Hello, I have a huge list of problems but I'm having difficulties with some of them. I need algorithms for these 3 problems (pseudo-code, c++, java or c#) as I can't find solutions for them:


1. For a set of n integer elements, generate all the subsets of that set that have the sum of all their elements an odd number.

2. Generate all the decompositions of a natural number n in sums of prime numbers.

3. For a given integer, n, generate all the growing functions f : {1, 2, 3, ..., n} -> {1, 2, 3, ..., n} with the property: f(x)<=x for any x in {1, 2, ..., n}.


Any help is appreciated! Thank you.