Generate Parentheses

本文介绍了如何使用栈实现生成给定数量的合法括号组合,包括Python代码实现及示例输出。

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leetcode 第二发

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:

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

看到这个题首先联想到的就是编译原理课上学到的词法分析和语法分析之类的内容,通过栈来实现。一下是Python实现可以没有通过LeetCode的时间限制

Python实现:

class Solution:
    # @param an integer
    # @return a list of string
    def generateParenthesis(self, n):
        l = []
        for i in range(1, 2*n+1):
            l.append(i)
        alls = list(itertools.permutations(l, 2*n))
        
        pResult = []
        
        for t in alls:
            s = []
            result = ['""']
            p = []
            for i in range(0, 2*n+1):
                if i == 0:
                    p.append("")
                elif i <=n:
                    p.append("(")
                else:
                    p.append(")")
            flag = True
            for i in t:
                if flag:
                    s.append(i)
                    flag = False
                    continue
                if len(s) == 0:
                    s.append(i)
                elif s[-1]<=n and i>n:
                    s.pop()
                else:
                    s.append(i)
            if len(s) == 0:
                for i in t:
                    result.append(p[i])
                result.append('"')
                parentheses = ''.join(result)
                if parentheses in pResult:
                    continue
                else:
                    pResult.append(parentheses)
        return pResult


#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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