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3. Vending Machines You've come across a collection of unusual vending machines. Each machine has a coin slot, a "buy" button, and a candy slot. Each coin slot only accepts nickels (5-cent coins) and dimes (10-cent coins). When the buyer presses the buy button, each machine has its own unique logic to determine whether or not the user should get candy based on the sequence of nickels and dimes they have entered. This logic is coded into the machine via something we're going to call a VM diagram. For example, one vending machine will give candy only if the buyer has entered a positive multiple of 10 cents when they press the buy button. Below is its VM diagram: This particular VM diagram has 3 circled states: Start, S1, and S2. Start represents the state before the buyer enters any money, S1 represents when the buyer has entered an amount of money that is a multiple of 5 cents but not 10 cents, and S2 represents when the buyer has entered a positive multiple of 10 cents. Notice that S2 is circled twice because it is the state where the machine is ready to give candy. The arrows show how the machine moves from state to state when the buyer puts in a nickel (N) or a dime (D). For instance, if the machine is currently in the start state and the buyer puts in a dime, the machine moves to the S2 state where it is ready to give candy. If the buyer then puts in a nickel, the machine moves to the S1 state where it will not give candy (because 15 cents is not a multiple of 10 cents). Note that the machine does not automatically give candy whenever it enters state S2. When the user pushes the buy button, if the machine is in the double-circled state, then it gives candy. If the user puts in a dime, then a nickel, then hits the buy button, they get nothing even though the machine was briefly in state S2. For a VM diagram to be valid, the following must be true: -There must be exactly one state labeled "start" -There must be exactly one state that gives candy (double circled) -Every state must have exactly two arrows coming from it: one N and one D a. Write a short sentence to describe when this machine gives candy: b. Below is a VM diagram that gives candy under some condition. Draw a VM diagram with fewer states that gives candy under the same condition and describe the condition. For each of the following vending machines, draw a VM diagram that meets the condition and uses the fewest possible number of states. Note that, like in part a, states may point back to the start state. You do not need to explain your diagrams. c. Gives candy if the buyer has entered exactly 15 cents. d. Gives candy if the buyer has entered a positive multiple of 20 cents, and the last coin entered was a dime. e. Gives candy if some consecutive sequence of coins entered adds up to 20 cents. (For example, DNDDND gives candy because it contains the consecutive sequence DD which adds to 20 cents)

3. Vending Machines
You've come across a collection of unusual vending machines. Each machine has a coin slot, a "buy" button, and a candy slot. Each coin slot only accepts nickels (5-cent coins) and dimes (10-cent coins). When the buyer presses the buy button, each machine has its own unique logic to determine whether or not the user should get candy based on the sequence of nickels and dimes they have entered. This logic is coded into the machine via something we're going to call a VM diagram.

For example, one vending machine will give candy only if the buyer has entered a positive multiple of 10 cents when they press the buy button. Below is its VM diagram:

This particular VM diagram has 3 circled states: Start, S1, and S2. Start represents the state before the buyer enters any money, S1 represents when the buyer has entered an amount of money that is a multiple of 5 cents but not 10 cents, and S2 represents when the buyer has entered a positive multiple of 10 cents. Notice that S2 is circled twice because it is the state where the machine is ready to give candy.

The arrows show how the machine moves from state to state when the buyer puts in a nickel (N) or a dime (D). For instance, if the machine is currently in the start state and the buyer puts in a dime, the machine moves to the S2 state where it is ready to give candy. If the buyer then puts in a nickel, the machine moves to the S1 state where it will not give candy (because 15 cents is not a multiple of 10 cents).

Note that the machine does not automatically give candy whenever it enters state S2. When the user pushes the buy button, if the machine is in the double-circled state, then it gives candy. If the user puts in a dime, then a nickel, then hits the buy button, they get nothing even though the machine was briefly in state S2.

For a VM diagram to be valid, the following must be true:
-There must be exactly one state labeled "start"
-There must be exactly one state that gives candy (double circled)
-Every state must have exactly two arrows coming from it: one N and one D

a. Write a short sentence to describe when this machine gives candy:

b. Below is a VM diagram that gives candy under some condition. Draw a VM diagram with fewer states that gives candy under the same condition and describe the condition.

For each of the following vending machines, draw a VM diagram that meets the condition and uses the fewest possible number of states. Note that, like in part a, states may point back to the start state. You do not need to explain your diagrams.

c. Gives candy if the buyer has entered exactly 15 cents.

d. Gives candy if the buyer has entered a positive multiple of 20 cents, and the last coin entered was a dime.

e. Gives candy if some consecutive sequence of coins entered adds up to 20 cents. (For example, DNDDND gives candy because it contains the consecutive sequence DD which adds to 20 cents)

3. Vending Machines
You've come across a collection of unusual vending machines. Each machine has a coin slot, a "buy" button, and a candy slot. Each coin slot only accepts nickels (5-cent coins) and dimes (10-cent coins). When the buyer presses the buy button, each machine has its own unique logic to determine whether or not the user should get candy based on the sequence of nickels and dimes they have entered. This logic is coded into the machine via something we're going to call a VM diagram.

For example, one vending machine will give candy only if the buyer has entered a positive multiple of 10 cents when they press the buy button. Below is its VM diagram:

This particular VM diagram has 3 circled states: Start, S1, and S2. Start represents the state before the buyer enters any money, S1 represents when the buyer has entered an amount of money that is a multiple of 5 cents but not 10 cents, and S2 represents when the buyer has entered a positive multiple of 10 cents. Notice that S2 is circled twice because it is the state where the machine is ready to give candy.

The arrows show how the machine moves from state to state when the buyer puts in a nickel (N) or a dime (D). For instance, if the machine is currently in the start state and the buyer puts in a dime, the machine moves to the S2 state where it is ready to give candy. If the buyer then puts in a nickel, the machine moves to the S1 state where it will not give candy (because 15 cents is not a multiple of 10 cents).

Note that the machine does not automatically give candy whenever it enters state S2. When the user pushes the buy button, if the machine is in the double-circled state, then it gives candy. If the user puts in a dime, then a nickel, then hits the buy button, they get nothing even though the machine was briefly in state S2.

For a VM diagram to be valid, the following must be true:
-There must be exactly one state labeled "start"
-There must be exactly one state that gives candy (double circled)
-Every state must have exactly two arrows coming from it: one N and one D

a. Write a short sentence to describe when this machine gives candy:

b. Below is a VM diagram that gives candy under some condition. Draw a VM diagram with fewer states that gives candy under the same condition and describe the condition.

For each of the following vending machines, draw a VM diagram that meets the condition and uses the fewest possible number of states. Note that, like in part a, states may point back to the start state. You do not need to explain your diagrams.

c. Gives candy if the buyer has entered exactly 15 cents.

d. Gives candy if the buyer has entered a positive multiple of 20 cents, and the last coin entered was a dime.

e. Gives candy if some consecutive sequence of coins entered adds up to 20 cents. (For example, DNDDND gives candy because it contains the consecutive sequence DD which adds to 20 cents)

Added by Yes H.

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