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Are you expected a sum of positive integers?Quote:
Originally posted by hometown
I have 2 positive integers m and n; could you tell me how to express m as an ordered sum of the integers which are smaller than n...
Must they be all of different values, or can they be of the same value?
If they can have the same value, we can always have 1+1+1+1+... until you reach m. Quick and dirty solution...
The expressing numbers will be chosen from 1~n and and they can have the same values as you have pointed out...
Here I will give an example to make it a little clearer...
For example, let m=5 and n=3, there will be 13 ways to express it...
- 3+2
- 3+1+1
- 2+3
- 2+2+1
- 2+1+2
- 2+1+1+1
- 1+3+1
- 1+2+2
- 1+2+1+1
- 1+1+3
- 1+1+2+1
- 1+1+1+2
- 1+1+1+1+1
That's not correct. You asked for an ordered sum.Quote:
Originally posted by hometown
Here I will give an example to make it a little clearer...
For example, let m=5 and n=3, there will be 13 ways to express it...
1 + 3 + 1 is not ordered.
After that, ordering from bigger to smaller or the opposite probably doesn't matter as long as you stick to the same rule for all solutions.
It will then give 5 different solutions:
3 + 2
3 + 1 + 1
2 + 2 + 1
2 + 1 + 1 + 1
1 + 1 + 1 + 1 + 1
Who is to say that he meant ordered from least to greatest (or the other way around). Even 1+2+1 is in a particular order. I believe what he meant was that the order (or each permutation) counts.
- Kevin
P.S. As far as how to express it, yikes, that seems difficult. I would start off trying to find all combinations and then from the combinations it would be easy to find all permutations (there are several articles on Codeguru and Codeproject that outline how to iterate through permutations).
Actually, he didn't ask for ALL permutations (ordered or notQuote:
Originally posted by KevinHall
Who is to say that he meant ordered from least to greatest (or the other way around). Even 1+2+1 is in a particular order. I believe what he meant was that the order (or each permutation) counts.
- Kevin
P.S. As far as how to express it, yikes, that seems difficult. I would start off trying to find all combinations and then from the combinations it would be easy to find all permutations (there are several articles on Codeguru and Codeproject that outline how to iterate through permutations).
), but just for a way to express this sum...
I was not told the integers must be positive. Then you can do things like.
0+0+0+0+...+1+1+1+1+1+...
-1+1-1+1-1+1+...
:D
Yes you were:Quote:
Originally posted by Doctor Luz
I was not told the integers must be positive. Then you can do things like.
0+0+0+0+...+1+1+1+1+1+...
-1+1-1+1-1+1+...
:D
Quote:
The expressing numbers will be chosen from 1~n and and they can have the same values as you have pointed out...
Oh! yes, sorry it was told in a post after the original question.Quote:
Originally posted by Elrond
Yes you were:
Right. The initial "question" (?) missed a few information ;)
Is the question how many partition's are there or how to write down all of the partitions of a number given the restriction?
http://www.research.att.com/cgi-bin/...gi?Anum=000041
Happy Birthday!
* * * * * * * * * * * * *
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Originally posted by Doctor Luz
Happy birthday young SeventhStar! :p
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Originally posted by souldog
Yup, Happy BDay!!
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Originally posted by Mick_2002
ohh yea...and happy birthday suit day.
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Originally posted by hometown
Happybirthday:)
Thank you all :D :D :DQuote:
Originally posted by solarflare
Happy Birthday!
Oh and mick actually in Bulgaria there's no limitation by law for noone (exept drivers that are driving) to consume alcohol... everything lies on the parents' consience ;)
Yes, they are in special order....Quote:
Originally posted by KevinHall
Who is to say that he meant ordered from least to greatest (or the other way around). Even 1+2+1 is in a particular order. I believe what he meant was that the order (or each permutation) counts.
- Kevin
I am sorry Eldrond, I was online at the time you just posted but I could not give any explanation because I didnot know how to explain more about the problem. If I went on giving more details you would know it immediately, and that would be like I was answering to my own question...
I know you dont believe in what I posted...You meant I was asking for assignment/project ? How could a teacher give his/her secondyear student tobe such a problem ? What I learnt about math at school was Algebraic, diff, integral fundamentals, and a little about numbers theory...This is true...I amnot lying...Quote:
P.S. As far as how to express it, yikes, that seems difficult. I would start off trying to find all combinations and then from the combinations it would be easy to find all permutations (there are several articles on Codeguru and Codeproject that outline how to iterate through permutations).
I am bad at maths because I always get C or B- and it is true that I have never had an A since I come to college but I like it...so I read some books and I found that problem...
Sir KevinHall, could you tell me what made you think of permutations ? Why didnt you figure out in another way like number sequences, number partitions as what Tom posted etc. Please give me your reasoning...I will like it, no matter what and how it is....I just want to know....Please ?
Thank you :)
PS
Aha, I have got to go out for dinner with my parents, I will be back at around 8:30 local time itis now 18:14 bye:) I am really happy today and wish you all a happy day:)
The guy who was picking the dollars is the guiltly one. No one was playing poker at the time so why did he have to get his dollars when the table was being fixed and the other guy busy doing something else. One question i have is did the three guys not hear the gun shot. naturally they would have all turned and looked around for the source of the sound. :confused: :D
i guess someone has a reeeeeeeealy slow internet connection :p :p :p :D :D :DQuote:
Originally posted by nevcode
The guy who was picking the dollars is the guiltly one. No one was playing poker at the time so why did he have to get his dollars when the table was being fixed and the other guy busy doing something else. One question i have is did the three guys not hear the gun shot. naturally they would have all turned and looked around for the source of the sound. :confused: :D