A magical string S consists of only '1' and '2' and obeys the following rules:

The string S is magical because concatenating the number of contiguous occurrences of characters '1' and '2' generates the stringS itself.

The first few elements of string S is the following:S = "1221121221221121122……"

If we group the consecutive '1's and '2's in S, it will be:

1 22 11 2 1 22 1 22 11 2 11 22 ......

and the occurrences of '1's or '2's in each group are:

1 2 2 1 1 2 1 2 2 1 2 2 ......

You can see that the occurrence sequence above is the S itself.

Given an integer N as input, return the number of '1's in the first N number in the magical stringS.

Note:N will not exceed 100,000.

Example 1:

Input: 6Output: 3Explanation: The first 6 elements of magical string S is "12211" and it contains three 1's, so return 3.
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計(jì)算題目中描述的有規(guī)律的字符串的前n個(gè)字符中‘1’的個(gè)數(shù)。先構(gòu)造這個(gè)字符串（大小大于n即可），然后計(jì)算其中‘1’的個(gè)數(shù)。規(guī)律是當(dāng)前i指向的數(shù)表示次數(shù)，當(dāng)前字符串的末尾的數(shù)的“相反數(shù)”表示要添加的數(shù)，比如“122”，i=2指向2，字符串末尾為“2”，即在字符串后加2個(gè)1.
代碼：
class Solution{public:	int magicalString(int n)	{		string s = "122";		int i = 2;		while(s.size() < n)		{			s += string(s[i++] - '0', s.back() == '1' ? '2' : '1');		}		return count(s.begin(), s.begin() + n, '1');	}};