I am supposed to show that the following problem is NP-complete by Karp reducing it to the Subset Sum Problem. The problem is to distribute vaccine doses among different age groups according to:
Given: D vaccine doses, n age groups, a1 to an as input, where age group k consists of ak individuals, d1 to dn as input and each individual in age group k receives dk doses, at least tk percent of each age group must be fully vaccinated, and the maximal number of left-over doses can be S.
I am supposed to prove this problem is NP-complete. One of the steps is making a Karp reduction between this problem and the Subset Sum problem. I have tried to do this reduction in various ways but not been successful. Any ideas? Pseudo-code would be ideal.
Note: The Subset Sum problem receives the following input: A set of positive integers and a target K. The goal is to find a subset of the set of integers which sum up to K.
I've been learning TSQL and need some help with a conversion CPU MIPS into PERCENTAGE.
I've built my code to get some data that I'm expecting. In addition to this, I want to add a column to my code which is to get the CPU%. I have a column that gives me TOTALCPU MIPS and want to use this in the code but in the form of percentage. Example, I have these values in my TOTAL CPU Column:
1623453.66897
0
0
2148441.01573933
3048946.946314
I want to convert these values into percentage and use them. I couldn't find much info on the internet.
Appreciate your response.
I assume that you have 5 numeric quantities (2 of them being zero) and you want to find the percentage that corresponds to each of them out of the addition of the five quantities. Is it so?
To find the percentage of a particular number in the addition you multiply the number by 100 and divide by the addition, the result is the percentage that that number is in relation with the addition.
The sum: 6820841.631023
The percentage of the first number (of MIPS):
1623453.668970 * 100 / 6820841.631023 = 23.80136876 =>
23.80136876% is the percentage of CPU used by the first program.
To give the answer some SQL looking, refering to Mips_Table as the view/table that contains the MIPs data:
select mips, mips/totMips*100 Pct_CPU
from Mips_Table,
(select sum(mips) TotMips from Mips_Table) k
Here is my problem:
Raw data 1
If there is a position 105 and 150, I need the material number of position 150. If there is only position 105, I need the material number of position 105.
On the right side of the picture you can see the correct selected material number.
Now I need to assign this data to position 100 (bc I will use a counter later on, which is depending on position 100).
Here you can see more of the raw data of the report (I can´t insert the complete report here, I use the details area only for testing).
I marked one "group" in which you can see why I can´t change the order of the positions. In this case I need to use position 105 to output the material number (number rightmost on the red border) because there is no position 150.
Raw data 2
Here is another example with position 150 used for the material number (the correct material number will be placed on position 105 every time):
Raw data 3
To use this material number in my following tables, it need to be assigned to position 100.
Thanks!
Right now, I see there are quick ways to get things like Sum/Avg/Max/Etc. for two or more rows or columns when building a table in GoodData.
quick total options
I am building a little table that shows last week and the week prior, and I'm trying to show the delta between them.
So if the first column is 100 and the second is 50, I want '-50'
If the first column is 25 and the second is 100, i want '75'
Is there an easy way to do this?
Let’s consider, that the first column contains result of calculating of metric #1 and the second column contains result of calculating of metric #2, you can simply create a metric #3, which would be defined as the (metric #1 - metric #2) or vice versa.
I basically need the answer to this SO question that provides a power-law distribution, translated to T-SQL for me.
I want to pull a last name, one at a time, from a census provided table of names. I want to get roughly the same distribution as occurs in the population. The table has 88,799 names ranked by frequency. "Smith" is rank 1 with 1.006% frequency, "Alderink" is rank 88,799 with frequency of 1.7 x 10^-6. "Sanders" is rank 75 with a frequency of 0.100%.
The curve doesn't have to fit precisely at all. Just give me about 1% "Smith" and about 1 in a million "Alderink"
Here's what I have so far.
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank] = ROUND(88799 * RAND(), 0)
But this of course yields a uniform distribution.
I promise I'll still be trying to figure this out myself by the time a smarter person responds.
Why settle for the power-law distribution when you can draw from the actual distribution ?
I suggest you alter the LastNames table to include a numeric column which would contain a numeric value representing the actual number of indivuduals with a name that is more common. You'll probably want a number on a smaller but proportional scale, say, maybe 10,000 for each percent of representation.
The list would then look something like:
(other than the 3 names mentioned in the question, I'm guessing about White, Johnson et al)
Smith 0
White 10,060
Johnson 19,123
Williams 28,456
...
Sanders 200,987
..
