Codeforces Round #334 (Div. 2) 604C Alternative Thinking(脑洞)

C. Alternative Thinking

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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 an alternating 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.

Sample test(s)

input

8
10000011

output

5

input

2
01

output

2

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.

题目链接:点击打开链接

给出一个字符串, 可以将连续的0变为1, 问形如"010" "101" "1010"类的字符串最长多长.

若字符串长度小于4, 则字符串最长的长度为字符串本身长度. 否则记录 s[i] != s[i - 1]数量, 加到ans上, ans初始化为3, 因为连续的000可

以变为010, 即长度为3. 最后如果求得的答案大于本身长度, 则答案为字符串本身长度.

AC 代码:

#include "iostream"
#include "cstdio"
#include "cstring"
#include "algorithm"
#include "queue"
#include "stack"
#include "cmath"
#include "utility"
#include "map"
#include "set"
#include "vector"
#include "list"
using namespace std;
typedef long long ll;
const int MOD = 1e9 + 7;
const int INF = 0x3f3f3f3f;
const int MAXN = 1e5 + 5;
int n, ans = 3;
char s[MAXN];
int main(int argc, char const *argv[])
{
    scanf("%d", &n);
    scanf("%s", s);
    for(int i = 1; i < n; ++i)
        ans += (s[i] != s[i - 1]);
    if(ans > n) ans = n;
    printf("%d\n", ans);
    return 0;
}