big theta algorithm analysis

prove a big theta bound for the algorithm below:

function F(n) begin

array A[1:n,1:n]

for i := 1 to n do

A[i, i] := 0

for m := 2 to n do

for i := 1 to n − m + 1 do begin

j := i + m – 1

A[i,j] := ∞
for k := i to j – 1 do

A[i, j] := min A[i, j], A[i, k] + A[k + 1, j] + ijk

end

return A[1, n]

end

Solution:

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