【432】COMP9024，Exercise9

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("%[ 	
]s", w);  // skip leading whitespace
   if ((getchar() != '#') ||
       (scanf("%d", &numV) != 1)) {
       fprintf(stderr, "missing number (of vertices)
");
       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
");
          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("
");
	   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
");
        	}
        }
    }
    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

---

unreachable.c

Write a program that uses a fixed-point computation to find all the vertices in a graph that are unreachable from the start vertex (assume it to be 0). Note the following:

• the fixed-point computation should be iterative

• you should not use recursion, or stacks or queues

If a graph is disconnected:

• then those vertices not reachable (say vertices 8 and 9) should be output as follows:

   Unreachable vertices = 8 9

If a graph is connected then all vertices are reachable and the output is :

•  Unreachable vertices = none

For example:

• Here is a graph that consists of 2 disconnected triangles:

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

  If the start vertex is 0, then the output should be:

   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> 
   Unreachable vertices = 3 4 5

  because obviously the vertices in the second triangle are not reachable from the first.
• here is a connected graph:

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

  Starting at any vertex, the result should be:

   V=5, E=8
   <0 1> <0 4> 
   <1 0> <1 2> <1 3> <1 4> 
   <2 1> <2 3> <2 4> 
   <3 1> <3 2> <3 4> 
   <4 0> <4 1> <4 2> <4 3> 
   Unreachable vertices = none

思路：

• 首先就是设置 outside数组，默认是都为 -1，一旦被访问了就赋值为 0，变为 inside
• 设置一个 changing 字符串，用来监测 outside 数组是否有变化
• 如果变化的话，就遍历所有inside的点的相连接的点，如果发现 outside，则将此点赋值为 inside，changing 赋值为1
• while 循环，继续遍历，知道所有 inside 点的邻接点都是 inside，遍历结束
• 因此会将所有一个连通图中的点放入在 inside 内部

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

#define UNVISITED -1
#define WHITESPACE 100

int readNumV(void) { // returns the number of vertices numV or -1
   int numV;
   char w[WHITESPACE];
   scanf("%[ 	
]s", w);  // skip leading whitespace
   if ((getchar() != '#') ||
       (scanf("%d", &numV) != 1)) {
       fprintf(stderr, "missing number (of vertices)
");
       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
");
          success = false;
       }
       else {
          insertE(g, newE(v1, v2));
       }
   }
   return success;
}

int *mallocArray(int numV) {              
  int *array = malloc(numV * sizeof(int));// l
  if (array == NULL) {                    // o
     fprintf(stderr, "Out of memory
");  // c
     exit(1);                             // a
  }                                       // l
  int i;                                  // f
  for (i=0; i<numV; i++) {                // u
     array[i] = UNVISITED;                // n
  }                                       // c
  return array;                           // t
}     

void showUnreach(Graph g, int numV, Vertex startv) {
	int *outside = mallocArray(numV);
	outside[startv] = 0;
	int changing = 1;
	while (changing) {
		changing = 0;
		for (Vertex v = 0; v < numV; v++) {
			if (!outside[v]) {
				for (Vertex w = 0; w < numV; w++) {
					if (isEdge(g, newE(v, w)) && outside[w] == UNVISITED) {
						outside[w] = 0;
						changing = 1;
					}
				}
			}
		}
	}
	printf("Unreachable vertices = ");
	int any = 0;
	for (Vertex v = 0; v < numV; v++) {
		if (outside[v] == UNVISITED) {
			printf("%d ", v);
			any = 1;
		}
	}
	if (!any) {
		printf("none");
	}
	putchar('
');
	return;
}

int main (void) { 
    int numV;
    if ((numV = readNumV()) >= 0) {
        Graph g = newGraph(numV);
        if (readGraph(numV, g)) {
        	showGraph(g);
        	showUnreach(g, numV, 0);
        }
    }
    else {
        return EXIT_FAILURE;
    }
    return EXIT_SUCCESS;
}

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

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

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