LeetCode - Magical String

Question Definition

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.

Java Solution

public int magicalString(int n) {
    if (n <= 0) return 0;
    if (n <= 3) return 1;

    int[] a = new int[n + 1];
    a[0] = 1; a[1] = 2; a[2] = 2;
    int head = 2, tail = 3, num = 1, result = 1;

    while (tail < n) {
        for (int i = 0; i < a[head]; i++) {
            a[tail] = num;
            if (num == 1 && tail < n) result++;
            tail++;
        }
        num = num ^ 3;
        head++;
    }

    return result;
}