October 3, 2023
October 3, 2023
October 3, 2023
###### Database-Management-System
October 3, 2023
 Question 17

Match the algorithms with their time complexities:

``` Algorithm                                     Time complexity
(P) Towers of Hanoi with n disks                       (i) Θ(n2)
(Q) Binary search given n stored numbers              (ii) Θ(n log⁡ n)
(R) Heap sort given n numbers at the worst case      (iii) Θ(2n)
(S) Addition of two n×n matrices                      (iv) Θ(log⁡ n)
```
 A P→(iii), Q→(iv), R→(i), S→(ii) B P→(iv), Q→(iii), R→(i), S→(ii) C P→(iii), Q→(iv), R→(ii), S→(i) D P→(iv), Q→(iii), R→(ii), S→(i)
Question 17 Explanation:
In this problem, we have to find Average case of different algorithms
→ Tower of Hanoi with n disks takes θ(2n) time
It is a mathematical game or puzzle.
It consists of three rods and a number of disks of different sizes, which can slide onto any rod.
The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.
The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:
1. Only one disk can be moved at a time.
2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack.
3. No disk may be placed on top of a smaller disk.
With 3 disks, the puzzle can be solved in 7 moves.
The minimal number of moves required to solve a Tower of Hanoi puzzle is 2n-1, where n is the number of disks.

→ Binary Search given n sorted numbers takes Ɵ(log2 n)
→ Heap sort given n numbers of the worst case takes Ɵ(n log n)
→ Addition of two n×n matrices takes Ɵ(n2)

Question 17 Explanation:
In this problem, we have to find Average case of different algorithms
→ Tower of Hanoi with n disks takes θ(2n) time
It is a mathematical game or puzzle.
It consists of three rods and a number of disks of different sizes, which can slide onto any rod.
The puzzle starts with the disks in a neat stack in ascending order of size on one rod, the smallest at the top, thus making a conical shape.
The objective of the puzzle is to move the entire stack to another rod, obeying the following simple rules:
1. Only one disk can be moved at a time.
2. Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack.
3. No disk may be placed on top of a smaller disk.
With 3 disks, the puzzle can be solved in 7 moves.
The minimal number of moves required to solve a Tower of Hanoi puzzle is 2n-1, where n is the number of disks.

→ Binary Search given n sorted numbers takes Ɵ(log2 n)
→ Heap sort given n numbers of the worst case takes Ɵ(n log n)
→ Addition of two n×n matrices takes Ɵ(n2)