DS 1 Long quiz

What is the minimum number of moves required to solve a Tower of Hanoi problem with 4 disks?

• 15

• 31

• 7

• 16

What is the recurrence relation for the Tower of Hanoi problem?

• T(n) = 2T(n-1) + 1

• T(n) = T(n-1) + T(n-2)

• T(n) = 3T(n-1) + 1

• T(n) = 2n

If there are 3 rods in the Tower of Hanoi, what is the role of the third rod?

• It holds the largest disk.

• It serves as a temporary storage to move disks.

• It is unused.

• It holds disks permanently.

What is the time complexity of the Tower of Hanoi problem for n disks?

• O(n)

• O(2^n)

• O(n^2)

• O(log n)

In the Tower of Hanoi, what is the key constraint for moving disks?

• No two disks can be on the same rod.

• A larger disk cannot be placed on a smaller disk.

• Disks can only be moved one at a time.

• Both b and c.

How many distinct lines can be formed by 4 points on a plane if no three points are collinear?

• 4

• 6

• 7

• 8

What is the recurrence relation used to calculate the maximum number of regions formed by n lines in a plane?

• R(n) = R(n-1) + n

• R(n) = R(n-1) + 2^n

• R(n) = 2R(n-1) + 1

• R(n) = n^2

If 5 lines divide the plane, what is the maximum number of regions they can form?

• 10

• 15

• 16

• 14

Which condition must be satisfied to achieve the maximum number of regions formed by n lines?

• All lines must be parallel.

• No two lines should be parallel, and no three lines should intersect at a single point.

• All lines must pass through a single point.

• All lines must be perpendicular to each other.

What is the formula for the maximum number of regions created by n lines in a plane?

• R(n) = n^2

• R(n) = n(n-1)/2 + 1

• R(n) = n(n+1)/2 + 1

• R(n) = n^2 - n + 1