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;
}
}