Generate Parentheses

本文介绍了一个使用递归方法生成所有有效括号组合的Java算法。该算法通过递归地添加左括号和右括号,并确保任何时候右括号的数量不超过左括号的数量来构造有效的括号字符串。
public class Solution {
    public ArrayList<String> generateParenthesis(int n) {
        // Start typing your Java solution below
        // DO NOT write main() function
     ArrayList<String> ret = new ArrayList<String>();
char[] chars = new char[2*n];
            solve(0,0,0,2*n,chars,ret);return ret;  }
}

public void solve(int position,int leftnum,int left,int total,char[] chars,List<String> list){
		if(position >= total){
			list.add(new String(chars));
			return;
		}
		if(leftnum == 0 && left < total/2){
			chars[position] = '(';
			solve(position+1,leftnum + 1,++left,total,chars,list);
		}else{
			if(left >= total/2){
				chars[position] = ')';
				solve(position+1,leftnum - 1,left,total,chars,list);
			}else{
				chars[position] = ')';
				solve(position+1,leftnum - 1,left,total,chars,list);
				chars[position] = '(';
				solve(position+1,leftnum + 1,++left,total,chars,list);
			}
		}
	}

#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?
03-08
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