【Codeforces Round #442 (Div. 2)】 B. Nikita and string （线性状态dp）

B. Nikita and string

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

One day Nikita found the string containing letters "a" and "b"
only.

Nikita thinks that string is beautiful if it can be cut into 3 strings (possibly empty) without changing the order of the letters, where the 1-st
and the 3-rd one contain only letters "a"
and the 2-nd contains only letters "b".

Nikita wants to make the string beautiful by removing some (possibly none) of its characters, but without changing their order. What is the maximum length of the string he can get?

Input

The first line contains a non-empty string of length not greater than 5 000 containing only lowercase English letters "a"
and "b".

Output

Print a single integer — the maximum possible size of beautiful string Nikita can get.

Examples

input

abba

output

4

input

bab

output

2

Note

It the first sample the string is already beautiful.

In the second sample he needs to delete one of "b" to make it beautiful.

#include <bits/stdc++.h>
using namespace std;
int dp[5005][3];
int main(){
string s;
cin >> s;
memset(dp, 0, sizeof(dp));
if(s[0] == 'a'){
dp[0][0] = dp[0][1] = 1;
}
else{
dp[0][2] = 1;
}
for(int i = 1; i < s.size(); ++i){
if(s[i] == 'a'){
for(int j = i - 1; j >= 0; --j){
dp[i][1] = max(dp[i][1], dp[j][1] + 1);

4000
dp[i][1] = max(dp[i][1], dp[j][2] + 1);
dp[i][0] = max(dp[i][0], dp[j][0] + 1);
}
}
else{
for(int j = i - 1; j >= 0; --j){
dp[i][2] = max(dp[i][2], dp[j][0] + 1);
dp[i][2] = max(dp[i][2], dp[j][2] + 1);
}
}
}
int ans = 0;
for(int i = 0; i < s.size(); ++i){
ans = max(max(ans, dp[i][0]), max(dp[i][1], dp[i][2]));
}
cout << ans << endl;
}

/*
题意：一个5000的字符串，只有a，b两个字符，现在可以可以删一下字符，使得剩下的字符可以裁剪成三段，第一段和第三段只含a，
第二段只含b。问删除后的字符串最长可以是多长。

思路：这题可以枚举区间来做，区间内只留黑色，当时这样想的，但是写挂了，，然后写dp，，也写挂了。。。渣。。
设dp[i][0]表示以第i个结尾且第i个为a时前面没有b的最大有效长度，dp[i][1]表示以第i个结尾且第i个为a时前面有b的最大有效长度，
dp[i][2]表示以第i个结尾且第i个为b时的最大有效长度。 5000的长度，枚举所有状态去转移就好了，，很简单。。。。
*/