题目描述：

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 string S 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 string S.

Note: N will not exceed 100,000.

Example 1:

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Input: 6
Output: 3
Explanation: The first 6 elements of magical string S is "12211" and it contains three 1's, so return 3.

按照一个序列中的数值往这个序列的末尾增加元素，要求1与2是间隔的，不能超过两个相同的值在一起。按照题目给出的规律生成这个序列就可以了。

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class Solution {
public:
    int magicalString(int n) {
        if(n == 0) return 0;
        vector<int> s(n + 1);
        s[0] = 1, s[1] = 2, s[2] = 2;
        int index1 = 3, index2 = 2;
        int ans = 1;
        while(index1 < n){
            int t = s[index1 - 1] == 1 ? 2 : 1;
            for(int i = 0; i < s[index2]; i++){
                s[index1 + i] = t;
            }
            if(t == 1){
                ans += s[index2];
            }
            index1 += s[index2];
            index2++;
        }
        if(index1 > n && s[index1 - 1] == 1) ans--; 
        return ans;
    }
};