Implementing Dijkstra Algorithm

Medium

Given a weighted, undirected and connected graph of V vertices and an adjacency list adj where adj[i] is a list of lists containing two integers where the first integer of each list j denotes there is edge between i and j , second integers corresponds to the weight of that  edge . You are given the source vertex S and You to Find the shortest distance of all the vertex's from the source vertex S. You have to return a list of integers denoting shortest distance between each node and Source vertex S.
 

Note: The Graph doesn't contain any negative weight cycle.

 

Example 1:

Input:
V = 2
adj [] = {{{1, 9}}, {{0, 9}}}
S = 0
Output:
0 9
Explanation:

The source vertex is 0. Hence, the shortest 
distance of node 0 is 0 and the shortest 
distance from node 1 is 9.

 

Example 2:

Input:
V = 3, E = 3
adj = {{{1, 1}, {2, 6}}, {{2, 3}, {0, 1}}, {{1, 3}, {0, 6}}}
S = 2
Output:
4 3 0
Explanation:

For nodes 2 to 0, we can follow the path-
2-1-0. This has a distance of 1+3 = 4,
whereas the path 2-0 has a distance of 6. So,
the Shortest path from 2 to 0 is 4.
The shortest distance from 0 to 1 is 1 .

 

Your Task:
You don't need to read input or print anything. Your task is to complete the function dijkstra()  which takes the number of vertices V and an adjacency list adj as input parameters and Source vertex S returns a list of integers, where ith integer denotes the shortest distance of the ith node from the Source node. Here adj[i] contains a list of lists containing two integers where the first integer j denotes that there is an edge between i and j and the second integer w denotes that the weight between edge i and j is w.

 

Expected Time Complexity: O(V²).
Expected Auxiliary Space: O(V²).

 

Constraints:
1 ≤ V ≤ 1000
0 ≤ adj[i][j] ≤ 1000

1 ≤ adj.size() ≤ [ (V*(V - 1)) / 2 ]
0 ≤ S < V