gen-bin-string.cpp

#include <bits/stdc++.h>

using namespace std;

int v[100];
int n;

void gen(int i) {
    if (i == n) {
        for (int j = 0; j < n; ++j) cout << v[j] << " ";
        cout << "\n";
        return;
    }
    for (int j = 0; j < 2; ++j) {
        v[i] = j;
        gen(i+1);
    }
}

int main() {
    n = 3;
    gen(0);
    return 0;
}

gen-sum-of-num.cpp

#include <bits/stdc++.h>

using namespace std;

vector<int> v;
int n;

void gen(int s) {
    for (int i = 1; i < n + 1; ++i) {
        if (s < i) {
            for (auto x : v) cout << x << " ";
            cout << s << "\n";
            return;
        }
        if (s > i) {
            v.push_back(i);
            gen(s-i);
            v.pop_back();
        }
    }
}

int main() {
    cin >> n;
    gen(n);
    return 0;
}