数据结构之(prim)最小生成树

首先将其转化为邻接矩阵；

然后设置一个辅助数组included[]，用来记录该顶点是否被访问，初始化为0；

        设置 一个数组previous[],用来代表访问的前驱，初始化为-1；

        设置distance[]数组用来存各边的距离。

i	0	1	2	3	4	5
Included[i]	1	0	0	0	0	0
previous[i]	-1	-1	-1	-1	-1	-1

初始时，从v1开始，此时included[0]=1;再从与v1的相连的边中找出一条权值最小的边，即顶点v3，与v1的距离为1，此时修改辅助数组included[2]=1，且previous[2]=0；然后继续循环，寻找权值最小的边，依此类推，直到included[]数组全部为1 ，即扫描完毕，最小生成树完成，打印出生成树的各边。

#include <stdio.h>
#include <malloc.h>

#define INF 1000
#define NODES 6

//The network
int network[6][6] = {
	{ 0, 6, 1, 5, INF, INF },
	{ 6, 0, 5, INF, 3, INF },
	{ 1, 5, 0, 5, 6, 4 },
	{ 5, INF, 5, 0, INF, 2 },
	{ INF, 3, 6, 5, 0, 6 },
	{ INF, INF, 4, 2, 6, 0 } };

//Previous node
int previous[6] = { -1, -1, -1, -1, -1, -1 };

//Is the current included?
int included[6] = { 0, 0, 0, 0, 0, 0 };

//Minimal distance from the existing set
int distance[6];

void prim(int paraStartNode) 
{
	int i, j;
	int tempMin;
	int tempNewNode;
	//Initialize the previous vector. 
	for (i = 0; i < NODES; i++) 
	{
		//The previous node is always the start node.
		previous[i] = paraStartNode;
		//The distance is the distance from the start node.
		distance[i] = network[paraStartNode][i];
	}//Of for i
	previous[paraStartNode] = -1;

	//Only the start node is included
	included[paraStartNode] = 1;

	//Add the other nodes one by one
	for (i = 0; i < NODES - 1; i++)
	{
		//Find one node to add
		tempMin = INF;
		tempNewNode = -1;
		for (j = 0; j < NODES; j++) {
			if (!included[j]) {
				if (tempMin > distance[j]) {
					tempMin = distance[j];
					tempNewNode = j;
				}//Of if
			}//Of if
		}//Of for j

		//Add the node
		included[tempNewNode] = 1;

		//Serve for others
		for (j = 0; j < NODES; j++) {
			if (!included[j]) {
				if (distance[j] > network[tempNewNode][j]) {
					distance[j] = network[tempNewNode][j];
					previous[j] = tempNewNode;
				}//Of if
			}//Of if
		}//Of for j
	}//Of for i
}//Of prim

void printTree() {
	int i;
	for (i = 0; i < NODES; i++) {
		printf("The previous node of %d is %d\r\n", i, previous[i]);
	}//Of for i
}//Of printTree

int main() {
	prim(0);
	printTree();
	return 0;
}