generate permutations of letters in a string

how to generate all permutations of the letters in a string? one method i like, for its intuitiveness - go to the last letter of the string and then recursively create strings by inserting previous letters in all possible positions. at each step a new list of strings will be created, with growing lengths

#include 
#include 
#include 

std::vector permute(std::string s, size_t index) {
    //std::cout << s << " " << index << std::endl;
    std::vector perms;
    if (index >= s.length()) {
        perms.push_back("");
        return perms;
    }
    
    std::string key = s.substr(index, 1);
    std::vector prev = permute(s, index + 1);
    for (size_t i = 0; i < prev.size(); ++i) {
        std::string p = prev[i];
        for (size_t j = 0; j <= p.length(); ++j) {
            std::string n = p.insert(j, key);
            perms.push_back(n);
            p = prev[i];
        }
    }
    return perms;
}

int main()
{
  std::string name = "12345";
  std::vector perms = permute(name, 0);
  for (auto& p : perms) {
    std::cout << p << std::endl;
  }
}

12345
21345
23145
23415
23451
13245
....