C++ implements Dijkstra algorithm to solve the shortest path

1. Principle steps

1. Find the direct path from the source point v0 to other points, record it in the dist array, dist[i] represents the distance from v0 to vi. If there is no direct access from v0 to vi, record dist[i] as infinity Max.

2. Find the point u in the dist array that has not been visited and has the shortest distance from v0.

3. Update the dist array through u. If the distance from v0 to vi through u is smaller than dist[i], update dist[i] to dist[u]+edge[u][i];

4. Continue with steps 2 and 3 for n-1 times. At this time, dist[i] represents the shortest distance from v0 to vi.

2. Examples

As shown in the figure, find the shortest path from v0 to other points. First initialize the dist array, dist[1] = 13, dist[2] = 18, dist[3] = Max, dist[4] = 30, dist[5] = Max, dist[6] = 32;

Find the shortest edge, dist[2]=8, compare the distance from v0 to vi and from v0 to v2 and then to vi, update dist[i], because dist[2] + edge[2][3] = 8 + 5 = 13 <dist[3] = Max, so dist[3] is updated to 13.

Continue to find the shortest edge, dist[1] = 13, compare the distance from v0 to vi and from v0 through v1 to vi, update dist[i], because dist[1] + edge[1][5] = 13 +9 = 22 <dist[5] = Max, so dist[5] is updated to 22. In the same way, dist[6] is updated to 20;

Continue the operation until n-1 times, and the algorithm ends.

3. Code implementation

#include<iostream>
using namespace std;
#define Max 9999

int n, m;
bool visited[Max];
int edge[Max][Max];
int dist[Max];

void Dijkstra()
{
    
    
	visited[0] = true;
	int min = Max;
	int index = 0;
	for (int i = 0; i < n-1; ++i)
	{
    
    
		min = Max;
		for (int j = 0; j < n; ++j)
		{
    
    
			if (!visited[j] && dist[j] < min) //寻找最短边
			{
    
    
				min = dist[j];
				index = j;
			}
		}
		visited[index] = true;
		for (int j = 0; j < n; ++j)
		{
    
    
			if (!visited[j] && dist[index] + edge[index][j] < dist[j])  //比较从v0经过u再到达vi的距离和dist[i]的大小
			{
    
    
				dist[j] = dist[index] + edge[index][j];
			}
		}
	}

	for (int i = 1; i < n; ++i)
	{
    
    
		cout << dist[i] << " ";
	}
}

int main()
{
    
    
	cout << "输入节点数: ";
	cin >> n;
	cout << "输入边数：";
	cin >> m;
	fill(edge[0], edge[0] + Max*Max, Max); //初始化各个数组
	fill(dist, dist + n, Max);
	fill(visited, visited + n, false);
	int u, v, w;
	cout << "输入各条边的信息：" << endl;
	for (int i = 0; i < m; ++i)
	{
    
    
		cin >> u >> v >> w;
		edge[u][v] = edge[v][u] = w;
	}
	dist[0] = 0;
	for (int i = 1; i < n; ++i)  //初始化从v0到其他各点的距离
	{
    
    
		dist[i] = edge[0][i];
	}

	Dijkstra();
	return 0;
}

Input and output information: