Question

Big O Exact Execution speed: Problem 2: for (int i 0 i< n; it+) Some Statement for (int j 0;j<n;j++) SomeStatement public class Countlt public long SnippetNesie d Loop (long n) long i, j.x0 i-0 x+ while (i<n) x++; xt+ isn SomeStatement i-0 j<n SomeStatement j++ x++ while (j<n) x++ x++ j++ x+ Can you explain why is this here? i+ it+x+ Can you explain why is this here? Ans: i < n retun x public static void main(Stringl] args) Countltr new Counth) Long t System.current TimeMillis0 System.out println( "x = " + rSnippet Nested Loop ( 100)); System.out.printin ("Time" + (System.curent TimeMillis()-1) Your task: Cut and paste this code into IntelliJ and using different values for the parameter (e.g., 100, 1000, 10000) graph the different times vs parameter values. Your task: Compare your return value (i.e., x = ...) to your "Exact Execution spee d:" equation see if they match. Using the space provided, graph the execution speed for each problem below use open office spread sheet (or similar program) to do so. to Time Different parameter values (N)

Determine the Big 0 provide the order (Big O) of the execution speed also determine the exact execution speed.

public class CountIt {
public long SnippetNestedLoop(long n) {

long i, j, x = 0; i=0; x++; while(i<n){ x++;

//i<n
// SomeStatement // j = 0;
// j < n
// SomeStatement // j++;

// Can you explain why is this here? // i++;

// Can you explain why is this here? Ans: i < n

} }

}
x++; return x;

x++;
j = 0; x++; while (j < n) { x++;

x++; j++; x++;

}
x++;
i++; x++;

}
public static void main(String[] args) {

CountIt r = new CountIt();
Long t = System.currentTimeMillis();
System.out.println("x = " + r.SnippetNestedLoop(100)); System.out.println ("Time:" + (System.currentTimeMillis() - t));

Answer 1

Problem 2)

The outer loop for i runs n times and the inner loop for j runs n times for each i.

Hence, the total time complexity of this code snippet is O(n²).

Similarly, the time taken by the class CountIt is given as:

T(n) = n² + C where C is a positive constant

Hence, T(n) = O(n²)

The execution speed of this code is given as:

x = 30502

Time:1