最短路径——Dijkstra算法

最新推荐文章于 2024-08-17 15:22:06 发布

原创最新推荐文章于 2024-08-17 15:22:06 发布 · 332 阅读

0 ·

CC 4.0 BY-SA版权

数据结构与算法专栏收录该内容

20 篇文章

订阅专栏

本文介绍了一个使用C++实现的Dijkstra最短路径算法。通过定义一个图类`MyGraph`来存储顶点和边，并利用Dijkstra算法计算从指定起点到其他所有顶点的最短路径。代码中详细展示了如何初始化图、读取边权重以及如何应用Dijkstra算法进行路径计算。

/*
0 1 10
0 3 30
0 4 100
3 4 60
3 2 20
1 2 50
2 4 10
*/
//Geeksun 2018.06.20
#include <iostream>
#include <String>
using namespace std;

const int maxSize = 10;
const int maxNum = 99999;
class MyGraph
{
public:
	MyGraph(char str[], int vertexNum, int arcNum);
	~MyGraph() {};
	friend void Dijstra(MyGraph G, int v);
private:
	int arc[maxSize][maxSize];
	string vertex[maxSize];
	int vertexNum, arcNum;
};
MyGraph::MyGraph(char str[], int vertexNum, int arcNum)
{
	this->arcNum = arcNum;
	this->vertexNum = vertexNum;
	for (int i = 0;i < vertexNum;i++)
	{
		vertex[i] = str[i];
	}
	for (int i = 0;i < maxSize;i++)
	{
		for (int j = 0;j < maxSize;j++)
		{
			if (i == j)
			{
				arc[i][j] = 0;
			}
			else
			{
				arc[i][j] = maxNum;
			}
		}
	}
	for (int k = 0;k < arcNum;k++)
	{
		int i, j, weight;
		cin >> i >> j >> weight;
		arc[i][j] = weight;
	}
}
void Dijstra(MyGraph G, int v)
{
	int num = 1;
	string path[maxSize];
	int S[maxSize];
	int dist[maxSize];
	for (int i = 0;i < G.vertexNum;i++)
	{
		dist[i] = G.arc[v][i];
		if (dist[i] != maxNum)
		{
			path[i] = G.vertex[v] + "->" + G.vertex[i];
			cout << path[i] << "----" << dist[i] << endl;
		}
		else
		{
			path[i] = "";
		}
	}
	S[0] = v;
	dist[v] = maxNum;
	int i, k;
	while (num < G.vertexNum)
	{
		for (i = 0, k = 0;i < G.vertexNum;i++)
		{
			if (dist[i] < dist[k] && dist[i] != 0)
			{
				k = i;
			}
		}
		S[num++] = k;
		for (int i = 0;i < G.vertexNum;i++)
		{
			if (dist[i] > dist[k] + G.arc[k][i])
			{
				dist[i] = dist[k] + G.arc[k][i];
				path[i] = path[k] + "->" + G.vertex[i];
				cout << path[i] << "----" << dist[i] << endl;
			}
		}
		dist[k] = 0;
	}
}
int main()
{
	char vertex[6] = "01234";
	MyGraph myGraph(vertex, 5, 7);
	Dijstra(myGraph, 0);
	return 0;
}