Question

I need an algorithmic solution in c++ for the partition-problem

Simple explanation: Find all sums that get a number n.
For example

• Input: 5
• Output:
  • 11111
  • 2111
  • 311
  • 41
  • 5
  • 221
  • 23

This problem seems so easy, but I couldn’t find a solution. I’m close to make this bruteforce, because the highest input is 11. The articles about that problem are highly mathematic and I don’t really get it.

Thank you all!

Answer 1

/*
E.g.
input number:5
5
1 4
1 1 3
1 1 1 2
1 1 1 1 1
1 2 2
2 3
*/
#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[level]=n;
    print(v, level);

    first=(level==0) ? 1 : v[level-1];

    for(int i=first;i<=n/2;i++){
        v[level]=i; /* replace last */
        part(n-i, v, level+1);
    }
}

int main(){
    int N;
    cout << "input number:";
    cin >> N;

    vector<int> v(N);

    part(N, v, 0);
}