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 s is 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 is s itself.

Given an integer n, return the number of 1's in the first n number in the magical string s.

  Example 1:

Input: n = 6
Output: 3
Explanation: The first 6 elements of magical string s is "122112" and it contains three 1's, so return 3.

Example 2:

Input: n = 1
Output: 1

  Constraints:

• 1 <= n <= 10^5

Solution (Java)

class Solution {
    public int magicalString(int n) {
        int[] a = new int[n + 2];
        int fast = 1;
        int slow = 1;
        int num = 1;
        while (fast <= n) {
            a[fast++] = num;
            if (a[slow++] == 2) {
                a[fast++] = num;
            }
            num = 3 - num;
        }
        int count = 0;
        for (int j = 1; j <= n; j++) {
            if (a[j] == 1) {
                count++;
            }
        }
        return count;
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).