LeetCode Online Judge 题目C# 练习 - Generate Parentheses

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:

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

 1         public static List<string> GenerateParenthesesDPOpt(int n)

 2         {

 3             List<HashSet<string>> ret = new List<HashSet<string>>();

 4             ret.Add(new HashSet<string>(){""});

 5 

 6             for (int i = 1; i <= n; i++)

 7             {

 8                 ret.Add(new HashSet<string>());

 9                 foreach (var s in ret[i - 1])

10                 {

11                     string temp = "()" + s;

12                     ret[i].Add(temp);

13 

14                     temp = s + "()";

15                     ret[i].Add(temp);

16 

17                     temp = "(" + s + ")";

18                     ret[i].Add(temp);

19 

20                     for (int j = 0; j < s.Length; j++) //Credit to ffengfrank, Thank you!

21                     {

22                         if (s[j] == '(')

23                         {

24                             temp = s.Insert(j + 1, "()");

25                             ret[i].Add(temp);

26                         }

27                     }

28                 }

29             }

30 

31             return ret[n].ToList();

32         }

 

代码分析：

　　DP

n = 1 : ()

n = 2 : ()(), ()()重复, (())

n = 3 : ()()(), ()()()重复, (()()), ()(()), (())(), ((()))

......

利用HASHSET<string>减少时间复杂度。 每次比较的时间从O(n)到O(1)

感谢ffengfrank找到的bug，添加了20 ~ 27代码。

 

 1 public static List<string> GenerateParenthesesRecursive(int n)

 2         {

 3             string result = "";

 4             List<string> ret = new List<string>();

 5             GenerateParenthesesRecursive(n, n, result, ret);

 6             return ret;

 7         }

 8 

 9         public static void GenerateParenthesesRecursive(int left, int right, string result, List<string> ret)

10         {

11             if (left == 0 && right == 0)

12             {

13                 ret.Add(result);

14             }

15             else

16             {

17                 if (left > 0)

18                 {

19                     result += "(";

20                     GenerateParenthesesRecursive(left - 1, right, result, ret);

21                     result = result.Remove(result.Length - 1);

22                 }

23                 if (right > left)

24                 {

25                     result += ")";

26                     GenerateParenthesesRecursive(left, right - 1, result, ret);

27                     result = result.Remove(result.Length - 1);

28                 }

29             }

30         }

 

代码分析：

　　递归做法。