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：（原文链接：http://blog.csdn.net/realxie/article/details/8036892 ）

 

#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 == left)      {          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;  }