Alternative Thinking CodeForces - 604C（思维）

最新推荐文章于 2021-05-18 09:46:55 发布

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本文探讨了一个有趣的算法问题，即如何通过翻转一个连续子序列来最大化一个二进制字符串中交替序列的长度。文章提供了详细的解析思路，并给出了一段C++实现代码。

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Kevin has just recevied his disappointing results on the USA Identification of Cows Olympiad (USAICO) in the form of a binary string of length n. Each character of Kevin's string represents Kevin's score on one of the n questions of the olympiad—'1' for a correctly identified cow and '0' otherwise.

However, all is not lost. Kevin is a big proponent of alternative thinking and believes that his score, instead of being the sum of his points, should be the length of the longest alternating subsequence of his string. Here, we define analternating subsequence of a string as a not-necessarily contiguous subsequence where no two consecutive elements are equal. For example, {0, 1, 0, 1}, {1, 0, 1}, and{1, 0, 1, 0} are alternating sequences, while {1, 0, 0} and {0, 1, 0, 1, 1} are not.

Kevin, being the sneaky little puffball that he is, is willing to hack into the USAICO databases to improve his score. In order to be subtle, he decides that he will flip exactly one substring—that is, take a contiguous non-empty substring of his score and change all '0's in that substring to '1's and vice versa. After such an operation, Kevin wants to know the length of the longest possible alternating subsequence that his string could have.

Input

The first line contains the number of questions on the olympiad n (1 ≤ n ≤ 100 000).

The following line contains a binary string of length n representing Kevin's results on the USAICO.

Output

Output a single integer, the length of the longest possible alternating subsequence that Kevin can create in his string after flipping a single substring.

Example

Input

8
10000011

Output

Input

2
01

Output

Note

In the first sample, Kevin can flip the bolded substring '10000011' and turn his string into '10011011', which has an alternating subsequence of length 5: '10011011'.

In the second sample, Kevin can flip the entire string and still have the same score.

思路：首先说审题：给定一个序列，你可以修改一个连续子序列，输出修改后能找到的最长交替序列，这里的最长交替序列不一定挨着。

任何一个序列：

1 ：它自己整体是交替的如： 101010

2 ：它由多个交替序列组成的。如 10 01 1 1 1 10

对于二当我们把中间的某个子序列求反后，左连接点会增加一个长度，右连接点会增加一个长度。但如果只有两部分，则只能增加一个长度。

所以，可以分三个情况：

1 整体交替

2 两部分交替序列组成

3 >=3部分组成

#include<iostream>
#include<cstdio>
#include<string>
#include<map>
using namespace std;

int main(){

 	int n;
    string s;
    cin >> n >> s;
    int ans = 1;
    for(int i = 1; i < n; i++)
        if(s[i] != s[i-1])
           ans++;
    if(ans == n) ans = n;  //情况1
    else if(ans == n-1) ans = n;  //情况 2
    else ans += 2;   // 情况 3
    printf("%d\n",ans);
	return 0;
}