481. 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.
``````

``````class Solution {
public:
int magicalString(int n) {
if (n <= 0) return 0;
if (n <= 3) return 1;
int res = 1, head = 2, tail = 3, num = 1;
vector<int> v{1, 2, 2};
while (tail < n) {
for (int i = 0; i < v[head]; ++i) {
v.push_back(num);
if (num == 1 && tail < n) ++res;
++tail;
}
num ^= 3;
}
return res;
}
};
``````

``````class Solution {
public:
int magicalString(int n) {
string s = "122";
int i = 2;
while (s.size() < n) {
s += string(s[i++] - '0', s.back() ^ 3);
}
return count(s.begin(), s.begin() + n, '1');
}
};
``````

https://discuss.leetcode.com/topic/74637/short-c

https://discuss.leetcode.com/topic/74917/simple-java-solution-using-one-array-and-two-pointers

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