图转换为树-最小生成树

利用prims和kruskal两种方法实现最小生成树。

直接上code吧。记录下

#include 
#include 

#define MAX 10
#define VertexNum 5

struct List
{
	int v1;
	int v2;
	int weight;
	int marked;
	struct List *next;
};

typedef struct List* Edge;

int g_Edges[10][3] = {
	{1, 2, 7},
	{1, 3, 6},
	{1, 4, 5},
	{1, 5, 12},
	{2, 3, 14},
	{2, 4, 8},
	{2, 5, 8},
	{3, 4, 3},
	{3, 5, 9},
	{4, 5, 2}
};
int g_kruskal_visited[MAX] = {0};

int g_prims_visited[MAX] = {0};

void mst_print_edge(Edge Head)
{
	Edge pointer;
	pointer = Head;
	while(pointer!=NULL)
	{
		printf("[%d,%d] (%d)",pointer->v1, pointer->v2, pointer->weight);
		pointer = pointer->next;
	}
	printf("\n");
}

void mst_free_edge(Edge Head)
{
	Edge pointer;
	
	while(Head!=NULL)
	{
		pointer = Head;
		Head = Head->next;
		free(pointer);
	}
}

Edge mst_insert_edge(Edge Head, Edge New)
{
	Edge pointer = Head;
	while(1)
	{
		if (New->weight < Head->weight)
		{
			/*插入在首节点之前*/
			New->next = Head;
			Head=New;
			break;
		}
		else if (pointer->next == NULL)
		{
			/*插在链表尾部*/
			pointer->next = New;
			break;
		}

		if (New->weight >= pointer->weight && New->weight < pointer->next->weight)
		{
			/*插入在中间*/
			New->next = pointer->next;
			pointer->next = New;
			break;
		}
		pointer = pointer->next;
	}
	return Head;
}

Edge mst_create_edge(Edge Head)
{
	Edge New;
	Edge pointer;
	int i;
	Head = (Edge)malloc(sizeof(struct List));
	if (Head == NULL)
		printf("malloc failed\n");
	else
	{
		Head->v1 = g_Edges[0][0];
		Head->v2 = g_Edges[0][1];
		Head->weight = g_Edges[0][2];
		Head->marked = 0;
		Head->next = NULL;

		for(i = 1; i < MAX; i++)
		{
			New = (Edge)malloc(sizeof(struct List));
			if (New)
			{
				New->v1 = g_Edges[i][0];
				New->v2 = g_Edges[i][1];
				New->weight = g_Edges[i][2];
				New->marked = 0;
				New->next = NULL;

				Head = mst_insert_edge(Head, New);

			}
		}
	}
	return Head;
}

void mst_kruskal(Edge Head)
{
	Edge pointer;
	int EdgeNum = 0;
	int weight = 0;

	pointer = Head;

	while (EdgeNum != (VertexNum-1))
	{
		if (g_kruskal_visited[pointer->v1] == 0 || g_kruskal_visited[pointer->v2] == 0)
		{
			printf("==>[%d %d %d] ", pointer->v1, pointer->v2, pointer->weight);
			weight += pointer->weight;
			EdgeNum++;
			g_kruskal_visited[pointer->v1] = 1;
			g_kruskal_visited[pointer->v2] = 1;
		}
		pointer = pointer->next;
		if (pointer == NULL)
		{
			printf("No Spanning Tree\n");
			break;
		}
	}
	printf("\nTotal weight = %d\n", weight);
}

void mst_prims(Edge Head, int index)
{
	Edge pointer;
	Edge MinEdge;
	int EdgeNum = 0;
	int weight = 0;
	g_prims_visited[index] = 1;
	int i = 0;
	while (EdgeNum != (VertexNum-1))
	{
		int MinEdge_weight = 100000;
		for (i = 1; i <= VertexNum; i++)
		{
			pointer = Head;
			if (g_prims_visited[i] == 1) 
			{
				/*已经在生成树的集合中*/
				
				while(pointer->marked == 1)
				{
					if (pointer->next == NULL)
						break;
					pointer = pointer->next;
						
				}

				while(pointer!=NULL)
				{
					/*如果两顶点都在生成树集合中， 表示是已经查找过的边*/
					//printf("check edge [%d %d %d] MinEdge weight %d\n",
					//	pointer->v1, pointer->v2, pointer->weight, MinEdge_weight);
					if (g_prims_visited[pointer->v1] == 1 && g_prims_visited[pointer->v2] == 1)
						pointer->marked = 1;

					if (MinEdge_weight > pointer->weight &&
						pointer->marked == 0 &&
						(pointer->v1 == i || pointer->v2 == i))
					{
						MinEdge_weight = pointer->weight;
						MinEdge = pointer;
						printf("Min Edge [%d %d %d]\n", MinEdge->v1, MinEdge->v2, MinEdge->weight);
					}

					pointer = pointer->next;
				}
				printf("----\n");
			}
		}
		g_prims_visited[MinEdge->v1] = 1;
		g_prims_visited[MinEdge->v2] = 1;
		EdgeNum++;
		weight += MinEdge->weight;
		printf("\t\t\t==>[%d %d %d]\n", MinEdge->v1, MinEdge->v2, MinEdge->weight);
	}
	printf("\nprims Total weight = %d\n", weight);
}

int main(int argc, char **argv)
{
	Edge Head = NULL;
	int i;
	Head = mst_create_edge(Head);
	if (Head)
	{
		printf("Kruskal Algo:\n");
		mst_print_edge(Head);
		mst_kruskal(Head);
		printf("Prims Algo:\n");
		mst_prims(Head, 5);
		mst_free_edge(Head);
	}
	return 0;
}