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753. Cracking the Safe 👍

  • Time: $O(k^{k^n}) \to O(k^n)$
  • Space: $O(k^n)$
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class Solution {
 public:
  string crackSafe(int n, int k) {
    string ans(n, '0');
    dfs(pow(k, n), n, k, {ans}, ans);
    return ans;
  }

 private:
  bool dfs(int passwordSize, int n, int k, unordered_set<string>&& seen,
           string& path) {
    if (seen.size() == passwordSize)
      return true;

    string prefix = path.substr(path.length() - n + 1);

    for (char c = '0'; c < '0' + k; ++c) {
      prefix.push_back(c);
      if (!seen.contains(prefix)) {
        seen.insert(prefix);
        path.push_back(c);
        if (dfs(passwordSize, n, k, std::move(seen), path))
          return true;
        path.pop_back();
        seen.erase(prefix);
      }
      prefix.pop_back();
    }

    return false;
  }
};

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class Solution {
  public String crackSafe(int n, int k) {
    final String allZeros = "0".repeat(n);
    StringBuilder sb = new StringBuilder(allZeros);
    dfs((int) Math.pow(k, n), n, k, new HashSet<>(Arrays.asList(allZeros)), sb);
    return sb.toString();
  }

  private boolean dfs(int passwordSize, int n, int k, Set<String> seen, StringBuilder path) {
    if (seen.size() == passwordSize)
      return true;

    StringBuilder prefix = new StringBuilder(path.substring(path.length() - n + 1));

    for (char c = '0'; c < '0' + k; ++c) {
      prefix.append(c);
      final String prefixStr = prefix.toString();
      if (!seen.contains(prefixStr)) {
        seen.add(prefixStr);
        path.append(c);
        if (dfs(passwordSize, n, k, seen, path))
          return true;
        path.deleteCharAt(path.length() - 1);
        seen.remove(prefixStr);
      }
      prefix.deleteCharAt(prefix.length() - 1);
    }

    return false;
  }
}

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class Solution:
  def crackSafe(self, n: int, k: int) -> str:
    passwordSize = k**n
    path = '0' * n
    seen = set()
    seen.add(path)

    def dfs(path: str) -> str:
      if len(seen) == passwordSize:
        return path

      for c in map(str, range(k)):
        node = path[-n + 1:] + c if n > 1 else c
        if node not in seen:
          seen.add(node)
          res = dfs(path + c)
          if res:
            return res
          seen.remove(node)

    return dfs(path)