最小生成树

一个有 n 个结点的连通图的生成树是原图的极小连通子图，且包含原图中的所有 n 个结点，并且有保持图连通的最少的边。

今天看了普利姆算法.记录一下.

<pre name="code" class="cpp">// bogo.cpp : 定义控制台应用程序的入口点。
//

#include "stdafx.h"
#include <stdio.h>
#include <iostream>
using namespace std;
#define MAX_PATH 65535

int date[9][9] = {
	{0,10,MAX_PATH,MAX_PATH,MAX_PATH,11,MAX_PATH,MAX_PATH,MAX_PATH},
	{10,0,18,MAX_PATH,MAX_PATH,MAX_PATH,16,MAX_PATH,12},
	{MAX_PATH,MAX_PATH,0,22,MAX_PATH,11,MAX_PATH,MAX_PATH,8},
	{MAX_PATH,MAX_PATH,22,0,20,MAX_PATH,MAX_PATH,16,21},
	{MAX_PATH,MAX_PATH,MAX_PATH,20,0,26,MAX_PATH,7,MAX_PATH},
	{11,MAX_PATH,MAX_PATH,MAX_PATH,26,0,17,MAX_PATH,MAX_PATH},
	{MAX_PATH,16,MAX_PATH,MAX_PATH,MAX_PATH,17,0,19,MAX_PATH},
	{MAX_PATH,MAX_PATH,MAX_PATH,16,7,MAX_PATH,19,0,MAX_PATH},
	{MAX_PATH,12,8,21,MAX_PATH,MAX_PATH,MAX_PATH,MAX_PATH,0}
};

int _tmain(int argc, _TCHAR* argv[])
{
	int lowest[9];//这个数组可以理解为下标为i的点,与现在已经加入生成树各点的最小权值.
	int adjvex[9];//a[i] = k 就是表示i点与树中的k点之间权值最小.如果目前树种没有与i相连,则a[i] = 0
	int min;
	int j,k;

	int length = 9;

	lowest[0] = 0;
	adjvex[0] = 0;

	int i;

	//初始化
	for (i = 1; i < length; i++)
	{
		adjvex[i] = 0;
		lowest[i] = date[0][i];
	}

	for (i = 1; i < length; i++)
	{
		//初始化最小权值为MAX
		min = MAX_PATH;
		j = 1;
		k = 0;
			while (j < length)
			{
				if (lowest[j] != 0&&lowest[j] < min)
				{
					min = lowest[j];
					k = j;
				}
				j++;
			}

		printf("%d %d
",adjvex[k],min);

		lowest[k] = 0;//表示此点已经加入了最小生成树

		for (j = 1; j < length; j++)
		{
			if (lowest[j] != 0&&date[k][j] < lowest[j])
			{
				lowest[j] = date[k][j];
				adjvex[j] = k;
			}
		}

	}

	return 0;
}