Task $0$: #include

#include

#include

#include

using namespace std;

typedef pair iPair;

void addEdge$($vector$>$ adj$[],$ int u$,$ int v$,$ int wt$)\{$

adj$[$u$].$push$\_$back$(\{$v$,$ wt$\})$;

adj$[$v$].$push$\_$back$(\{$u$,$ wt$\})$; $//$ for undirected graph

$\}$

void shortestPath$($vector$>$ adj$[],$ int V$,$ int src$)\{$

$//$ Initialize priority queue to store vertices with their distances

priority$\_$queue, greater$>$ pq;

$//$ Initialize distances array to store shortest distances from source

vector dist$($V$,$ numeric$\_$limits::max$())$;

$//$ Insert source vertex into priority queue with distance $0$

pq$.$push$(\{0,$ src$\})$;

dist$[$src$]=0$;

$//$ Dijkstra's algorithm

while $(!$pq$.$empty$())\{$

$//$ Extract the vertex with the minimum distance from the priority queue

int u $=$ pq$.$top$().$second;

pq$.$pop$()$;

$//$ Update distances of adjacent vertices

for $($auto& edge : adj$[$u$])\{$

int v $=$ edge.first;

int weight $=$ edge.second;

$//$ If a shorter path is found, update the distance and insert vertex into priority queue

if $($dist$[$u$]+$ weight $$ dist$[$v$])\{$

dist$[$v$]=$ dist$[$u$]+$ weight;

pq$.$push$(\{$dist$[$v$],$ v$\})$;

$\}$

$\}$

$\}$

$//$ Output shortest paths from source vertex to all other vertices

cout $$ "Shortest paths from source vertex $"$ src to all other vertices:

$"$;

for $($int i $=0$; i $$ V; $++$i$)\{$

cout $$ "Vertex $"$ i : Distance $="$ dist$[$i

$"$;

$\}$

$\}$

int main$()\{$

$//$ Graph representation

vector$>$ adj$[6]$;

addEdge$($adj$,0,1,2)$;

addEdge$($adj$,0,2,4)$;

addEdge$($adj$,1,2,1)$;

addEdge$($adj$,1,3,7)$;

addEdge$($adj$,2,4,3)$;

addEdge$($adj$,3,4,2)$;

addEdge$($adj$,3,5,1)$;

addEdge$($adj$,4,5,5)$;

$//$ Source vertex

int src $=0$;

$//$ Number of vertices

int V $=6$;

$//$ Find shortest paths from source vertex

shortestPath$($adj$,$ V$,$ src$)$;

return $0$;

$\}$