Question

In: Computer Science

You have been asked to create a program that builds a tower base on the number...

You have been asked to create a program that builds a tower base on the number of items given as input.

When the only 1 item is given you create no tower you just place the item on top of the stand.

When 2 items are given you build the base of the tower with one foot to the right and one foot to the left.

The feet will be in the ground and support the tower.

For every additional item you must keep the tower balanced by placing half on the right and half on the left each side

What is the height of the tower for the number 5? _________

What is the height of the tower for the number 10? ________

Write the a function to calculate the height. _______

If this was coded recursively what would be the base case? _________

If this was done recursively what would be the Time Complexity? _____

Solutions

Expert Solution

Answer :

What is the height of the tower for the number 5?

Height is 2. Make a base with 3 items and place two item on them. Like shown in figure.

What is the height of the tower for the number 10?

Height is 4.

Write the a function to calculate the height.

start with size of base x = 1,
subtract x from n
now increase x by 1
check if we can make new base or not i.e. x < n. If yes go to step 2
return height

C++ function :

int height(int n, int x=1)
{
   if(n < x)
       return 0;

   return 1 + height(n-x, ++x);
}

call using height(n);

If this was coded recursively what would be the base case?

It should check the remaining item can make new base layer of size x or not.

If this was done recursively what would be the Time Complexity?

Time complexity : O(logn)

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