README.md

Caminho de Euler

Overview

This C script checks for the existence of an Eulerian path in a graph represented by an adjacency matrix.

Author

• Silas Vasconcelos
• GitHub: S-v7

Language

C

Script Description

The script defines a function funcao_Impar to check whether a given degree is odd. The main function Caminho_De_Euler checks if there exists an Eulerian path in the graph based on the Eulerian path conditions. It then prompts the user to input the size of the graph and uses a predefined adjacency matrix M to check for the existence of the Eulerian path.

Code

#include<stdio.h>

// Function to check if a degree is odd
int funcao_Impar(int grau){
  if(grau % 2 == 1){
    return 1;
  }
  return 0;
}

// Function to check for the existence of an Eulerian path
int Caminho_De_Euler(int Matriz[5][5], int n){
    int total = 0; // Number of nodes found so far
    int grau = 0;  // Node degree
    int i = 1, j = 1; // Matrix indices

    while(total <= 2 && i < n){
      grau = 0;
      for(j = 1; j < n; j++){
        grau += Matriz[i][j]; // Find the degree of node i(*)
      }
      if(funcao_Impar(grau)){
        total += 1; // Found another odd node
      }
      i += 1;
    }
    if(total > 2){
      printf("Não existe um Caminho de Euler\nTotal: %d ", total);
    } else {
      printf("Existe um Caminho de Euler\nTotal: %d ", total);
    }
    return 0;
}

int main(){
    int t = 0;
    int M[5][5] = {{0,2,1,0,0}, // Adjacency Matrix
                   {2,0,1,0,0},
                   {1,1,0,1,1},
                   {0,0,2,0,2},
                   {0,0,1,2,0}};

    printf("Digite o valor de n: ");
    scanf("%d", &t);

    Caminho_De_Euler(M, t);

    return 0;
}

Usage

• 1. Compile the script using a C compiler.
• 2. Run the executable.
• 3. Input the size of the graph when prompted.
• 4. View the output indicating the existence of an Eulerian path

Notes

• This script checks the existence of an Eulerian path based on the degree of nodes in a graph represented by an adjacency matrix.
• Users should input the size of the graph n when prompted