C++最短路径Dijkstra算法的分析与具体实现详解

  #define MAXVERTEX 6
  bool final[MAXVERTEX];
  int dist[MAXVERTEX];
  int path[MAXVERTEX];

#include<iostream>
using namespace std;
// 模拟实现Dijkstra算法，不适用于存在负值的带权图
#define MAXVERTEX 6
typedef struct {
	char Vertex[MAXVERTEX]; //顶点集
	int Edge[MAXVERTEX][MAXVERTEX]; // 存放权值
	int vernum, arcnum; // 顶点数和边数
}MGraph;

// 初始化图
void InitGraph(MGraph& G) {
	G.Vertex[0] = 'A';
	G.Vertex[1] = 'B';
	G.Vertex[2] = 'C';
	G.Vertex[3] = 'D';
	G.Vertex[4] = 'E';
	G.vernum = 5;
	G.arcnum = 10;

	// 图中边权值均设为无穷大
	for (int i = 0; i < G.vernum; i++) {
		for (int j = 0; j < G.vernum; j++) {
			G.Edge[i][j] = INT_MAX;
		}
	}
	// 根据具体图形设置具体权值
	G.Edge[0][1] = 10; // 诸如此类
	G.Edge[0][4] = 5;
	G.Edge[1][2] = 1;
	G.Edge[1][4] = 2;
	G.Edge[4][1] = 3;
	G.Edge[2][3] = 4;
	G.Edge[3][2] = 6;
	G.Edge[4][3] = 2;
	G.Edge[3][0] = 7;
	G.Edge[4][2] = 9;
}
bool final[MAXVERTEX];
int dist[MAXVERTEX];
int path[MAXVERTEX];

void Dijkstra(MGraph G,int v) {
	for (int i = 0; i < G.vernum; i++) {
		final[i] = false;
		dist[i] = G.Edge[v][i];
		path[i] = (G.Edge[v][i] == INT_MAX ? -1 : v);
	}
	final[v] = true;
	dist[v] = 0;
	// 第一轮
	int index =v; // 权值最小的边顶点下标
	int para = INT_MAX;
	for (int j = 0; j < G.vernum; j++) {
		if (final[j] == false && G.Edge[v][j] < para) {
			para = G.Edge[v][j];
			index = j;
		}
	}
	// 第二轮及以后
	for (int i = 0; i < G.vernum; i++) {
		for (int c = 0; c < G.vernum; c++) {
			if (final[c] ==false && G.Edge[index][c] < INT_MAX) {
				if (G.Edge[index][c] + dist[index] < dist[c]) {
					dist[c] = G.Edge[index][c] + dist[index];
					path[c] = index;
				}
			}
		}
		// 找到final 为false的顶点中权值最小的顶点下标
		int temp = INT_MAX;
		int in = v;
		for (int i = 0; i < G.vernum; i++) {
			if (final[i] == false && dist[i] < temp) {
				temp = dist[i];
				in = i;
			}
		}
		index = in; // 更新下标
		final[index] = true;
	}
}

void print_path(MGraph G ,int v) {
	cout << "对应的最短路径为：";
	cout << G.Vertex[v] << "->";
	for (int i = 0; i < G.vernum; i++) {
		if (path[v] != 1) {
			cout << G.Vertex[path[v]] << "->";
			v = path[v];
		}
	}
	cout << G.Vertex[1] << endl;
}

int main() {
	MGraph G;
	InitGraph(G);
	Dijkstra(G, 1);
	cout << "顶点B到顶点D的最小花费为："<< dist[3] << endl;
	print_path(G, 3);
}

Dijkstra(G,0);
// dist[2];
cout<<"顶点A到顶点C的最短路径为"<<dist[2]<<endl;
void print_path(MGraph G ,int v) {
	cout << "对应的最短路径为：";
	cout << G.Vertex[v] << "->";
	for (int i = 0; i < G.vernum; i++) {
		if (path[v] != 0) {
			cout << G.Vertex[path[v]] << "->";
			v = path[v];
		}
	}
	cout << G.Vertex[0] << endl;
}