the relationship depicted in the graph then it can be either a directed graph or an undirected graph. There can be weighted where each edge possesses some cost; otherwise can be unweighted where each edge is similar to the other edge.

Graph algorithms may be used to solve a number of problems and may involve solving a 'path 'problem, developing a 'connection' between the nodes, determining the 'degree of connectedness', checking for the existence of 'cyclic' paths and/or calculating the 'shortest path'.

In this post, we will use graph ideas to solve different problems:

Problem: Can Strings Form a Circle?

Problem Statement: Find out whether you can chain together a variety of threads to create a circle. Only when the last character of one string matches the initial character of the subsequent string may one string follow another. The objective is to determine if the whole array of strings can be structured so that a circle is formed by the last character of the last string matching the first character of the first string.

Approach

The problem can be represented as a graph problem where:

• Each string is a node.
• An edge exists from string A to string B if the last character of A matches the first character of B. The task is to check whether this graph can form an Eulerian circuit, meaning that:

1. All vertices with non-zero degree are connected.
2. Every node in a directed graph has an equal in degree and out degree, the in-degree of a node defines how many nodes point to this node while out-degree defines the number of nodes which are pointed by this node.

Algorithm

• Create a Graph: If the strings can be linked together as an entity, the shape of the graph is actually nodes connecting anything with everything, proceeding from an edge from two characters to an edge from every character.
• Check the degree conditions: Ensure that each vertex's in-degree and out-degree are the same.
• Verify the connectivity of the graph: Examine the graph's connectedness by seeing if any paths link any two nodes. If this is the case, the chaining process's vertices ought to be strongly connected.
• Result: If both conditions are satisfied, the strings can be connected to form a circle.

File Name: StringChainCircle.java

Output:

 true false