Bracket Printing

You are given an integer. You have to print the valid paranthesis set corresponding to the number n.
Example: Number n = 2 Valid paranthesis set is ( ) ( ) ( ( ) )
Number n = 3 Valid paranthesis set is ( ) ( ) ( ) ( ( ) ( ) ) ( ( ( ) ) )

Logic:

Represent the bracket pairs as a combination of 1 and 0. Like ( ) is 1 0, ( ( ) ) is 1 1 0 0, ( ( ( ) ) ) is 1 1 1 0 0 0
When you get n as the input create a tree having the right child as 1 and left child as 0
for n = 2 structure of the tree would be

-----------------(1)
----------------/ \
---------------/-- \
--------------(0) (1)
--------------\---- /
---------------\ --/
--------------(1) (0)
---------------/-- /
--------------/ --/
------------(0) -(0)

Printing the brackets: Traverse if u find the value as 1 put the character ( in the array else put the character ) in the array.
WHen the length of the array becomes equal to the number given as input. You are done print the array.

Pseudo Code to create the tree:

createTree(struct node * null, int n, int OneCount, int ZeroCount)
{
if(root == Null)
{
root = makenode(1);
OneCount++;
}

if( ZeroCount <>left = makenode(0);
createTree(root->left,n,OneCount,ZeroCount);
}

if(OneCount <>right = makenode(1);
createTree(root->right,n,OneCount,ZeroCount);
}
}

PseudoCode To Read the Tree:

First Call will be made to this fucntion like PrintBrackets( root, n, array, 0);


PrintBrackets(struct node *root, int n, int * array, int index)
{

if(root == null)
return;

if(root->data == 1)
array[index]= '(';

if(root->data == 0)
array[index] = ")';

if(index == n-1)
puts(array);
return;

if(root->left)
PrintBrackets(root->left, n,array,index+1)

if(root->right)
PrintBrackets(root->right, n,array,index+1)

}