# Magical String

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.```

Solution:

```class Solution {
public int magicalString(int n) {
if (n == 0) return 0;
if (n <= 3) return 1;
int[] arr = new int[n];
arr[0] = 1; arr[1] = 2; arr[2] = 2;
int head = 2, tail = 3, num = 1, result = 1;
while (tail < n) {
for (int i = 0; i < arr[head] && tail < n; i ++) {
arr[tail] = num;
if (num == 1) result ++;
tail ++;
}
head ++;
num = 3 - num;
}
return result;
}
}```