Alderink 999,997
And the name selection would be
SELECT TOP 1 [LastName]
FROM [LastNames] as LN
WHERE LN.[number_described_above] < ROUND(100000 * RAND(), 0)
ORDER BY [number_described_above] DESC
That's picking the first name which number does not exceed the [uniform distribution] random number. Note how the query, uses less than and ordering in desc-ending order; this will guaranty that the very first entry (Smith) gets picked. The alternative would be to start the series with Smith at 10,060 rather than zero and to discard the random draws smaller than this value.
Aside from the matter of boundary management (starting at zero rather than 10,060) mentioned above, this solution, along with the two other responses so far, are the same as the one suggested in dmckee's answer to the question referenced in this question. Essentially the idea is to use the CDF (Cumulative Distribution function).
Edit:
If you insist on using a mathematical function rather than the actual distribution, the following should provide a power law function which would somehow convey the "long tail" shape of the real distribution. You may wan to tweak the #PwrCoef value (which BTW needn't be a integer), essentially the bigger the coeficient, the more skewed to the beginning of the list the function is.
DECLARE #PwrCoef INT
SET #PwrCoef = 2
SELECT 88799 - ROUND(POWER(POWER(88799.0, #PwrCoef) * RAND(), 1.0/#PwrCoef), 0)
Notes:
- the extra ".0" in the function above are important to force SQL to perform float operations rather than integer operations.
- the reason why we subtract the power calculation from 88799 is that the calculation's distribution is such that the closer a number is closer to the end of our scale, the more likely it is to be drawn. The List of family names being sorted in the reverse order (most likely names first), we need this substraction.
Assuming a power of, say, 3 the query would then look something like
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank]
= 88799 - ROUND(POWER(POWER(88799.0, 3) * RAND(), 1.0/3), 0)
Which is the query from the question except for the last line.
Re-Edit:
In looking at the actual distribution, as apparent in the Census data, the curve is extremely steep and would require a very big power coefficient, which in turn would cause overflows and/or extreme rounding errors in the naive formula shown above.
A more sensible approach may be to operate in several tiers i.e. to perform an equal number of draws in each of the, say, three thirds (or four quarters or...) of the cumulative distribution; within each of these parts list, we would draw using a power law function, possibly with the same coeficient, but with different ranges.
For example
Assuming thirds, the list divides as follow:
First third = 425 names, from Smith to Alvarado
Second third = 6,277 names, from to Gainer
Last third = 82,097 names, from Frisby to the end
If we were to need, say, 1,000 names, we'd draw 334 from the top third of the list, 333 from the second third and 333 from the last third.
For each of the thirds we'd use a similar formula, maybe with a bigger power coeficient for the first third (were were are really interested in favoring the earlier names in the list, and also where the relative frequencies are more statistically relevant). The three selection queries could look like the following:
-- Random Drawing of a single Name in top third
-- Power Coef = 12
SELECT [LastName]
FROM [LastNames] as LN
WHERE LN.[Rank]
= 425 - ROUND(POWER(POWER(425.0, 12) * RAND(), 1.0/12), 0)
-- Second third; Power Coef = 7
...
WHERE LN.[Rank]
= (425 + 6277) - ROUND(POWER(POWER(6277.0, 7) * RAND(), 1.0/7), 0)
-- Bottom third; Power Coef = 4
...
WHERE LN.[Rank]
= (425 + 6277 + 82097) - ROUND(POWER(POWER(82097.0, 4) * RAND(), 1.0/4), 0)
Instead of storing the pdf as rank, store the CDF (the sum of all frequencies until that name, starting from Aldekirk).
Then modify your select to retrieve the first LN with rank greater than your formula result.
I read the question as "I need to get a stream of names which will mirror the frequency of last names from the 1990 US Census"
I might have read the question a bit differently than the other suggestions and although an answer has been accepted, and a very through answer it is, I will contribute my experience with the Census last names.
I had downloaded the same data from the 1990 census. My goal was to produce a large number of names to be submitted for search testing during performance testing of a medical record app. I inserted the last names and the percentage of frequency into a table. I added a column and filled it with a integer which was the product of the "total names required * frequency". The frequency data from the census did not add up to exactly 100% so my total number of names was also a bit short of the requirement. I was able to correct the number by selecting random names from the list and increasing their count until I had exactly the required number, the randomly added count never ammounted to more than .05% of the total of 10 million.
I generated 10 million random numbers in the range of 1 to 88799. With each random number I would pick that name from the list and decrement the counter for that name. My approach was to simulate dealing a deck of cards except my deck had many more distinct cards and a varing number of each card.
Do you store the actual frequencies with the ranks?
Converting the algebra from that accepted answer to MySQL is no bother, if you know what values to use for n. y would be what you currently have ROUND(88799 * RAND(), 0) and x0,x1 = 1,88799 I think, though I might misunderstand it. The only non-standard maths operator involved from a T-SQL perspective is ^ which is just POWER(x,y) == x^y.