432COMP9024，Exercise9

Posted 2022-07-12 alex-bn-lee

eulerianCycle.c

1. What determines whether a graph is Eulerian or not?
2. Write a C program that reads a graph, prints the graph, and determines whether an input graph is Eulerian or not.
   • if the graph is Eulerian, the program prints an Eulerian path
     • you should start with vertex 0

     • note that you may use the function findEulerianCycle() from the lecture on Graph Search Applications

   • if it is not Eulerian, the program prints the message Not Eulerian

For example,

• The graph:

    #4
    0 1 0 2 0 3 1 2 2 3

  is not Eulerian (can you see why?). Using this as input, your program should output:

    V=4, E=5
    <0 1> <0 2> <0 3> 
    <1 0> <1 2> 
    <2 0> <2 1> <2 3> 
    <3 0> <3 2> 
    Not Eulerian

• In the above-named lecture I showed a ‘concentric squares‘ graph (called concsquares):

    #8
    0 7 7 5 5 1 1 0
    6 0 6 7
    2 5 2 7
    4 1 4 5
    3 0 3 1

  which is Eulerian, although I‘ve labelled the vertices differently here. For this input your program should produce the output:

    V=8, E=12
    <0 1> <0 3> <0 6> <0 7> 
    <1 0> <1 3> <1 4> <1 5> 
    <2 5> <2 7> 
    <3 0> <3 1> 
    <4 1> <4 5> 
    <5 1> <5 2> <5 4> <5 7> 
    <6 0> <6 7> 
    <7 0> <7 2> <7 5> <7 6> 
    Eulerian cycle: 0 1 4 5 2 7 5 1 3 0 6 7 0 

  Draw concsquares, label it as given in the input file above, and check the cycle is indeed Eulerian.

• The function findEulerCycle() in the lecture notes does not handle disconnected graphs. In a disconnected Eulerian graph, each subgraph has an Eulerian cycle.

  • Modify this function to handle disconnected graphs.
  • With this change, your program should now work for the graph consisting of 2 disconnected triangles:

       #6
       0 1 0 2 1 2 3 4 3 5 4 5

    It should now find 2 Eulerian paths:

       V=6, E=6
       <0 1> <0 2> 
       <1 0> <1 2> 
       <2 0> <2 1> 
       <3 4> <3 5> 
       <4 3> <4 5> 
       <5 3> <5 4> 
       Eulerian cycle: 0 1 2 0 
       Eulerian cycle: 3 4 5 3

思路：经过一条边就删掉一个，通过遍历查找是否遍历完（针对不连通的graph）

#include <stdio.h>
#include <stdlib.h>
#include <stdbool.h>
#include "Graph.h"
#include "Quack.h"

#define UNVISITED -1
#define WHITESPACE 100

void dfsR(Graph g, Vertex v, int numV, int *order, int *visited);
Vertex getAdjacent(Graph g, int numV, Vertex v);

int readNumV(void)  // returns the number of vertices numV or -1
   int numV;
   char w[WHITESPACE];
   scanf("%[ \t\n]s", w);  // skip leading whitespace
   if ((getchar() != ‘#‘) ||
       (scanf("%d", &numV) != 1)) 
       fprintf(stderr, "missing number (of vertices)\n");
       return -1;
   
   return numV;


int readGraph(int numV, Graph g)  // reads number-number pairs until EOF
   int success = true;             // returns true if no error
   int v1, v2;
   while (scanf("%d %d", &v1, &v2) != EOF && success) 
       if (v1 < 0 || v1 >= numV || v2 < 0 || v2 >= numV) 
          fprintf(stderr, "unable to read edge\n");
          success = false;
       
       else 
          insertE(g, newE(v1, v2));
       
   
   return success;


void findEulerCycle(Graph g, int numV, Vertex startv) 
   Quack s = createQuack();
   push(startv, s);
   
   int allVis = 0;
   while (!allVis) 
   	   printf("Eulerian cycle: ");
	   while (!isEmptyQuack(s)) 
		  Vertex v = pop(s); // v is the top of stack vertex and ...
		  push(v, s);        // ... the stack has not changed
		  Vertex w;
		  if ((w = getAdjacent(g, numV, v)) >= 0) 
		     push(w, s);     // push a neighbour of v onto stack
		     removeE(g, newE(v, w)); // remove edge to neighbour
		  
		  else 
		     w = pop(s);
		     printf("%d ", w);
		  
	   
	   printf("\n");
	   allVis = 1;

	   for (Vertex v = 0; v < numV && allVis; v++) 
	   	  for (Vertex w = 0; w < numV && allVis; w++) 
	   	  	 if (isEdge(g, newE(v, w))) 
	   	  	 	allVis = 0;
	   	  	 	push(v, s);
	   	  	 
	   	  
	   
   


Vertex getAdjacent(Graph g, int numV, Vertex v) 
   // returns the Largest Adjacent Vertex if it exists, else -1
   Vertex w;
   Vertex lav = -1; // the adjacent vertex
   for (w=numV-1; w>=0 && lav==-1; w--) 
      Edge e = newE(v, w);
      if (isEdge(g, e)) 
         lav = w;
      
   
   return lav;


int isEulerian(Graph g, int numV) 
	int count = 0;
	for (Vertex w = 0; w < numV; w++) 
		count = 0;
		for (Vertex v = 0; v < numV; v++) 
			if (isEdge(g, newE(w, v))) 
				count++;
			
		
		if (count % 2 != 0) 
			return 0;
		
	
	return 1;



int main (void)  
    int numV;
    if ((numV = readNumV()) >= 0) 
        Graph g = newGraph(numV);
        if (readGraph(numV, g)) 
        	showGraph(g);
        	
        	if(isEulerian(g, numV)) 
        		findEulerCycle(g, numV, 0);
        	
        	else 
        		printf("Not Eulerian\n");
        	
        
    
    else 
        return EXIT_FAILURE;
    
    return EXIT_SUCCESS;


// clear && gcc dfs_EulerCycle.c GraphAM.c Quack.c && ./a.out < input_1.txt

// clear && gcc dfs_EulerCycle.c GraphAM.c Quack.c && ./a.out < input_2.txt

// clear && gcc dfs_EulerCycle.c GraphAM.c Quack.c && ./a.out < input_3.txt