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.
struct Solution;
impl Solution {
fn magical_string(n: i32) -> i32 {
if n == 0 {
return 0;
}
if n <= 3 {
return 1;
}
let n = n as usize;
let mut a = vec![1, 2, 2];
let mut i = 2;
let mut x = 1;
let mut res = 1;
loop {
for _ in 0..a[i] {
if x == 1 {
res += 1;
}
a.push(x);
if a.len() >= n {
return res;
}
}
x = 3 - x;
i += 1;
}
}
}
#[test]
fn test() {
let n = 6;
let res = 3;
assert_eq!(Solution::magical_string(n), res);
}