Silver-Hat

tfgjfghjtfg gdfgd htfghftgtj India Djiktra's theoram-shortest path

Djiktra's algorithm

Dijkstra doesn’t work for Graphs with negative weight edges, Bellman-Ford works for such graphs.

import java.util.; import java.lang.; import java.io.*;

class ShortestPath {

static final int V = 9; 
int minDistance(int dist[], Boolean sptSet[]) 
{ 
  
    int min = Integer.MAX_VALUE, 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; 
} 

void printSolution(int dist[]) 
{ 
    System.out.println("Vertex \t\t Distance from Source"); 
    for (int i = 0; i < V; i++) 
        System.out.println(i + " \t\t " + dist[i]); 
} 

void dijkstra(int graph[][], int src) 
{ 
    int dist[] = new int[V]; // The output array. dist[i] will hold 

    Boolean sptSet[] = new Boolean[V]; 

    for (int i = 0; i < V; i++) { 
        dist[i] = Integer.MAX_VALUE; 
        sptSet[i] = false; 
    } 

    dist[src] = 0; 

    for (int count = 0; count < V - 1; count++) { 
     
        int u = minDistance(dist, sptSet); 

        
        sptSet[u] = true; 

      
        for (int v = 0; v < V; v++) 

        
            if (!sptSet[v] && graph[u][v] != 0 && dist[u] != Integer.MAX_VALUE && dist[u] + graph[u][v] < dist[v]) 
                dist[v] = dist[u] + graph[u][v]; 
    } 

    printSolution(dist); 
}

class Graph {

class Edge { 
    int src, dest, weight; 
    Edge() 
    { 
        src = dest = weight = 0; 
    } 
}; 

int V, E; 
Edge edge[]; 

Graph(int v, int e) 
{ 
    V = v; 
    E = e; 
    edge = new Edge[e]; 
    for (int i = 0; i < e; ++i) 
        edge[i] = new Edge(); 
} 


void BellmanFord(Graph graph, int src) 
{ 
    int V = graph.V, E = graph.E; 
    int dist[] = new int[V]; 


    for (int i = 0; i < V; ++i) 
        dist[i] = Integer.MAX_VALUE; 
    dist[src] = 0; 


    for (int i = 1; i < V; ++i) { 
        for (int j = 0; j < E; ++j) { 
            int u = graph.edge[j].src; 
            int v = graph.edge[j].dest; 
            int weight = graph.edge[j].weight; 
            if (dist[u] != Integer.MAX_VALUE && dist[u] + weight < dist[v]) 
                dist[v] = dist[u] + weight; 
        } 
    } 

   
    for (int j = 0; j < E; ++j) { 
        int u = graph.edge[j].src; 
        int v = graph.edge[j].dest; 
        int weight = graph.edge[j].weight; 
        if (dist[u] != Integer.MAX_VALUE && dist[u] + weight < dist[v]) { 
            System.out.println("Graph contains negative weight cycle"); 
            return; 
        } 
    } 
    printArr(dist, V); 
} 
void printArr(int dist[], int V) 
{ 
    System.out.println("Vertex Distance from Source"); 
    for (int i = 0; i < V; ++i) 
        System.out.println(i + "\t\t" + dist[i]); 
} 

Dijkstra doesn’t work for Graphs with negative weight edges, Bellman-Ford works for such graphs.