Generate Parentheses

本文介绍了如何通过递归函数生成指定数量的合法括号组合,详细解释了算法的实现过程,并提供了C++代码实现。

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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:

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


题目解析:

1、主要是根据与第一个括号的结合程度:

例如n为3的时候

(1) “()+n为2的时候”

(2)“(n为1的时候)+n为1的时候”

(3)“(n为2的时候)”


#include <iostream>
#include <vector>
#include <string>

using namespace std;

vector<string> generateParenthesis(int n) {
	vector<string> res;
	if(n <= 0)
		return res;
	if(n == 1)
	{
		string str;
		str.push_back('(');
		str.push_back(')');
		res.push_back(str);
		return res;
	}

	for(int i=0;i<n;i++)
	{
		vector<string> vs1 = generateParenthesis(i);
		vector<string> temp;
		if(vs1.size()==0)
		{
			string str(2,' ');
			str.at(0) = '(';
			str.at(1) = ')';
			temp.push_back(str);
		}
		for(size_t j=0;j<vs1.size();j++)
		{
			string str((1+i)*2,' ');
			str.at(0) = '(';
			str.at((1+i)*2-1) = ')';
			string ss = vs1[j];
			for(size_t k=0;k<ss.size();k++)
			{
				str.at(k+1) = ss[k];
			}
			temp.push_back(str);
		}
		vector<string> vs2 = generateParenthesis(n-i-1);
		for(size_t p = 0;p<temp.size();p++)
		{
			string ss = temp[p];
			if(vs2.size() == 0)
			{
				res.push_back(ss);
			}
			for(size_t q = 0;q<vs2.size();q++)
			{
				string sss = ss;
				string ss2 = vs2[q];
				sss.append(ss2);
				res.push_back(sss);
			}
		}

	}
	return res;
}

void printStringList(vector<string> &res)
{
	vector<string>::iterator it = res.begin();
	for(;it!=res.end();it++)
	{
		cout << *it << endl;
	}
}

int main(void)
{
	vector<string> res = generateParenthesis(3);
	printStringList(res);
	system("pause");
	return 0;
}


#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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