784. Letter Case Permutation

Given a string S, we can transform every letter individually to be lowercase or uppercase to create another string.  Return a list of all possible strings we could create.

Examples:
Input: S = "a1b2"
Output: ["a1b2", "a1B2", "A1b2", "A1B2"]

Input: S = "3z4"
Output: ["3z4", "3Z4"]

Input: S = "12345"
Output: ["12345"]

Note:

• S will be a string with length between 1 and 12.
• S will consist only of letters or digits.

Approach #1: BFS. [C++].

class Solution {
public:
    vector<string> letterCasePermutation(string S) {
        set<string> memo;
        memo.insert(S);
        
        helper(S, 0, memo);
        
        vector<string> ans(memo.begin(), memo.end());
        
        return ans;
    }
    
private:
    void helper(string S, int idx, set<string>& memo) {
        if (idx >= S.length()) return;
        vector<string> temp(memo.begin(), memo.end());
        //cout << idx << endl;
        for (string s : temp) {
            if (isalpha(s[idx])) {
                char c;
                if (isupper(s[idx])) c = tolower(s[idx]);
                else c = toupper(s[idx]);
                //cout << c << endl;
                string temp = s;
                temp[idx] = c;
                if (!memo.count(temp)) memo.insert(temp);
                //helper(S, idx+1, memo);
            }
        }
        helper(S, idx+1, memo);
    }
};