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Example: Computing Prefix Averages (cont)

A quadratic alogrithm to compute prefix averages: 

prefixAverages1(X):
|  Input  array X of n integers
|  Output array A of prefix averages of X
|
|  for all i=0..n-1 do          O(n)
|  |  s=X[0]                    O(n)
|  |  for all j=1..i do         O(n2)
|  |     s=s+X[j]               O(n2)
|  |  end for
|  |  A[i]=s/(i+1)              O(n)
|  end for
|  return A                     O(1)

2·O(n2) + 3·O(n) + O(1) = O(n2)

⇒ Time complexity of algorithm prefixAverages1 is O(n2)