22. Generate Parentheses

本文介绍了一个生成所有合法括号组合的算法。通过递归方法,根据左括号和右括号的数量来确定添加条件,最终生成合法的括号字符串集合。

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一,题目

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:

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

二,思路

使用递归
1,left表示左括号的个数,right表示右括号的个数
2,right等于n表示已经生成一个结果
3,生成合法规则
left>right可以添加左括号也可以添加右括号
left==right必须添加左括号


三,代码

public  List<String> generateParenthesis(int n) {
		List<String> result = new ArrayList<String>();
		if (n <= 0) {
			return result;
		}
		dfs(n, 0, 0, "", result);
		return result;
	}

	private  void dfs(int n, int left, int right, String sb, List<String> result) {
		if (right == n) {
			result.add(sb.toString());
			return;
		}
		
		if (left > right) {
			if (left < n) {
				dfs(n, left + 1, right, sb+"(", result);
			}
			dfs(n, left, right + 1, sb+")", result);
		} else if (left == right) {
			dfs(n, left + 1, right, sb+"(", result);
		}

	}


#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::vectorstd::string res; ///< Contains all possible valid patterns void makeStrings(std::string str, int n, int closed, int open); public: std::vectorstd::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::vectorstd::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::vectorstd::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; } 在这段代码的基础上为C++初学者出几个练习题?
03-08
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