Traverse in lexicographical order using DFS

Introduction

Graph traversal could be a principal operation in computer science that includes going by all nodes of a graph. In certain scenarios, it may be fundamental to navigate the graph in the lexicographical order of nodes, which suggests going by the nodes in climbing numerical order. In this article, we'll investigate two distinctive approaches to performing a lexicographical DFS traversal of a graph utilizing the C language. These approaches point to creating the same correct yield while giving elective executions and viewpoints. They offer an establishment for understanding a wide extent of graph-related issues, empowering productive investigation, and analysis of graph structures.

Traversing in Lexicographical Order

Traversing a graph in the lexicographical order of nodes utilizing depth-first search (DFS) is a curious issue that emerges in different domains, counting network examination, social systems, and graph calculations. Sometime recently diving into the particular approaches, let's briefly examine the fundamental hypothesis and ideas related to graph traversal and DFS.

A graph could be a collection of nodes (vertices) associated with edges. Graph traversal alludes to the precise going by of all nodes in a graph, ensuring that each node is gone by as it were once. DFS could be a well-known graph traversal calculation that investigates as distant as conceivable along each department time recent backtracking. It utilizes a stack to keep track of the nodes to be gone by.

When considering the lexicographical order of nodes, we point to visiting the nodes in rising numerical order. This ordering is frequently basic in scenarios where nodes speak to values or substances that have a common order. To realize a lexicographical DFS traversal, we ought to carefully control the order in which we visit adjoining nodes.

These approaches share the objective of creating the same adjust output—traversing the graph in lexicographical order. By carefully controlling the order of going to adjoining nodes, they guarantee that the nodes are going to be in climbing numerical order, in this way accomplishing the specified lexicographical traversal.

Understanding and executing these approaches give profitable bits of knowledge into graph traversal and DFS calculations.

Approach 1: Recursive DFS Traversal

Algorithm

• Step 1 −  Make an adjacency matrix representation of the graph.

• Step 2 − Initialize a boolean array gone by to keep track of nodes.

• Step 3 − Execute the traverseGraph() function. Within the main function set the number of nodes within the graph.

• Step 4 − Initialize the matrix and call traverseGraph() function.

• Step 5 − Display the traversal order.

Example

#include <stdio.h>
#define MAX_NODES 100

int graph[MAX_NODES][MAX_NODES];
int visited[MAX_NODES] = {0};

void dfs(int node) {
   visited[node] = 1;
   printf("%d ", node);
  
   for (int i = 0; i < MAX_NODES; i++) {
      if (graph[node][i] && !visited[i]) {
         dfs(i);
      }
   }
}

void traverseGraph(int numNodes) {
   dfs(0);  

   for (int i = 0; i < numNodes; i++) {
      if (!visited[i]) {
         dfs(i);
      }
   }
}

int main() {
   int numNodes = 7;  
    
   printf("Traversal order: ");
   traverseGraph(numNodes);

   return 0;
}

Output

Traversal order: 0 1 2 3 4 5 6

Approach 2: Adjusted Recursive DFS Traversal

Algorithm

• Step 1 − Create an adjacency matrix representation of the graph.

• Step 2 − Define the dfs() function and use for loop to set the number of nodes within the graph.

• Step 3 − Initialize the adjacency matrix.

• Step 4 − Invoke traverseGraph() function.

Example

#include <stdio.h>
#define MAX_NODES 100

int graph[MAX_NODES][MAX_NODES];
int visited[MAX_NODES] = {0};

void dfs(int node) {
   visited[node] = 1;
   printf("%d ", node);

   for (int i = 0; i < MAX_NODES; i++) {
      if (graph[node][i] && !visited[i]) {
         dfs(i);
      }
   }
}

void traverseGraph(int numNodes) {
   for (int i = 0; i < numNodes; i++) {
      if (!visited[i]) {
         dfs(i);
      }
   }
}

int main() {
   int numNodes = 7; 
   
   printf("Traversal order: ");
   traverseGraph(numNodes);

   return 0;
}

Output

Traversal order: 0 1 2 3 4 5 6

Conclusion

Traversing a graph in the lexicographical order of nodes utilizing DFS is a common assignment in different graph-based applications. In this article, we displayed two approaches within the C language to achieve this assignment. Approach 1 utilized recursive DFS traversal, whereas Approach 2 presented a modified version of recursive DFS traversal. Despite the contrasts in execution, all two approaches pointed to delivering the same rectify output—traversing the graph in lexicographical order. By understanding these approaches and their steps, designers can select the foremost reasonable solution based on their requirements and constraints. These usages give an establishment for advanced investigation and optimization of graph traversal calculations in real-world applications.