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Help analyzing how many times each step is executed.
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So I'm trying to figure out how many times each step in this algorithm is executed as a function of n.

for i =1 to n do
    for j = 1 to n do
        D[i,j] = 0
        for k = 1 to n do 
            D[i,j] = D[i,j]   D[i,k]
        end for
    end for
end for

Now I was able to come up with following answer:

 for i =1 to n do                      #n 1
    for j = 1 to n do                  #n(n 1)
        D[i,j] = 0                     #n^2
        for k = 1 to n do              #(n^2 n)*(n 1)
            D[i,j] = D[i,j]   D[i,k]   #n^3
        end for                        #n^3
    end for                            #n^2
end for                                #n

Does this seem right? I feel as if I am missing something.

Note I am not trying to get a general formula, but am trying to find out how many times EACH line is executed relative to n

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9 years ago