[LeetCode] 38. Count and Say 計數和讀法

 

The count-and-say sequence is the sequence of integers with the first five terms as following:

1.     1
2.     11
3.     21
4.     1211
5.     111221

1 is read off as "one 1" or 11.
11 is read off as "two 1s" or 21.
21 is read off as "one 2, then one 1" or 1211.

Given an integer n where 1 ≤ n ≤ 30, generate the nth term of the count-and-say sequence.

Note: Each term of the sequence of integers will be represented as a string.

 

Example 1:

Input: 1
Output: "1"

Example 2:

Input: 4
Output: "1211" 

 

這道計數和讀法問題還是第一次遇到，看似挺復雜，其實仔細一看，算法很簡單，就是對於前一個數，找出相同元素的個數，把個數和該元素存到新的 string 里。代碼如下：

 

class Solution {
public:
    string countAndSay(int n) {
        if (n <= 0) return "";
        string res = "1";
        while (--n) {
            string cur = "";
            for (int i = 0; i < res.size(); ++i) {
                int cnt = 1;
                while (i + 1 < res.size() && res[i] == res[i + 1]) {
                    ++cnt;
                    ++i;
                }
                cur += to_string(cnt) + res[i];
            }
            res = cur;
        }
        return res;
    }
};

 

博主出於好奇打印出了前 12 個數字，發現一個很有意思的現象，不管打印到后面多少位，出現的數字只是由 1, 2 和3 組成，網上也有人發現了並分析了原因，參見這個帖子，前十二個數字如下：

 

1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
3 1 2 2 1 1
1 3 1 1 2 2 2 1
1 1 1 3 2 1 3 2 1 1
3 1 1 3 1 2 1 1 1 3 1 2 2 1
1 3 2 1 1 3 1 1 1 2 3 1 1 3 1 1 2 2 1 1
1 1 1 3 1 2 2 1 1 3 3 1 1 2 1 3 2 1 1 3 2 1 2 2 2 1
3 1 1 3 1 1 2 2 2 1 2 3 2 1 1 2 1 1 1 3 1 2 2 1 1 3 1 2 1 1 3 2 1 1

 

Github 同步地址：

https://github.com/grandyang/leetcode/issues/38

 

類似題目：

Encode and Decode Strings

String Compression

 

參考資料：

https://leetcode.com/problems/count-and-say/

https://leetcode.com/problems/count-and-say/discuss/16000/Show-an-Answer-in-Java

https://leetcode.com/problems/count-and-say/discuss/16043/C%2B%2B-solution-easy-understand

 

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