對於2對左右括號，其排列方式有：

( ( ) )
( ) ( )
4對括號的排列方式有：
( ( ( ( ) ) ) )
( ( ( ) ( ) ) )
( ( ( ) ) ( ) )
( ( ( ) ) ) ( )
( ( ) ( ( ) ) )
( ( ) ( ) ( ) )
( ( ) ( ) ) ( )
( ( ) ) ( ( ) )
( ( ) ) ( ) ( )
( ) ( ( ( ) ) )
( ) ( ( ) ( ) )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) )
( ) ( ) ( ) ( )

下面給出生成排列的程式碼：

#include <iostream>
#include <vector>
using namespace std;

//Print the legal combination
void PrintBrackets(const vector<char> & brackets)
{
	for (vector<char>::const_iterator it = brackets.begin(); it != brackets.end(); ++it)
		cout << *it <<" ";
	cout <<endl;
}

// bracketsNum: the sum of left bracket and right bracket
void MatchBrackets(int bracketsNum, vector<char> & brackets)
{
	int left (0), right(0);
	for (vector<char>::iterator it = brackets.begin(); it != brackets.end(); ++it)
	{
		if ('(' == *it) left ++;
		else right ++;
	}
	// The num of left bracket should not be less than the number of right bracket at any position
	if (right > left) return;
	
	if (left == right && left + right == bracketsNum)
	{
		PrintBrackets(brackets);
		return ;
	}
	
	if (left + right >= bracketsNum)
	{
		return ;
	}
	
	// The number of left bracket equal to the number of right bracket,
	// so we can only append the left bracket '(' now.
	if (left == right)
	{
		brackets.push_back('(');
		MatchBrackets(bracketsNum, brackets);
		brackets.pop_back();
	}
	// The number of the left bracket equal to bracketsNum/2
	// no need to append '('.
	else if (bracketsNum - left == right)
	{
		brackets.push_back(')');
		MatchBrackets(bracketsNum, brackets);
		brackets.pop_back();
	}
	// It`s legal to append '(' and ')'
	else
	{
		brackets.push_back('(');
		MatchBrackets(bracketsNum, brackets);
		brackets.pop_back();
		
		brackets.push_back(')');
		MatchBrackets(bracketsNum, brackets);
		brackets.pop_back();
	}
}

int main()
{
	int braNum;
	while (cin>> braNum && braNum)
	{
		vector<char> brackets;
		MatchBrackets(braNum, brackets);
	}
	return 0;
}