数据结构-图-Dijkstra迪杰斯特拉算法

问题：找出如下图中v0 到各点的最短距离，并输出距离及路径

程序运行截图：

分析：
在图中找到V0到各点的最小短距离路径：** 使用dijkstra算法求单源最短路径**

• 用dist[]数组来存储v0到各点的最短距离，path[]来存储路径，path[w]= v即w点经过v，collected[]记录该点是否被收入s
• 第一步：初始化，所有dist设置为无穷大，path设置为-1
• 第二步:进入主循环前，v0的邻接点初始化，path和dist初始化，再将v0并入S集
• 第三步：进入主循环，在未收录的找到v0到其余n-1个顶点最短路径的顶点，并入S，如果找不到这样的点，退出循环
• 第四步：遍历v的每个邻接点，更新当前最短路径及距离

dijkstra函数

void Dijkstra(MGraph N, int v0, PathMatrix path, ShortPathLength dist)
/*在图中找到V0到各点的最小短距离路径*/
{
	int i,v,w;
	int min;//最短路径
	int collected[MaxSize];//存储顶点是否收录到S
	for (v = 0; v < N.vexnum; v++) // 初始化v0到v的距离,
	{
		if (N.arc[v0][v].adj < INFINITY)//邻接点
		{
			path[v] = 0;
			dist[v] = N.arc[v0][v].adj;
		}
		else
		{
			path[v] = -1;
			dist[v] = INFINITY;
		}
		collected[v] = 0;
	}

	collected[v0] = 1;//先将v0并入s
	dist[v0] = 0;
	//path[0] = 0;
	//开始主循环
	while (1)
	{
		v = 0;
		min = INFINITY;
		for (w = 0; w < N.vexnum ; w++) //在未收录的顶点中找到距离最小的顶点
		{
			if(collected[w] == 0)
				if (dist[w] < min)
				{
					v = w;
					min = dist[w];
				}
		}
		if (v == 0) //如果这样的v不存在
			break;
		collected[v] = 1;//将该并入s


		for (w = 0; w < N.vexnum ; w++) ////在V的邻接点中更新当前最短路径及距离
		{
			if(N.arc[v][w].adj < INFINITY)
				if (collected[w] == 0)
					if (dist[v] + N.arc[v][w].adj < dist[w])
					{
						dist[w] = dist[v] + N.arc[v][w].adj;
						path[w] = v;
					}
		}
	}
	

}

所有代码

#include "pch.h"
#include <iostream>
#include<stdio.h>
#include<stdlib.h>

typedef char VertexType; //相当于VertexType 为char[4]
#define INFINITY 65535 //最大值
#define MaxSize 50 //最大顶点个数
typedef enum{DG,DN,UDG,UDN}GrandKind;//有向图，有向网，无向图，无向网
typedef int VRType; //顶点关系类型，无权图用0或1，有权图，则为权值类型
typedef char InfoPtr;

typedef struct
{
	VRType adj;//对于无权图用0或1表示，1表示相邻，0表示不相邻；对于带权值得图存储权值
	InfoPtr * info;//该弧相关信息指针，与弧或边的相关信息
} ArcNode, AdjMatrix[MaxSize][MaxSize];

typedef struct //图的类型定义
{
	VertexType vex[MaxSize][4];//相当于char[MaxSize][4],用于储存顶点
	AdjMatrix arc; // 邻接矩阵，存储边或弧的信息
	int vexnum, arcnum;//顶点数和弧的数目
	GrandKind kind;//图的定义
}MGraph;


typedef int PathMatrix[MaxSize];//保存最短路径的数组
typedef int ShortPathLength[MaxSize];//定义一个保存从顶点到V的最短距离的数组

void CreateGraph(MGraph *N);
int LocateVertex(MGraph N, VertexType *v);
void DestroyGraph(MGraph *N);
void DisplayGraph(MGraph N);
void Dijkstra(MGraph N, int v0, PathMatrix path, ShortPathLength dist);//Dijkstra算法

void PrintPath(MGraph N, int v, PathMatrix path)//递归打印路径
{
	/*if (v != 0)
	{
		printf("-%s", N.vex[path[v]]);
		PrintPath(N, path[v], path);
	}
	else
		return;*/
	
	while (v!=-1)
	{
		
			printf("%s-", N.vex[v]);
			v = path[v];
		
