Experimental analysis for prefixAverage1:

With the reference to the textbook, the prefixAverage1 algorithm computes the prefix averages in quadratic time O(n2). Now let us take the given algorithm from the textbook for analysis to draw the visualization representation as follows:

Algorithm: prefixAverage1(X,n)

Input: array x on n integers

Output: Array A of prefix averages of X

//Line1

A<- new array of n integers

//Line2

for i<-0 to n-1 do

//Line3

S<-X[0]

//Line4

for j<-1 to i do

//Line5

S<-S+X[j]

// Line6

A[i]<-s/(i+1)

//Line7

return A

Explanation:

In the above algorithm,

• The Line1 is to initialize the array of "n" integers and it takes O(n) time.
• Next the Line2 is the outer for loop which act as counter and executed "n" number of times and it takes O(n) times to complete the loop.
• The Line3 is assigning the initial element of array to variable "s" and this executes in O(n) time.
• Line4 is the inner body of for loop executes based on the outer for loop and it follows sum up operation such as 1+2+3+...(n-1). So, this line executes in O(n2) time.
• Similar to Line4 and Line 5 follows same running time O(n2) because it performs sum up operation inside the for loop.
• On Line6, it calculates the averages for the sum of elements and this is executed in O(n) time because the operation is directly proportional.
• On Line7, the value is returned and it is executed in constant time O(1).

Visualization representation of algorithm prefixAverage1 in log-log graph:

As the running time of prefixAverage1 is O(1+2+...+n) and the sum of first "n" integers is n(n+1)2