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 Sitself.

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

思路：

不斷生成這個字串的新內容，例如：

1 2 2
    ^ ^
    | value pointer
    generate prointer

題解：

int magicalString(int n) {
    if (n == 0) return 0;
    std::string magical{true, false, false};
    int num1s = 1;
    int countIter = 3;
    int generateIter = 2;
    bool flagValue = true;

    while(countIter < n) {
        bool numGenerateValues = magical[generateIter++];
        magical.push_back(flagValue);
        ++countIter;
        num1s += flagValue;
        if (countIter >= n) break;
        if (numGenerateValues == false) { // false --> 2
            ++countIter;
            num1s += flagValue;
            magical.push_back(flagValue);
        }
        flagValue = !flagValue;
    }

    return num1s;
}