	}

}

int main()
{
	MGraph N;
	ShortPathLength dist;
	PathMatrix path;
	int i;

	printf("创建有向网：\n");
	CreateGraph(&N);
	DisplayGraph(N);
	//DestroyGraph(&N);
	Dijkstra(N, 0, path, dist);
	printf("顶点%s到各个顶点的最短距离：\n", N.vex[0]);
	for (i = 0; i < N.vexnum; i++)
	{
		printf("%s--%s:  dist = %d \n", N.vex[0], N.vex[i], dist[i]);
		printf("路径：");
		PrintPath(N, i, path);
		//printf("%s", N.vex[0]);
		printf("\n");
	}


	return 0;
}

void CreateGraph(MGraph *N)
//
{
	int i,j,k,weight;
	VertexType v1[4], v2[4];
	printf("请输入有向网的顶点数和弧数（以逗号分开）：\n");
	scanf_s("%d,%d", &(N->vexnum), &(N->arcnum));
	printf("请输入%d个顶点的值（<%d个字符)\n", N->vexnum, MaxSize);
	for (i = 0; i < N->vexnum; i++)//存储顶点
	{
		scanf_s("%s", N->vex[i],sizeof(N->vex[0]));
	}

	for (i = 0; i < N->vexnum; i++)// 初始化邻接矩阵
	{
		for (j = 0; j < N->vexnum; j++)
		{
			N->arc[i][j].adj = INFINITY;
			N->arc[i][j].info = NULL;
		}
	}

	printf("输入两个顶点和弧的权值（以空格隔开）：\n");
	for (k = 0; k < N->arcnum; k++)
	{
		scanf_s("%s %s %d", v1,sizeof(4), v2,sizeof(4) ,&weight);
		i = LocateVertex(*N, v1);//找到弧尾顶点的下标
		j = LocateVertex(*N, v2);//找到弧顶顶点的下标
		N->arc[i][j].adj = weight;

	}
	N->kind = DN; //类型为有向网

}

int LocateVertex(MGraph N, VertexType *v)
//定位
{
	int  i;
	for (i = 0; i < N.vexnum; i++)
	{
		if (strcmp(N.vex[i],v)== 0)
			return i;
	}
	return -1;
}

void DestroyGraph(MGraph *N)
//销毁邻接表
{
	int i, j;
	for (i = 0; i < N->vexnum; i++)
	{
		for (j = 0; j < N->vexnum; j++)
		{
			if (N->arc[i][j].info != NULL)
			{
				free(N->arc[i][j].info);
				N->arc[i][j].info = NULL;
			}
		}
	}
	N->arcnum = N->vexnum = 0;

}

void DisplayGraph(MGraph N)
//显示邻接表
{
	int i, j, k;
	printf("输出网的结点和弧：\n");
	printf("该网有%d个顶点，%d条弧\n",N.vexnum,N.arcnum);
	printf("顶点依次是：");
	for (i = 0; i < N.vexnum;i++)
	{
		printf("%s ", N.vex[i]);
	}
	printf("网：\n");
	printf("i=    ");
	for (i = 0; i < N.vexnum; i++)
	{
		printf("%8d", i);
	}
	printf("\n");
	for (i = 0; i < N.vexnum; i++)
	{
		printf("%8d", i);
		for (j = 0; j < N.vexnum; j++)
		{
			printf("%8d", N.arc[i][j].adj);
		}
		printf("\n");
	}

}

void Dijkstra(MGraph N, int v0, PathMatrix path, ShortPathLength dist)
/*在图中找到V0到各点的最小短距离路径*/
{
	int i,v,w;
	int min;//最短路径
	int collected[MaxSize];//存储顶点是否收录到S
	for (v = 0; v < N.vexnum; v++) // 初始化v0到v的距离,
	{
		if (N.arc[v0][v].adj < INFINITY)//邻接点
		{
			path[v] = 0;
			dist[v] = N.arc[v0][v].adj;
		}
		else
		{
			path[v] = -1;
			dist[v] = INFINITY;
		}
		collected[v] = 0;
	}

	collected[v0] = 1;//先将v0并入s
	dist[v0] = 0;
	//path[0] = 0;
	//开始主循环
	while (1)
	{
		v = 0;
		min = INFINITY;
		for (w = 0; w < N.vexnum ; w++) //在未收录的顶点中找到距离最小的顶点
		{
			if(collected[w] == 0)
				if (dist[w] < min)
				{
					v = w;
					min = dist[w];
				}
		}
		if (v == 0) //如果这样的v不存在
			break;
		collected[v] = 1;//将该并入s


		for (w = 0; w < N.vexnum ; w++) ////在V的邻接点中更新当前最短路径及距离
		{
			if(N.arc[v][w].adj < INFINITY)
				if (collected[w] == 0)
					if (dist[v] + N.arc[v][w].adj < dist[w])
					{
						dist[w] = dist[v] + N.arc[v][w].adj;
						path[w] = v;
					}
		}
	}
	

}