# Question: question 01 complexity analysis consider the following method one public...

###### Question details

**Question 01: Complexity
Analysis**

**Consider the following method
one.**

public static int one(int n){

int x = 0;

for(int i=n*n; i > 0; i/=2){

if(i < n )

x += two(i); //statement 1

else for(int j= i; j<=i; j++)

x += i*j;

x += three(i);

}

return x;

}

public static int two(int n){

int x = 0;

for(int i = n; i > n / 2; i--)

x ++; //statement 2

return n+x;

}

public static int three(int n){

int x = 0;

for(int i = 1; i < 500 ; i*=2)

x ++; //statement 3

return n+x;

}

It is assumed that each simple instruction such as addition, multiplication, division, comparison and assignment is O(1).

** **

- Count the number of times
*statement1*,*statement2*and*statement3*get executed in terms of the input number*n*. - Express the overall cost of method one as a function
*f*(*n*), where*n*is the problem size, by finding the cost of the most expensive operation. Clearly indicate that most expensive operation. - Determine the Big-O() time complexity of method one.