1. Sit-In Lab 4
Queues & Stacks
© Nicholas Lum

2. Cake
Queues

3. Cake Your friend baked a long cake and cut it into pieces
Some pieces have raisins, which you hate
You can only take home a contiguous slice of pieces
You want to maximise the chocolate on your slice
But you are limited to a certain number of raisin pieces
Input:
N – number of pieces of cake
C – number of raisins pieces allowed
Followed by N lines of:
T – state of the piece (raisin or not)
X – amount of chocolate on that piece
Output the maximum amount of chocolate you can gain

4. Ask yourself… Store the original cake in what data structure?
Take one piece of cake at a time and check it
If there is no raisin, then no problem
If there is a raisin, are we allowed to simply take it?
How to compare between different slices of cake?
How to keep track of previous amounts of chocolate?

5. Visualisation 1 2 10 2 3 4 5 Current Chocs  0 Max Chocs  0
Legend
Green == No Raisin
Orange == Has Raisin
Number inside == num of Choc
Original Cake 1 2 10 2 3 4 5
Current Chocs  0
Max Chocs  0
Raisin Pieces Taken  0
Max Raisin Pieces  2

6. Visualisation 2 10 2 3 4 5 1 Only chocolate, so just take it
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 2 10 2 3 4 5
Only chocolate, so just take it
Current Chocs  1
Max Chocs  0
Raisin Pieces Taken  0
Max Raisin Pieces  2 1
Potential Take Home Slice

7. Visualisation 10 2 3 4 5 1 2 Only chocolate, so just take it
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 10 2 3 4 5
Only chocolate, so just take it
Current Chocs  3
Max Chocs  0
Raisin Pieces Taken  0
Max Raisin Pieces  2 1 2
Potential Take Home Slice

8. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 2 3 4 5
Raisin piece. We still have leeway to take it
Current Chocs  13
Max Chocs  0
Raisin Pieces Taken  1
Max Raisin Pieces  2 1 2 10
Potential Take Home Slice

9. Visualisation 3 4 5 1 2 10 2 Only chocolate, so just take it
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 3 4 5
Only chocolate, so just take it
Current Chocs  15
Max Chocs  0
Raisin Pieces Taken  1
Max Raisin Pieces  2 1 2 10 2
Potential Take Home Slice

10. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 4 5
Raisin piece. We still have leeway to take it. But it’s the last one we can have in this slice
Current Chocs  18
Max Chocs  0
Raisin Pieces Taken  2
Max Raisin Pieces  2 1 2 10 2 3
Potential Take Home Slice

11. Visualisation 5 1 2 10 2 3 4 Only chocolate, so just take it
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
Only chocolate, so just take it
Current Chocs  22
Max Chocs  0
Raisin Pieces Taken  2
Max Raisin Pieces  2 1 2 10 2 3 4
Potential Take Home Slice

12. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
Raisin piece. We don’t have leeway to take it.
What we have here is a potential take-home slice with a certain amount of chocolate
Current Chocs  22
Max Chocs  0
Raisin Pieces Taken  2
Max Raisin Pieces  2 1 2 10 2 3 4
Potential Take Home Slice

13. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
Compare this slice against our max chocolates so far and record the higher value
Current Chocs  22
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 1 2 10 2 3 4
Potential Take Home Slice

14. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
Now we need to remove the first raisin piece so that we can consider the new piece.
Current Chocs  22
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 1 2 10 2 3 4
Potential Take Home Slice

15. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
To exclude the first raisin piece, we need to also exclude all pieces that come before it.
Current Chocs  22
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 1 2 10 2 3 4
Potential Take Home Slice

16. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
To exclude the first raisin piece, we need to also exclude all pieces that come before it.
Current Chocs  21
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 2 10 2 3 4
Potential Take Home Slice

17. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
To exclude the first raisin piece, we need to also exclude all pieces that come before it.
Current Chocs  19
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 10 2 3 4
Potential Take Home Slice

18. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake 5
Now that we have excluded the first raisin piece, we have space for the new raisin piece.
Current Chocs  9
Max Chocs  22
Raisin Pieces Taken  1
Max Raisin Pieces  2 2 3 4
Potential Take Home Slice

19. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake
Take the raisin piece and add its chocolate amount
Current Chocs  14
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 2 3 4 5
Potential Take Home Slice

20. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake
We have checked all the slices in the original cake.
Now we have another potential take-home slice.
Current Chocs  14
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 2 3 4 5
Potential Take Home Slice

21. Visualisation
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake
Compare the amount of chocolate in this slice with the max chocolate so far.
There is no change in the max.
Current Chocs  14
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 2 3 4 5
Potential Take Home Slice

22. Visualisation Max Chocs  22 2 3 4 5
Legend
Green == No Raisin
Orange == Has Raisin
White == Taken
Number inside == num of Choc
Original Cake
Since the cake has been fully checked, we just return the max chocolate amount, 22.
Current Chocs  14
Max Chocs  22
Raisin Pieces Taken  2
Max Raisin Pieces  2 2 3 4 5
Potential Take Home Slice

23. Cake class Main method: Why queue?
Read in the inputs N and C
For each of the N subsequent lines:
Read in T and X
Construct a Piece object that encapsulates these information
Store the Piece objects in a queue
Solve the question and print the output
Why queue?
FIFO
We want to consider the Pieces in the same order that they were read in
Can we use Stack instead? Why or why not?

24. Piece class The encapsulation of the information on each piece
Attributes:
raisin – boolean
amountChocolate – int
Getters:
hasRaisin()
getChocolate()

25. Algorithm Sketch (1) Refer to the diagrams when tracing this algorithm
Keep track of the following variables:
The allowed number of raisins
Given in the question. This does not change
Another Queue to hold the take-home slice
Why queue? Because we need the FIFO property!
Max chocolate amount so far
Updated before we consider a new take-home slice
Current chocolate amount in the take-home slice
Kept updated with every piece taken or removed from the slice
Raisin count in the take-home slice

26. Algorithm Sketch (2) Repeat until the cake queue is empty:
Dequeue the next cake piece
If it has raisins:
Increment the raisin count
If we exceeded the allowed number of raisins:
Compare the current chocolate against the max chocolate and take the higher value as the new max: use Math.max(a, b)
Remove all pieces up to and including the first raisin piece from the take home slice. Decrement the current chocolate while removing. Reduce the raisin count by 1 after removing.
Regardless of whether it has raisins:
Increment the current chocolate amount with the piece’s amount
Enqueue the piece into the take-home slice
Finally return the higher value between the max chocolate and the current chocolate

27. Questions?
Cake