+1 vote
636 views

I read that the space complexity of Dijasktra is $O(V^2)$ . (http://igraph.wikidot.com/algorithm-space-time-complexity)

But how ????

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+1
In worst case, it is a complete graph and have to visit every edge

So, space complexity will be $\binom{v}{2}=\frac{v(v-1)}{2}=\theta \left ( v^{2}\right )$
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Yeah,  when the graph is complete then we use adjacency matrix which gives O(v^2)
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@amitpandey675 - No, the adjacency matrix is given as an input to the algorithm, so it would not be considered in the calculation of space complexity.
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@ hardik NO

when you calculate space complexity you add both input and extra space in total taken...here Space complexity=input space+extra space= O(V^2)+O(1)=O(V^2).

why O(V^2) in above comments its explained.
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@Shubham Shukla - The input space is not considered while calculating space complexity.
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@ hardik

can you show me where it is written.?
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Both input and extra space taken by the algorithm during its running time is considered during calculating the time complexities

In the worst case scenario,i.e. in a complete graph, no. of edges become v(v-1)/2 i.e e~v^2.

Now,even with adjacency list implementation,which takes O(V + E),as E~V^2 , O(V+E)~O(V^2).
by Junior (909 points)
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It is wrong. It will be O(V).