481. Magical String

Problem:

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:

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

思路：

Solution (C++):

int magicalString(int n) {
    string s = "122";
    int i = 2;
    while (s.size() < n) {
        if (i & 1)
            s.append(s[i++]-'0', '2');
        else 
            s.append(s[i++]-'0', '1');
    }
    return count(s.begin(), s.begin()+n, '1');
}

性能：

Runtime: 24 ms  Memory Usage: 7.6 MB

思路：

Solution (C++):

性能：

Runtime: ms  Memory Usage: MB