Question

Provide the Big‐O notation for the following lines of Java code, make sure you include all the necessary steps to reach your answer to receive any credit:

a. for (i = 10; i < n – 8; i++)

{

for( j = 1; j < m; j *= 2)

x = i + j;

}

b. for(k = 0; k <= m; k += 2)

{

l = 0;

while(l < n/2)

{ y = l * 4 – x; l++; }

}

c. k = n;

while (k > 1)

{

for(j = 4; j < n; j++) ;

for(i = 1; i <= n; i++)

{

System.out.println(i+k);

z = i * k;

}

k /= 2;

}

Answer 1

a.
Number of values for i are n-8-10 = n-18
Number of values for j are log(m) as j is incrementing twice every time.
So, Total time complexity = O(nlog(m))

b.
Number of values for k are m/2
Number of values for l are n
So, Total time complexity = O(mn)

c.
Number of values for k are log(n) as k is decrementing by 2 every time.
Number of values for i are n
Number of values for j are n-4
As two for loop as are not nested (They are parallel)
So, Total time complexity = O(log(n)(n+n-4)) = O(nlog(n))