输出括号所有合法匹配

原文链接:http://blog.csdn.net/doc_sgl/article/details/8917476

简答题最后一题，编程实现所有括号的合法匹配

如输入3

输出："((()))”, “(()())”, “(())()”, “()(())”, “()()()”

思路：深搜+剪枝，关键在于记录已经用掉的左括号个数和右括号的个数，

1，当用过的左括号个数小于右括号则非法；

2，当二者个数和大于2N则非法；

3，当二者个数相等且数目等于2N此时输出。

#include <iostream>
using namespace std;

void DFS_bracket(char* str,int n, int left_used, int right_used)
{
    if(left_used == right_used && left_used + right_used == 2*n)
    {
        for(int i = 0; i < left_used*2; ++i)
            cout<<str[i];
        cout<<endl;
        return;
    }
    if(left_used < right_used || left_used + right_used >= 2*n)
    {
        return ;
    }
    int index = left_used + right_used;
    str[index] = ‘(‘;
    DFS_bracket(str, n, left_used + 1, right_used);

    str[index] = ‘)‘;
    DFS_bracket(str, n, left_used, right_used + 1);
}
int main()
{
    int parenthesisnum;
    cin>>parenthesisnum;

    char* str = new char[parenthesisnum*2+1];
    DFS_bracket(str,parenthesisnum,0,0);
    return 0;
}