Maths question on using the minimum amount of DVD disc

In summary, to burn 14 files onto the minimum number of DVD discs, you should arrange them starting with the largest file and filling each disc with as many files as possible. Some files may need to be split across discs. This is known as the bin packing problem and for a small number of files, a brute force approach should suffice. Alternatively, you can use compression programs to split the files across multiple discs.
  • #1
kenny1999
235
4
this is a practical question

I have 14 files to burn on a single layer DVD5 disc in which each of them has a size approximately 4.37GB

Those 14 files are of the size (in GB)

2.25
2.25
1.15
3.05
1.16
2.40
0.65
2.05
1.36
1.97
1.11
1.14
2.48
2.65

All values are in GB

If I want to burn these 14 files into minimum number of DVD discs for environmental and economic purposes, how should these files be arranged? I think at least a few discs could be saved if the files are arranged correctly, and I want to learn the concept. thanks
 
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  • #2
Basically you want to pack each disk as much as possible. You could figure it out like this. Start with your largest file and burn it on a disk. Then you'll have 4.37-3.05=1.32 space. There is not enough room for the two smallest files to fit on that disk, so just put the largest file on their with less than 1.32. In other words, the 1.16. So your first disk is
(3.05, 1.16).
Cross those off your list and continue this process. Next step you load
(2.65, 1.36), so cross those off the list.
Then you load 2.48 and notice you have 1.89 space left. Your largest available file is 1.15 which leaves you enough room to squeeze on the .65, so you got
(2.48, 1.15, .65)
Next
(2.40, 1.97) an exact fillup. Hopefully that one actually fits :)
You could probably figure out the last five.

Now you only have 7 left...
 
  • #3
Vargo said:
Basically you want to pack each disk as much as possible. You could figure it out like this. Start with your largest file and burn it on a disk. Then you'll have 4.37-3.05=1.32 space. There is not enough room for the two smallest files to fit on that disk, so just put the largest file on their with less than 1.32. In other words, the 1.16. So your first disk is
(3.05, 1.16).
Cross those off your list and continue this process. Next step you load
(2.65, 1.36), so cross those off the list.
Then you load 2.48 and notice you have 1.89 space left. Your largest available file is 1.15 which leaves you enough room to squeeze on the .65, so you got
(2.48, 1.15, .65)
Next
(2.40, 1.97) an exact fillup. Hopefully that one actually fits :)
You could probably figure out the last five.

Now you only have 7 left...

Thanks i ll try
 
  • #4
Several of the files are bigger than half the size of the DVD.

You con't fit two of those files onto the same DVD, so that gives you the minimum possible number of disks.

You then need to check that you can actually fit all the files onto that many disks.
 
  • #5
Your task is what's called the bin packing problem. For such a small number of files, any brute force approach probably will be satisfactory. Another possibility: If you don't need to store the files in their native format, most compression programs will allow you to split the files across multiple discs. That feature allows you to fill up each disc before going to the next one.
 

1. How many DVD discs are needed to store a given amount of data?

The minimum number of DVD discs needed depends on the amount of data that needs to be stored. A standard DVD disc can hold up to 4.7 GB of data, so the number of discs needed will depend on the total size of the data.

2. Is there a formula for determining the minimum number of DVD discs needed?

Yes, there is a formula for determining the minimum number of DVD discs needed. It is given by: Number of discs = (Total data size in GB) / 4.7 This will give you the minimum number of discs needed to store the data.

3. Can the data be split across multiple DVD discs?

Yes, the data can be split across multiple DVD discs. This is often necessary when the total data size exceeds the capacity of a single DVD disc. However, it is important to note that the minimum number of discs needed will still be determined by the total data size.

4. What is the most efficient way to use the minimum number of DVD discs?

The most efficient way to use the minimum number of DVD discs is to fill each disc to its full capacity before using another disc. This will ensure that the minimum number of discs are used and minimize any wasted space.

5. Can the minimum number of DVD discs needed be reduced?

In most cases, the minimum number of DVD discs needed cannot be reduced. However, if the data can be compressed, it may be possible to store it on fewer discs. This would require using a data compression software and may result in a loss of data quality.

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