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2. (20 points) Suppose you have a pizza shop and you advertise a sale for a 4-topping pizza. Your 14 toppings are listed below: • Pepperoni • Black Olives • Green Olives • Peppers • Onions • Anchovies • Mushrooms • Sausage • Eggplant • Basil • Ham • Pineapple • Meatball • Pesto (a) Count the number of possible 4-topping pizzas (from the set of 14 toppings) (b) How many bits would you need for the most efficient encoding of a 4-topping pizza? (c) Develop your own encoding/decoding algorithm where the code uses this number of bits. (d) Use your encoding to encode the following 4-topping pizzas: • {Pepperoni, Onions, Black Olives, Pesto} 1 • {Anchovies, Green Olives, Mushrooms, Basil} (e) Use your decoding to decode the following strings: (put "non-decodable" if you can't decode the string:) • 0101010101 • 0011001100

          2. (20 points) Suppose you have a pizza shop and you advertise a sale for a 4-topping pizza.
Your 14 toppings are listed below:
• Pepperoni
• Black Olives
• Green Olives
• Peppers
• Onions
• Anchovies
• Mushrooms
• Sausage
• Eggplant
• Basil
• Ham
• Pineapple
• Meatball
• Pesto
(a) Count the number of possible 4-topping pizzas (from the set of 14 toppings)
(b) How many bits would you need for the most efficient encoding of a 4-topping pizza?
(c) Develop your own encoding/decoding algorithm where the code uses this number of bits.
(d) Use your encoding to encode the following 4-topping pizzas:
• {Pepperoni, Onions, Black Olives, Pesto}
1
• {Anchovies, Green Olives, Mushrooms, Basil}
(e) Use your decoding to decode the following strings: (put "non-decodable" if you can't decode the
string:)
• 0101010101
• 0011001100

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2 20 points suppose you have a pizza shop and you advertise a sale for a 4 topping pizza your 14 toppings are listed below pepperoni black olives green olives peppers onions anchovies mushro 95362

Added by Jose Francisco C.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Sri K

06/18/2023

Step 1

This is a combination problem, and we can use the formula: $$ \binom{n}{k} = \frac{n!}{k!(n-k)!} $$ where n is the total number of items (14 toppings) and k is the number of items to choose (4 toppings). Show more…

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2. (20 points) Suppose you have a pizza shop and you advertise a sale for a 4-topping pizza. Your 14 toppings are listed below: • Pepperoni • Black Olives • Green Olives • Peppers • Onions • Anchovies • Mushrooms • Sausage • Eggplant • Basil • Ham • Pineapple • Meatball • Pesto (a) Count the number of possible 4-topping pizzas (from the set of 14 toppings) (b) How many bits would you need for the most efficient encoding of a 4-topping pizza? (c) Develop your own encoding/decoding algorithm where the code uses this number of bits. (d) Use your encoding to encode the following 4-topping pizzas: • {Pepperoni, Onions, Black Olives, Pesto} 1 • {Anchovies, Green Olives, Mushrooms, Basil} (e) Use your decoding to decode the following strings: (put "non-decodable" if you can't decode the string:) • 0101010101 • 0011001100

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Transcript

00:01 So, in this problem, first of all we will write the given text.

00:05 So the given text is oovha2ohh22vvov2o2a3.

00:33 So we will now form the frequency table.

00:39 So how we form the frequency table? we just count the number of the different variables in the given text.

00:45 So first of all, we will write the variable which are given that is oovha2.

00:56 You see that o appears five times in the text, v appears five times, h appears three times, a appears two times, 2 appears five times.

01:09 So this is our frequency table.

01:14 We'll just box this off and this gives us our necessary frequency table.

01:26 So now we will form the hoffman tree.

01:30 So for hoffman tree, at the base, we will write all the different variables that we have, that is hav2o.

01:46 And we will write the respective frequency.

01:48 H is a frequency of three.

01:51 V is a frequency of two.

01:54 We have to round that out also.

01:56 V is a frequency of five.

01:58 2 is a frequency of five.

02:00 O is a frequency of, so we know that three plus two gives us five.

02:08 So we get two plus two is five and five plus five will give us 10, will give us 10.

02:26 And this side also five plus five will give us 10...

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