Question

1. What is the Big-Oh runtime complexity of the following algorithm?

A. for (i = 5; i <= 2 * n; i++)

    cout << 2 * n + i – 1; << enld;

2. State the preconditions &/or postcondition for each of the following.

A. ) if (x >= 0) y = x + y;

    else y = y - x;

B.) /* precondition: m <= n */

   s = 0;

   for (i = m; i <= n; i++)

       s += i;

C.) i = 1;

       c = 0;

     while (i <= n) {

       if (a[i] == 17) c = c + 1;

      i = i + 1; }

D.) m = a[1];

    i = 2;

      while (i <= n) {

           if ( a[i] > m ) m = a[i];

           i = i +1;

      }

Answer 1

1.

for (i = 5; i <= 2 * n; i++)  

• In this i value runs for 5 to 2n.
• The increment operation of i done linearly(Since i value incremented by 1 every time)

The Number of times loop runs is 2n-5.

f(n) = 2n-5

g(n) = 2n

By the definition of Big O

f(n) ≤ C g(n)

2n-5 ≤ 1*(2n)

Where c=1

Similarly

cout << 2 * n + i – 1; << enld; // Complexity is O(n)

Therefore the complexity of the program is O(n).

According to HomeworkLib guidelines i have to solve first question only please do next post for remaining answers.