$2$ a$.$ You are given the following table containing symbols and their frequencies:

CO$2$

i$)$ Build the Huffman code tree and find the codewords for each character.

ii$)$ Decode $100010111001010$ using the Huffman code that you generated.

b$.$ You are given the arrival and departure times of eight trains for a railway platform, each in

CO$4$ the following format: $[$arrival time, departure time$).$ Only one train can use the platform

at a time.

Suppose, you have got the following train$-$use requests for the next day.

$\{[8,13),[6,9),[11,14),[2,7),[1,7),[12,20),[7,13),[13,20)\}$

i$)$ Find the maximum number of trains that can use the platform without any collision.

ii$)$ Determine the minimum number of platforms that needs to be there to ensure the

arrival and departure of all these trains without collision.

handwritten answer only please