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This is a generator that generates all tuples of n integers (>=0) with a given sum s. The generator can make the difference between tuples (3,0,0) and (0,3,0) or not (see order parameter).

Python, 32 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32``` ```from itertools import permutations def tuples_sum(nbval,total,order=True) : """ Generate all the tuples L of nbval positive or nul integer such that sum(L)=total. The tuples may be ordered (decreasing order) or not """ if nbval == 0 and total == 0 : yield tuple() ; raise StopIteration if nbval == 1 : yield (total,) ; raise StopIteration if total==0 : yield (0,)*nbval ; raise StopIteration for start in range(total,0,-1) : for qu in tuples_sum(nbval-1,total-start) : if qu<=start : sol=(start,)+qu if order : yield sol else : l=set() for p in permutations(sol,len(sol)) : if p not in l : l.add(p) yield p if __name__=='__main__' : print("How to obtain 5 by adding a+b+c (>=0) ? ") print("Give me the list of (a,b,c) tuples.") g=tuples_sum(3,5,order=False) print(list(g)) print("How to obtain 6 by adding 3 positive or nul integers ?") g=tuples_sum(3,6,order=True) print(list(g)) ```

If you run the module, you will get :

`````` How to obtain 5 by adding a+b+c (>=0) ?
Give me the list of (a,b,c) tuples.
[(5, 0, 0), (0, 5, 0), (0, 0, 5), (4, 1, 0), (4, 0, 1), (1, 4, 0), (1, 0, 4), (0, 4, 1),
(0, 1, 4), (3, 2, 0), (3, 0, 2), (2, 3, 0), (2, 0, 3), (0, 3, 2), (0, 2, 3), (3, 1, 1),
(1, 3, 1), (1, 1, 3), (2, 2, 1), (2, 1, 2), (1, 2, 2)]
How to obtain 6 by adding 3 positive or nul integers ?
[(6, 0, 0), (5, 1, 0), (4, 2, 0), (4, 1, 1), (3, 3, 0), (3, 2, 1), (2, 2, 2)]
`````` Created by SnarkTurne on Tue, 16 Jul 2013 (MIT)