Generate Parentheses

本文介绍了一种递归算法来生成所有合法的n对括号组合。通过递归调用并确保左括号的数量不超过右括号的数量,该算法能够有效地生成所有可能的合法括号序列。

题目描述

Given n pairs of parentheses, write a function to generate all combinations of well-formed parentheses.

For example, given n = 3, a solution set is:

"((()))", "(()())", "(())()", "()(())", "()()()" 

Solution:

递归遍历即可,注意两个条件,要插入‘(’的时候一定要剩余的数目大于0,要插入‘)’的时候一定要剩余的数目大于0 并且剩余的)的数目大于剩余的( 的数目.

题目大意:

给一个数目n要求组合成一个由n对括号组成的字符串,要求输出所有的可能排列情况。

实现代码:

            class Solution {
public:
    vector<string> generateParenthesis(int n) {
        vector<string> res;  
        string tmp(n+n,0);
        generate(res,n,n,tmp,0);  
        return res;  
    }  
private:  
    void generate(vector<string>& res,int l,int r,string tmp,int index)
    {  
        if(l==0 && r==0)//左右括号全部用完;
        {  
            res.push_back(tmp);  
            return;  
        }  
        if(l>0) //l表示左括号剩下的个数;必须先放左括号;
        {  
            tmp[index]='(';  
            generate(res,l-1,r,tmp,index+1);  
        }  
        if(r>0 && r>l) //r表示右括号剩下的个数,但是必须大于左括号剩下的个数;
        {  
            tmp[index]=')';  
            generate(res,l,r-1,tmp,index+1);  
        }  
    }
};

                


#include <cassert> /// for assert #include <iostream> /// for I/O operation #include <vector> /// for vector container /** * @brief Backtracking algorithms * @namespace backtracking */ namespace backtracking { /** * @brief generate_parentheses class */ class generate_parentheses { private: std::vector<std::string> res; ///< Contains all possible valid patterns void makeStrings(std::string str, int n, int closed, int open); public: std::vector<std::string> generate(int n); }; /** * @brief function that adds parenthesis to the string. * * @param str string build during backtracking * @param n number of pairs of parentheses * @param closed number of closed parentheses * @param open number of open parentheses */ void generate_parentheses::makeStrings(std::string str, int n, int closed, int open) { if (closed > open) // We can never have more closed than open return; if ((str.length() == 2 * n) && (closed != open)) { // closed and open must be the same return; } if (str.length() == 2 * n) { res.push_back(str); return; } makeStrings(str + ')', n, closed + 1, open); makeStrings(str + '(', n, closed, open + 1); } /** * @brief wrapper interface * * @param n number of pairs of parentheses * @return all well-formed pattern of parentheses */ std::vector<std::string> generate_parentheses::generate(int n) { backtracking::generate_parentheses::res.clear(); std::string str = "("; generate_parentheses::makeStrings(str, n, 0, 1); return res; } } // namespace backtracking /** * @brief Self-test implementations * @returns void */ static void test() { int n = 0; std::vector<std::string> patterns; backtracking::generate_parentheses p; n = 1; patterns = {{"()"}}; assert(p.generate(n) == patterns); n = 3; patterns = {{"()()()"}, {"()(())"}, {"(())()"}, {"(()())"}, {"((()))"}}; assert(p.generate(n) == patterns); n = 4; patterns = {{"()()()()"}, {"()()(())"}, {"()(())()"}, {"()(()())"}, {"()((()))"}, {"(())()()"}, {"(())(())"}, {"(()())()"}, {"(()()())"}, {"(()(()))"}, {"((()))()"}, {"((())())"}, {"((()()))"}, {"(((())))"}}; assert(p.generate(n) == patterns); std::cout << "All tests passed\n"; } /** * @brief Main function * @returns 0 on exit */ int main() { test(); // run self-test implementations return 0; } 解释一下这段代码?
最新发布
03-08
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