图相关算法-最短路径

迪杰斯特拉算法（D算法）

#include<iostream>
#include<vector>
#include<limits>
using namespace std;
void ShortestPath_Dijkstra(vector<vector<int>>& arc, int numVex, vector<int>& Patharc, vector<int>& ShortPath)
{
	int k=0, MIN=INT_MAX;
	vector<bool>flag(numVex);
	for (int i = 0; i < numVex; i++)
	{
		flag[i] = false;
		ShortPath[i] = arc[0][i];
	}
	flag[0] = true;
	ShortPath[0] = 0;
	for (int v = 1; v < numVex; v++)
	{
		MIN = INT_MAX;
		for (int j = 0; j < numVex; j++)
		{
			if (!flag[j] && ShortPath[j] < MIN)
			{
				MIN = ShortPath[j];
				k = j;
			}
		}
		flag[k] = true;
		for (int i = 0; i < numVex; i++)
		{
			if (!flag[i] && arc[k][i] != INT_MAX && (arc[k][i] + MIN) < ShortPath[i])
			{
				ShortPath[i] = arc[k][i] + MIN;
				Patharc[i] = k;
			}
		}
	}
	
}
int main()
{
	//创建图
	int numVex,numEdge;
	cout << "请输入图中的点数和边数：" << endl;
	cin >> numVex >> numEdge;
	vector<vector<int>>arc(numVex, vector<int>(numVex,INT_MAX));
	cout << "请输入变得信息：" << endl;
	for (int i = 0; i < numEdge; i++)
	{
		int e1, e2, weight;
		cin >> e1 >> e2 >> weight;
		arc[e1][e2] = weight;
		arc[e2][e1] = weight;
	}
	//寻找顶点0到其他顶点的最短距离
	vector<int>Patharc(numVex);
	vector<int>ShortPath(numVex);
	ShortestPath_Dijkstra(arc, numVex, Patharc, ShortPath);
	for (int i = 1; i < numVex; i++)
	{
		cout << "节点0到节点" << i << "的最短路径为：" << ShortPath[i] << endl;
	}
	return 0;
}

• 弗洛伊德算法（F算法）

  #include<iostream>
  #include<vector>
  #define MAX 0x0f0f0f0f
  using namespace std;
  void ShortestPath_Floyd(int numVex,vector<vector<int>>& D, vector<vector<int>>& P)
  {
  	for (int k = 0; k < numVex; k++)
  	{
  		for (int v = 0; v < numVex; v++)
  		{
  			for (int w = 0; w < numVex; w++)
  			{
  				if (D[v][w] > D[v][k] + D[k][w])
  				{
  					D[v][w] = D[v][k] + D[k][w];
  					P[v][w] = P[v][k];
  				}
  			}
  		}
  	}
  }
  int main()
  {
  	int numVex, numEdge;
  	cout << "请输入图中的点数和边数：" << endl;
  	cin >> numVex >> numEdge;
  	vector<vector<int>>D(numVex, vector<int>(numVex, MAX));
  	vector<vector<int>>P(numVex, vector<int>(numVex));
  	cout << "请输入边的信息：" << endl;
  	for (int i = 0; i < numEdge; i++)
  	{
  		int e1, e2, weight;
  		cin >> e1 >> e2 >> weight;
  		D[e1][e2] = weight;
  		D[e2][e1] = weight;
  	}
  	for (int v = 0; v < numVex; v++)
  	{
  		D[v][v] = 0;
  		for (int w = 0; w < numVex; w++)
  		{
  			P[v][w] = w;
  		}
  	}
  	//F算法 （寻找各个顶点之间的最短距离）
  	ShortestPath_Floyd(numVex,D, P);
  	cout << "各个顶点之间的最短距离为：" << endl;
  	for (int i = 0; i < numVex; i++)
  	{
  		for (int j = 0; j < numVex; j++)
  		{
  			cout << D[i][j] << " ";
  		}
  		cout << endl;
  	}
  	return 0;
  }