How to print all possible balanced parentheses for an expression?

Question

For example, with elements a,b,c,d, there are 5 possible ways to take neighboring elements and reduce them into a single element, where exactly two elements mus

Answer 1

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**Run this to generate all balanced parantheses:
//sudosuhan
#include
#include
#include
#define MAX_SIZE 200
void _printParenthesis(int pos, int n1, int open1, int close1, int n2, int open2, int close2, int n3, int open3, int close3);
void printParenthesis(int n1 , int n2 , int n3 )
{
  if(n1 > 0 || n2 > 0 || n3 > 0)
     _printParenthesis(0, n1, 0, 0, n2, 0, 0, n3, 0, 0);
  return;
}
void _printParenthesis(int pos, int n1, int open1, int close1, int n2, int open2, int close2, int n3, int open3, int close3)
{
  static char str[MAX_SIZE];     

  if(close1 == n1 && close2 == n2 && close3 == n3 ) 
  {
    printf("%s \n", str);
    return;
  }
  else
  {
    bool run1 = open1 > close1;
    bool run2 = open2 > close2;
    bool run3 = open3 > close3;
    if(run3)
    {
      str[pos] = ')';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2, close2, n3, open3, close3+1);

      if(open3 < n3)
      {
      str[pos] = '(';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2, close2, n3, open3+1, close3);
      }
    }
    else if(run2 && !run3)
    {
      str[pos] = '}';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2, close2+1, n3, open3, close3);

      if(open3 < n3)
      {
      str[pos] = '(';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2, close2, n3, open3+1, close3);
      }
      if(open2 < n2)
      {
      str[pos] = '{';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2+1, close2, n3, open3, close3);
      }
    }
    else if(run1 && !run2 && !run3)
    {
      str[pos] = ']';
      _printParenthesis(pos+1, n1, open1, close1+1, n2, open2, close2, n3, open3, close3);

      if(open3 < n3)
      {
      str[pos] = '(';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2, close2, n3, open3+1, close3);
      }
      if(open2 < n2)
      {
      str[pos] = '{';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2+1, close2, n3, open3, close3);
      }
      if(open1 < n1)
      {
      str[pos] = '[';
      _printParenthesis(pos+1, n1, open1+1, close1, n2, open2, close2, n3, open3, close3);
      }
    }
    else if(!run1 && !run2 && !run3)
    {
      if(open3 < n3)
      {
       str[pos] = '(';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2, close2, n3, open3+1, close3);
      }
      if(open2 < n2)
      {
      str[pos] = '{';
      _printParenthesis(pos+1, n1, open1, close1, n2, open2+1, close2, n3, open3, close3);
      }
      if(open1 < n1)
      {
      str[pos] = '[';
      _printParenthesis(pos+1, n1, open1+1, close1, n2, open2, close2, n3, open3, close3);
      }
    }

  }
}
/* driver program to test above functions */
int main()
{
  int n1, n2, n3;
  n1 = 6;
  n2 = 1;
  n3 = 1;
  printParenthesis(n1, n2, n3);
  return 0;
}**

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