Generate Parentheses

本文介绍了一种使用回溯法生成所有合法括号组合的算法。针对输入的整数n,该算法能有效生成所有可能的合法括号组合,并提供了一个具体的Java实现案例。
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:
"((()))", "(()())", "(())()", "()(())", "()()()"

之前在[url=http://kickcode.iteye.com/blog/2264122]Parentheses总结 [/url]讲过这道题目,用回溯法解决,想看更多类似的题目可以参考上面那篇文章。代码如下:

public class Solution {
public List<String> generateParenthesis(int n) {
List<String> list = new ArrayList<String>();
int left = n;
int right = n;
generateP(2 * n, left, right, "", list);
return list;
}
public void generateP(int n, int left, int right, String s, List<String> list) {
if(s.length() == n) list.add(s);
if(left > 0) generateP(n, left - 1, right, s + '(', list);
if(right > left) generateP(n, left, right - 1, s + ')', 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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