Question

(a) Prove that n log^3 n is O(n^2). Prove that n^3 is not O(n^2 log n). (b) The multi Pop (i) method pops i items from the top of a stack. Analyse the amortized complexity of the multiPop (i) method.

Answer 1

to be able to pop i elements out of a stack we must first check if the stack actually has i or more elements and return false if it doesnt. If it does, we will count i elements and make top point to the i+1 ^{th element} from the top of the stack

bool multipop(i, node* top)

{

    node * temp = ⊤ int count = 1;

   while(count<i)

{

     if(temp->next == NULL)

            return false;

       else

       {

            temp = temp->next; count ++;

       }

}

top = &temp;

return true;

}

this process takes O(i) time.