Generate N proper pairs of parenthesis.

parenthesis.cpp

void parn( int index, int max, vector<set<string>> &all){
    string *me, *one, *two, *three;
    set<string> x;
    if (index < 0 || index >= max ) return;
    else if (index == 0){
        string *d = new string("()");       
        all[index].insert(*d); 
        parn(index+1, max, all);
    }
    else{
      //  cout << index << endl;
        for( auto i = all[0].begin(); i != all[0].end(); ++i)
            //cout << *i << "-";
         
        for( auto i = all[index-1].begin(); i != all[index-1].end(); ++i){
            me = new string(*i);
           // cout << "ME->" << *me << endl;
            one = new string("(" + *me + ")");
          //  cout << *one << endl;
            two =  new string(*me+ "()");
           // cout << *two << endl;
            three = new string("()" +*me);
            //cout << *three << endl;
            x.insert( *one );
           // cout << "ONE PUSH " << endl;
            x.insert( *two );
           // cout << "TWO PUSH " << endl;         
            x.insert( *three );    
            //cout << "DONE PUSH " << endl;    
        }
        all[index] = x;

        //cout << "HERE" << endl;
        parn(index+1, max, all);
    }
}

int main(){
    int pairs = 3;
    vector<set<string>> p(pairs, set<string>());
    parn(0, pairs, p);
    for( auto i = p.begin(); i != p.end(); ++i){
        for( auto j = i->begin(); j != i->end(); ++j){
            cout << *j << " ";
        }
        cout << endl;
    }
    cout << endl <<"done" <<endl;
    cin.get();
    return 0;
}

parenthiswithoutsets.cpp

#include <iostream>
#include <string>
#include <vector>
#include <math.h>
#include <map>
#include <fstream>
#include < ctime >
#include <algorithm>
#include <numeric>
#include <set>
#include <queue>
using namespace std;

void par(int left, int right, int &pairs, string &x){
    int level = left-right;
    if ( level < 0 ) return;
    if( x.length() > 0 && level == 0) cout << x << endl;
    if ( left == pairs && right == pairs ){
        return;
    }
    string a = x+"(";
    string b=  x+")";
    if ( left < pairs )
        par(left+1, right, pairs, a);
    par(left, right+1, pairs, b);    
}

int main(){
    string d = "";
    int n = 4;
    par(0,0,n,d);
    cout << endl <<"done" <<endl;
    cin.get();
    return 0;
}