打印所有括号匹配排列方式

对于2对左右括号，其排列方式有：

( ( ) )
( ) ( )
4对括号的排列方式有：
( ( ( ( ) ) ) )
( ( ( ) ( ) ) )
( ( ( ) ) ( ) )
( ( ( ) ) ) ( )
( ( ) ( ( ) ) )
( ( ) ( ) ( ) )
( ( ) ( ) ) ( )
( ( ) ) ( ( ) )
( ( ) ) ( ) ( )
( ) ( ( ( ) ) )
( ) ( ( ) ( ) )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) )
( ) ( ) ( ) ( )

下面给出生成排列的代码：

#include <iostream>#include <vector>using namespace std;//Print the legal combinationvoid 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 bracketvoid 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 positionif (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;}