1. Consider the Tower of Hanoi Problem (see attached image) a. If each move takes 1 microsecond, how long (in days) would it take to solvethe Towers of Hanoi problem with 37 discs? Provide your answer to a precision of twodecimal places.b. What are the last three moves of the Towers of Hanoi problem with 343 discs?c. What is the Towers of Hanoi's O() performance? Is it good? Explain. The image depicts a classic Tower of Hanoi puzzle with three pegs labeled A, B, and C. - **Peg A**: This peg contains all the disks, stacked in decreasing size from bottom to top. The disks are aligned on the peg with the largest at the bottom and the smallest at the top.- **Peg B**: This peg is empty, with no disks on it.- **Peg C**: This peg is also empty, similar to Peg B.The objective of the Tower of Hanoi puzzle is to move the entire stack of disks from Peg A to another peg, typically Peg C, while adhering to the following 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 or on an empty peg.3. No disk may be placed on top of a smaller disk.The puzzle serves as a problem-solving and algorithmic exercise, often used in teaching computer science concepts such as recursion.

- We have to work on problems related to tower of hanoi. a). How long it takes for 37 discs ? - 1 move : 1 microsecond :: 10-6 second. Number of discs :: 37 Number of moves :: 237 - 1 :: 137438953472 - 1 Total moves :: 137438953471 In seconds :: 137438953471 * 10-6 seconds Time :: 137438.953471 seconds Days :: 137438.953471 / (24*60*60) = 137438.953471 / 86400 = 1.59 days ( Precision of two decimal places) Total time taken :: 1.59 days b). What are the last three moves of the Towers of Hanoi problem with 343 discs? - In last three moves the tower will be sorted and placed in the 3rd bar. 3rd last move :: The smallest disc will be placed from bar B to bar A. 2nd last move :: The second smallest disc will be moved from bar B to bar C. Last move :: The smallest disc will be moved from bar A to bar C. So, this way the tower of hanoi will be completed with all discs in 3rd bar and all small discs above the big ones. c). What is the Towers of Hanoi's O() performance? Is it good? Explain. - The tower of hanio problem is a complex problem whose time complexity is very large. Time complexity is exponential in Towers of Hanoi. Time complexity of Towers of Hanoi :: O(2n) - This time complexity is not good. As exponential time complexities are considered to be one of the worst complexities to solve a problem . Explanation :: As the number of discs increase the number of moves increase exponentially. For 4 discs :: 15 moves But for 64 discs :: 18,446,744,073,709,551,616 So, computing till this is very difficult and that's why this problem is very difficult.