Partition of an Integer + Number of partitions

Question

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

Answer 1

Essentially what Codor said, plus you don't need to recurse further into part() once you found a partition of the target length since they would be longer:

#include 
#include 

using namespace std;

void print (vector& v, int level){
    for(int i=0;i<=level;i++)
        cout << v[i] << " ";
    cout << endl;
}

void part(int n, vector& v, int level, int r){
    int first; /* first is before last */

    if(n<1) return ;
    v[level]=n;
    if( level+1 == r ) {
        print(v, level);
        return;
    }

    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, r);
    }
}

int main(){
    int num,r;
    cout << "Enter a number:";
    cin >> num;
    cout << "Enter size (r):";
    cin >> r;

    vector v(num);

    part(num, v, 0, r);
}

Output:

Enter a number:5
Enter size (r):2
1 4
2 3