All Possible Braces

editor-page-cover

Problem Statement

Print all braces combinations for a given value n so that they are balanced. Here are a few examples:

widget

Hint

  • Recursion

Try it yourself

vector<vector<char>> print_all_braces(int n) {
  //TODO: Write - Your - Code
  vector<vector<char>> result;
  return result;
}

Solution

void print(vector<vector<char>> result){
  for(int i = 0; i < result.size(); i++){
    cout << "[ ";
    for(int j = 0; j < result[i].size(); j++){
      cout << result[i][j] << ", "; 
    }
    cout << "]" << endl;
  }
}

void print_all_braces_rec(
    int n,
    int left_count,
    int right_count,
    vector<char>& output, vector<vector<char>>& result) {

  if (left_count == n && right_count == n) {
    result.push_back(output);
  }

  if (left_count < n) {
    output.push_back('{');
    print_all_braces_rec(n, left_count + 1, right_count, output, result);
    output.pop_back();
  }

  if (right_count < left_count) {
    output.push_back('}');
    print_all_braces_rec(n, left_count, right_count + 1, output, result);
    output.pop_back();
  }
}

vector<vector<char>> print_all_braces(int n) {
  vector<vector<char>> result;
  vector<char> output;
  print_all_braces_rec(n, 0, 0, output, result);
  return result;
}

int main() {
  vector<vector<char>> result = print_all_braces(3);
  print(result);
}

Solution Explanation

Runtime complexity

The runtime complexity of this solution is exponential, 2n2^{n}

Memory complexity

The memory complexity of this solution is linear, O(n).


Solution Breakdown

The solution is to maintain counts of left_braces and right_braces. The basic algorithm is as follows:​

left_braces count: 0
right_braces count: 0
 
if left_braces count is less than n:
  add left_braces and recurse further
if right_braces count is less than left_braces count:
  add right_braces and recurse further
stop recursing when left_braces and right_braces counts are both equal to n