Write down dijkstra''s algorithm, Basic Computer Science

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QUESTION

(a) Write down the Update Step in the Dijkstra's algorithm explaining its complexity.

(b) Propose a Generic Algorithm for Depth-First Search Algorithm, assuming the Initialisation procedure has already been implemented.

(c) Below is the algorithm of a flow decomposition algorithm.

begin

Initialize

while y ≠Ø do

begin

Select(s, y)

Search(s, y)

if a cycle C is found then do

begin

let D = Capacity(C, y)

Add Flow(D, C) to cycle flows

Subtract Flow(D, C) from y.

end

if a path P is found then do

begin

let D = Capacity(P, y)

Add Flow(D, P) to path flows

Subtract Flow(D, P) from y.

end

end

Describe the complexity of the following:

i) Selecting the initial node,

ii) Finding a cycle or a path,

iii) Update step.

(c) Write down Dijkstra's Algorithm, clearly indicating the variables used.


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