图的最短路径问题

#include<iostream>
#include<cstring>
using namespace std;
#define MaxInt 32767
#define MVNum 100
typedef char VerTexType[20];
typedef int ArcType;
int Path[MVNum][MVNum];
int D[MVNum][MVNum];
typedef struct {
	VerTexType vexs[MVNum];
	ArcType arcs[MVNum][MVNum];
	int vexnum, arcnum;
}AMGraph;
int LocateVex(AMGraph G, VerTexType v)
{
	for (int i = 0; i < G.vexnum; i++)
	{
		if (!strcmp(G.vexs[i], v))
		{
			return i;
		}
	}
	return -1;
}
void CreateUDN(AMGraph& G)
{
	cout << "请输入总标志点数，总可通道路数：";
	cin >> G.vexnum >> G.arcnum;
	cout << "输入标志点的名称" << endl;
	for (int i = 0; i < G.vexnum; i++)
	{
		cout << "请输入第" << i + 1 << "个标志点的名称：";
		cin >> G.vexs[i];
	}
	cout << endl;
	for (int i = 0; i < G.vexnum; i++)
	{
		for (int j = 0; j < G.vexnum; j++)
		{
			if (j != i)
			{
				G.arcs[i][j] = MaxInt;
			}
			else
			{
				G.arcs[i][j] = 0;
			}
		}
	}
	cout << "输入道路依附的标志点及权值" << endl;
	for (int k = 0; k < G.arcnum; k++)
	{
		VerTexType v1, v2;
		ArcType w;
		cout << "请输入第" << k + 1 << "条道路依附的标志点及路长：";
		cin >> v1 >> v2 >> w;
		int i = LocateVex(G, v1);
		int j = LocateVex(G, v2);
		G.arcs[i][j] = G.arcs[j][i] = w;
	}

}
void ShortestPath_Floyed(AMGraph G)
{
	for (int i = 0; i < G.vexnum; i++)
	{
		for (int j = 0; j < G.vexnum; j++)
		{
			D[i][j] = G.arcs[i][j];
			if (D[i][j] < MaxInt && i != 1)
			{
				Path[i][j] = 1;  //如果i和j之间有弧，则将j的前驱置为i
			}
			else
			{
				Path[i][j] = -1;  //如果i和j之间无弧，则将j的前驱置为-1
			}
		}
	}
	for (int k = 0; k < G.vexnum; k++)
	{
		for (int i = 0; i < G.vexnum; i++)
		{
			for (int j = 0; j < G.vexnum; j++)
			{
				if (D[i][k] + D[k][j] < D[i][j])  //从i经k到j的一条路径更短
				{
					D[i][j] = D[i][k] + D[k][j];
					Path[i][j] = Path[k][j];  
				}
			}
		}
	}
}
void DisplayPath(AMGraph G, int begin, int temp)
{
	if (Path[begin][temp] != -1)
	{
		DisplayPath(G, begin, Path[begin][temp]);
		cout << G.vexs[Path[begin][temp]] << "-->";
	}
}
int main()
{
	cout << "***********图及其应用(校园导航)**********" << endl;
	AMGraph G;
	char start[20], destination[20];
	int num_start, num_destination ;
	CreateUDN(G);
	ShortestPath_Floyed(G);
	cout << "请依次输入路径的起点与终点的名称：";
	cin >> start >> destination;
	num_start = LocateVex(G, start);
	num_destination = LocateVex(G, destination);
	DisplayPath(G, num_start, num_destination);
	cout << G.vexs[num_destination] << endl;
	cout << "最短路径的长度为：" << D[num_start][num_destination] << endl;
	return 0;
}

标签：vexnum,cout,int,路径,MVNum,问题,++,Path
来源： https://blog.csdn.net/weixin_54418006/article/details/122016497