[LeetCode] Magical String 神奇字符串

 

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.

 

這道題介紹了一種神奇字符串，只由1和2組成，通過計數1組和2組的個數，又能生成相同的字符串。而讓我們求前n個數字中1的個數說白了其實就是讓我們按規律生成這個神奇字符串，只有生成了字符串的前n個字符，才能統計出1的個數。其實這道題的難點就是在於找到規律來生成字符串，這里我們就直接說規律了，因為博主也沒有自己找到，都是看了網上大神們的解法。根據第三個數字2開始往后生成數字，此時生成兩個1，然后根據第四個數字1，生成一個2，再根據第五個數字1，生成一個1，以此類推，生成的數字1或2可能通過異或3來交替生成，在生成的過程中同時統計1的個數即可，參見代碼如下：

 

解法一：

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;
            ++head;
        }
        return res;
    }
};

 

下面這種解法的思路跟上面一樣，但是寫法上面大大的簡潔了，感覺很叼！

 

解法二：

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');
    }
};

 

參考資料：

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

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

 

LeetCode All in One 題目講解匯總(持續更新中...)