753. Cracking the Safe

There is a box protected by a password. The password is a sequence of n digits where each digit can be one of the first k digits 0, 1, ..., k-1.

While entering a password, the last n digits entered will automatically be matched against the correct password.

For example, assuming the correct password is "345", if you type "012345", the box will open because the correct password matches the suffix of the entered password.

Return any password of minimum length that is guaranteed to open the box at some point of entering it.

Example 1:

Input: n = 1, k = 2
Output: "01"
Note: "10" will be accepted too.

Example 2:

Input: n = 2, k = 2
Output: "00110"
Note: "01100", "10011", "11001" will be accepted too.

Note:

1. n will be in the range [1, 4].

2. k will be in the range [1, 10].

3. k^n will be at most 4096.

// Greedy Method
string crackSafe(int n, int k) { // time: O(k^(n + 1)); space: O(k^n)
    string res = string(n, '0'); // start with n 0s
    unordered_set<string> visited({res});
    for (int i = 0; i < pow(k, n); ++i) {
        string pre = res.substr(res.size() - (n - 1), n - 1);
        for (int j = k - 1; j >= 0; --j) {
            string cur = pre + to_string(j);
            if (!visited.count(cur)) {
                visited.insert(cur);
                res += to_string(j);
                break;
            }
        }
    }
    return res;
}

// Greedy Method with Recursion
void helper(int n, int k, int total, unordered_set<string>& visited, string& res) {
    if (visited.size() == total) return;
    string pre = res.substr(res.size() - (n - 1), n - 1);
    for (int i = k - 1; i >= 0; --i) {
        string cur = pre + to_string(i);
        if (visited.count(cur)) continue;
        visited.insert(cur);
        res += to_string(i);
        helper(n, k, total, visited, res);
    }
}
string crackSafe(int n, int k) { // time: O(k^(n + 1)); space: O(k^n)
    string res = string(n, '0');
    unordered_set<string> visited({res});
    helper(n, k, pow(k, n), visited, res);
    return res;
}