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How can I uderstand dijkstra algorithm

Member 11879193 asked:

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// A C# program for Dijkstra's single 
// source shortest path algorithm. 
// The program is for adjacency matrix 
// representation of the graph 
using System; 
  
class GFG { 
    // A utility function to find the 
    // vertex with minimum distance 
    // value, from the set of vertices 
    // not yet included in shortest 
    // path tree 
    static int V = 9; 
    int minDistance(int[] dist, 
                    bool[] sptSet) 
    { 
        // Initialize min value 
        int min = int.MaxValue, min_index = -1; 
  
        for (int v = 0; v < V; v++) 
            if (sptSet[v] == false && dist[v] <= min) { 
                min = dist[v]; 
                min_index = v; 
            } 
  
        return min_index; 
    } 
  
    // A utility function to print 
    // the constructed distance array 
    void printSolution(int[] dist) 
    { 
        Console.Write("Vertex \t\t Distance "
                      + "from Source\n"); 
        for (int i = 0; i < V; i++) 
            Console.Write(i + " \t\t " + dist[i] + "\n"); 
    } 
  
    // Funtion that implements Dijkstra's 
    // single source shortest path algorithm 
    // for a graph represented using adjacency 
    // matrix representation 
    void dijkstra(int[, ] graph, int src) 
    { 
        int[] dist = new int[V]; // The output array. dist[i] 
        // will hold the shortest 
        // distance from src to i 
  
        // sptSet[i] will true if vertex 
        // i is included in shortest path 
        // tree or shortest distance from 
        // src to i is finalized 
        bool[] sptSet = new bool[V]; 
  
        // Initialize all distances as 
        // INFINITE and stpSet[] as false 
        for (int i = 0; i < V; i++) { 
            dist[i] = int.MaxValue; 
            sptSet[i] = false; 
        } 
  
        // Distance of source vertex 
        // from itself is always 0 
        dist[src] = 0; 
  
        // Find shortest path for all vertices 
        for (int count = 0; count < V - 1; count++) { 
            // Pick the minimum distance vertex 
            // from the set of vertices not yet 
            // processed. u is always equal to 
            // src in first iteration. 
            int u = minDistance(dist, sptSet); 
  
            // Mark the picked vertex as processed 
            sptSet[u] = true; 
  
            // Update dist value of the adjacent 
            // vertices of the picked vertex. 
            for (int v = 0; v < V; v++) 
  
                // Update dist[v] only if is not in 
                // sptSet, there is an edge from u 
                // to v, and total weight of path 
                // from src to v through u is smaller 
                // than current value of dist[v] 
                if (!sptSet[v] && graph[u, v] != 0 && dist[u] != int.MaxValue && dist[u] + graph[u, v] < dist[v]) 
                    dist[v] = dist[u] + graph[u, v]; 
        } 
  
        // print the constructed distance array 
        printSolution(dist); 
    } 
  
    // Driver Code 
    public static void Main() 
    { 
        int[, ] graph = new int[, ] { { 0, 4, 0, 0, 0, 0, 0, 8, 0 }, 
                                      { 4, 0, 8, 0, 0, 0, 0, 11, 0 }, 
                                      { 0, 8, 0, 7, 0, 4, 0, 0, 2 }, 
                                      { 0, 0, 7, 0, 9, 14, 0, 0, 0 }, 
                                      { 0, 0, 0, 9, 0, 10, 0, 0, 0 }, 
                                      { 0, 0, 4, 14, 10, 0, 2, 0, 0 }, 
                                      { 0, 0, 0, 0, 0, 2, 0, 1, 6 }, 
                                      { 8, 11, 0, 0, 0, 0, 1, 0, 7 }, 
                                      { 0, 0, 2, 0, 0, 0, 6, 7, 0 } }; 
        GFG t = new GFG(); 
        t.dijkstra(graph, 0); 
    } 
} 


What I have tried:

Please, someone understand this many zeros in "graph"?
I´m seeing many videos of this algorithm, but i can figure out what are those zeros.
Can somebody help me?
Tags: C#, Algorithms

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