Generate Parentheses***

本文介绍了一个生成所有合法括号组合的算法。对于给定的正整数n,该算法能够生成所有可能的由n对括号组成的合法组合,并确保每个组合中的括号都是正确匹配的。例如当n为3时,输出包括((()))、(()())等五种合法括号组合。

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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:

[
"((()))",
"(()())",
"(())()",
"()(())",
"()()()"]

public List<String> generateParenthesis(int n) {
        List<String> res = new ArrayList<String>();
        helper(n, n, "", res);
        return res;
    }
    void helper(int left, int right, String out, List<String> res) {
        if (left < 0 || right < 0 || left > right) return;
        if (left == 0 && right == 0) {
            res.add(out);
            return;
        }
        helper(left - 1, right, out + "(", res);
        helper(left, right - 1, out + ")", res);
    }
    

转载于:https://www.cnblogs.com/bingo2-here/p/7875259.html

#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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