Find Case Combinations of a String, C++ (gcc)

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/* #21 Find Case Combinations of a String
Find all the combinations of a string in lowercase and uppercase. 
For example, string "ab" >>> "ab", "Ab", "aB", "AB". 
So, you will have 2^n (n = number of chars in the string) output strings. 
The goal is for you to test each of these strings and see if it matchs a hidden string.
*/ 
// 1 -> 2 
// 2 -> 2*2, ... n=> 2^n  (0000 - 1111) 
// 
#include <vector>
#include <iostream> 
using namespace std;

char lower(char x){
    if(x>='A' && x<='Z') return x-'A'+'a';
    else return x;
}
char upper(char x) {
    if(x>='a' && x<='z') return x-'a'+'A';
    return x; 
}
void flip(string& s, int i){
    if(s[i]>='A' && s[i]<='Z') 
        s[i] = s[i]+'a'-'A';
    else
        s[i] = s[i]+'A'-'a';
}

vector<string> getCombination(string s){
    vector<string> res; 
    //all 2^n combinations 
    int n = s.size(); 
    for(int i=0; i<(1<<n); i++){
        int x = i; 
        string t = s; 
        for(int j=0; j<n; j++){
            int y = x>>j; 
            y &= 1; // the last bit 
            if(y&1) 
                flip(t,j);
        }
        res.push_back(t);
    }
    return res;
}

int main(){
    string x = "ABC";// 
    vector<string> res = getCombination(x);
    for(auto x: res)
        cout << x << endl;
    return 0;
}

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Compilation time: 0.42 sec, absolute running time: 0.07 sec, cpu time: 0.01 sec, memory peak: 3 Mb, absolute service time: 0,5 sec