integer-partition

A partition of an integer n is a way of writing n as a sum of positive integers. For example, for n=7, a partition is 1+1+5. I need a program that finds all the partitions of an integer 'n' using 'r' integers. For example, all the partitions of n=7 using r=3 integers are 1+1+5 , 1+2+4 , 1+3+3 , 2+2+3 . This is what I have so far: #include <iostream> #include <vector> using namespace std; void print (vector<int>& v, int level){ for(int i=0;i<=level;i++) cout << v[i] << " "; cout << endl; } void part(int n, vector<int>& v, int level){ int first; /* first is before last */ if(n<1) return ; v

I'm trying to find or develop Integer Partitioning code for Python. FYI, Integer Partitioning is representing a given integer n as a sum of integers smaller than n. For example, an integer 5 can be expressed as 4 + 1 = 3 + 2 = 3 + 1 + 1 = 2 + 2 + 1 = 2 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1 I've found a number of solutions for this. http://homepages.ed.ac.uk/jkellehe/partitions.php and http://code.activestate.com/recipes/218332-generator-for-integer-partitions/ However, what I really want is to restrict the number of partitions. Say, # of partition k = 2, a program only need to show 5 = 4 + 1 = 3 + 2

Finding how many combinations of a sum number (the variable n in code). For ex.: 3 = 1+1+1 = 2+1 = 3 => ANS is 3 5 = 5 = 4+1 = 3+2 = 3+1+1 = 2+2+1 = 2+1+1+1 = 1+1+1+1+1 => ANS is 7 In the following example, m is the max number and n is sum, the aim is to find how many (sum) combination does it have. I just want to know why do p(n, m) = p(n, m - 1) + p(n - m, m) ? The code here: int p (int n, int m) { if (n == m) return 1 + p(n, m - 1); if (m == 0 || n < 0) return 0; if (n == 0 || m == 1) return 1; return p(n, m - 1) + p(n - m, m); } Appreciated! Consider all ways of resulting n by adding some