最短路径 Dijkstra算法

最新推荐文章于 2020-09-20 17:18:42 发布

DataChat.Club

最新推荐文章于 2020-09-20 17:18:42 发布

阅读量541

点赞数

CC 4.0 BY-SA版权

文章标签：算法 include struct path

本文链接：https://blog.youkuaiyun.com/wangbaomi/article/details/7457738

c 专栏收录该内容

15 篇文章

订阅专栏

本文介绍了一个基于邻接矩阵实现的最短路径算法，通过不断迭代更新最短路径和路径前驱节点来找到图中任意两点之间的最短路径。文章详细展示了算法的实现过程，并提供了完整的C语言代码示例。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

#include "stdio.h"

#define INFINITY 100
#define MAX_VERTEX_NUM 20

struct MGraph {
	char vexs[MAX_VERTEX_NUM];
	int arcs[6][6];
	int vexnum, arcnum;
};

/*记录路径的数组, to[i].before 表示 v0 到 vi 的次短路径节点*/
struct PathArray{
	int before;
}to[6];

/*lenth[i]表示v0到vi的最短路径长度*/
void myshortestpathfun(MGraph g, int v0, PathArray to[6], int lenth[6])
{
	int i, j, k, t, num, temp[6];//temp[i]=1表示vi已经在最短路径上了，temp[i]= 0表示vi还不在最短路径上;

	/*初始化*/
	for (i = 0; i < 6; i++)
	{
		to[i].before = INFINITY;
		lenth[i] = INFINITY;
		temp[i] = 0;
	}

	/*第一轮比较*/
	for (i = 0; i < 6; i ++)
	{
		if (g.arcs[v0][i] < INFINITY)
		{
			to[i].before = v0;
			lenth[i] = g.arcs[v0][i];
		}
		
	}
	temp[v0] = 1; //v0已经在最短路径了;

	/*找出v0到vi中最短的一点vi，将节点下标保存到t中*/
	int temp2 = INFINITY;
	for (i = 0; i < 6; i++)
	{
		if (1 == temp[i]) 
			continue; //从不在最短路径上的那些点中找出最短的;
		if (lenth[i] < temp2)
		{
			temp2 = lenth[i];
			t = i;
		}
	}

	for (num = 0; num < 5; num++) //再比较5轮;
	{
		for (i = 0; i < 6; i++)
		{
			if (g.arcs[t][i] + lenth[t] < lenth[i])
			{			
				to[i].before = t;
				lenth[i] = g.arcs[t][i] + lenth[t];
			}
		}
		temp[t] = 1; //vt已经在最短路径了;

		temp2 = INFINITY;
		for (i = 0; i < 6; i++)
		{
			if (1 == temp[i])
				continue;
			if (lenth[i] < temp2)
			{
				temp2 = lenth[i];
				t = i;
			}
		}
	}

	printf("\nv%d 到各点的最短距离是：\n\n",v0);

	for (num = 0; num < 6; num++)
	{
		printf("v%d -> v%d : %d\n", v0, num, lenth[num]);
	}
	printf("\n\n");

	printf("v%d 到各点的最短路径： \n\n",v0);
	for (j = 0; j < 6; j++)
	{
		printf("v%d -> v%d path:\t ",v0, j);
		printf("v%d <- ", j);
		for (i = j; to[i].before != v0; )
		{
			printf("v%d <- ", to[i].before);
			i = to[i].before;
		
		}
		printf("v%d", v0);
		printf("\n");
	}
}

int main()
{
	int i,j;
	int p[6];
	int d[6];

	PathArray to[6];
	int lenth[6];

	MGraph a;

	int arcs1[6][6]=
					{
					 INFINITY,5,INFINITY,7,INFINITY,INFINITY,
					 INFINITY,INFINITY,4,INFINITY,INFINITY,INFINITY,
					 8,INFINITY,INFINITY,INFINITY,INFINITY,9,
					 INFINITY,INFINITY,5,INFINITY,INFINITY,6,
					 INFINITY,INFINITY,INFINITY,5,INFINITY,INFINITY,
                     3,INFINITY,INFINITY,INFINITY,1,INFINITY};
	int vexs1[] = {1,2,3,4,5,6};
	for(i = 0; i < 6;i++)
	{
		 a.vexs[i] = vexs1[i];
	}
	
	/*初始化*/
	a.vexnum = 6;
	a.arcnum = 10;

	for(i = 0;i < a.vexnum; i++ )
		for(j = 0;j < a.vexnum;j++)
		{
			a.arcs[i][j] = arcs1[i][j];
		}

	printf("各节点的邻接关系为 :\n\n");

	for (i = 0; i < 6; i++)
	{
		printf("\tv%d",i);
	}

	printf("\n");

	for (i = 0; i < a.vexnum; i++)
	{
		printf("v%d\t",i);

		for(j = 0; j < a.vexnum; j++)
		{
			printf("%d\t",a.arcs[i][j]);
		}

		printf("\n");
	}

	for (i = 0; i < 6; i++)
	{
		myshortestpathfun(a, i, to, lenth);
		printf("\n");
	}

	return 0;
}