## C++ Program to Find the Shortest Path from Source Vertex to All Other Vertices in Linear Time using Dijkstra’a Shortestpath algorithm

C++ Program to find the shortest path in linear time. This can be done by using Dijkstra’a Shortest path algorithm. Here is source code of the C++ Program to Find the Shortest Path from Source Vertex to All Other Vertices in Linear Time. The C++ program is successfully compiled and run on a Linux system. The program output is also shown below…
``#include <stdio.h>#include <limits.h>#include <iostream> using namespace std; // Number of vertices in the graph#define V 9 // A utility function to find the vertex with minimum distance value, from// the set of vertices not yet included in shortest path treeint minDistance(int dist[], bool sptSet[]){    // Initialize min value    int min = INT_MAX, min_index;     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 arrayint printSolution(int dist[], int n){    cout << "Vertex   Distance from Sourcen";    for (int i = 0; i < V; i++)        printf("%d tt %dn", i, dist[i]);} // Funtion that implements Dijkstra's single source shortest path algorithm// for a graph represented using adjacency matrix representationvoid dijkstra(int graph[V][V], int src){    int dist[V]; // The output array.  dist[i] will hold the shortest    // distance from src to i     bool sptSet[V]; // sptSet[i] will true if vertex i is included in shortest    // path tree or shortest distance from src to i is finalized     // Initialize all distances as INFINITE and stpSet[] as false    for (int i = 0; i < V; i++)        dist[i] = INT_MAX, 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] && dist[u] != INT_MAX && dist[u]                    + graph[u][v] < dist[v])                dist[v] = dist[u] + graph[u][v];    }     // print the constructed distance array    printSolution(dist, V);} int main(){    int graph[V][V] =            { { 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, 0, 10, 0, 2, 0, 0 }, { 0, 0, 0, 14,                            0, 2, 0, 1, 6 }, { 8, 11, 0, 0, 0, 0, 1, 0, 7 }, {                            0, 0, 2, 0, 0, 0, 6, 7, 0 } };     dijkstra(graph, 0);     return 0;}``

`Output:\$ g++ LinearTimeShortestPath.cpp\$ a.out Vertex   Distance from Source0    01    42    123    194    215    116    97    88    14 ------------------(program exited with code: 0)Press return to continue`
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