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ambitious

Find the longest valid slice of a sequence of brackets after performing at most K bracket rotations.

Programming language:
Spoken language:

A bracket sequence is considered to be a valid bracket expression if any of the following conditions is true:

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

You are given a sequence of brackets S and you are allowed to rotate some of them. Bracket rotation means picking a single bracket and changing it into its opposite form (i.e. an opening bracket can be changed into a closing bracket and vice versa). The goal is to find the longest slice (contiguous substring) of S that forms a valid bracket sequence using at most K bracket rotations.

Write a function:

int solution(char *S, int K);

that, given a string S consisting of N brackets and an integer K, returns the length of the maximum slice of S that can be transformed into a valid bracket sequence by performing at most K bracket rotations.

For example, given S = "`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

Given S = "`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

Given S = "`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A bracket sequence is considered to be a valid bracket expression if any of the following conditions is true:

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

You are given a sequence of brackets S and you are allowed to rotate some of them. Bracket rotation means picking a single bracket and changing it into its opposite form (i.e. an opening bracket can be changed into a closing bracket and vice versa). The goal is to find the longest slice (contiguous substring) of S that forms a valid bracket sequence using at most K bracket rotations.

Write a function:

int solution(string &S, int K);

that, given a string S consisting of N brackets and an integer K, returns the length of the maximum slice of S that can be transformed into a valid bracket sequence by performing at most K bracket rotations.

For example, given S = "`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

Given S = "`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

Given S = "`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

A bracket sequence is considered to be a valid bracket expression if any of the following conditions is true:

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

You are given a sequence of brackets S and you are allowed to rotate some of them. Bracket rotation means picking a single bracket and changing it into its opposite form (i.e. an opening bracket can be changed into a closing bracket and vice versa). The goal is to find the longest slice (contiguous substring) of S that forms a valid bracket sequence using at most K bracket rotations.

Write a function:

class Solution { public int solution(string S, int K); }

that, given a string S consisting of N brackets and an integer K, returns the length of the maximum slice of S that can be transformed into a valid bracket sequence by performing at most K bracket rotations.

For example, given S = "`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

Given S = "`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

Given S = "`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);
- expected worst-case space complexity is O(N) (not counting the storage required for input arguments).

Copyright 2009–2018 by Codility Limited. All Rights Reserved. Unauthorized copying, publication or disclosure prohibited.

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

func Solution(S string, K int) int

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

class Solution { public int solution(String S, int K); }

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

function solution(S, K);

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

function solution(S, K)

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

int solution(NSString *S, int K);

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

function solution(S: PChar; K: longint): longint;

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

function solution($S, $K);

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

sub solution { my ($S, $K)=@_; ... }

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

def solution(S, K)

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

def solution(s, k)

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

object Solution { def solution(s: String, k: Int): Int }

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

public func solution(inout S : String, _ K : Int) -> Int

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

public func solution(_ S : inout String, _ K : Int) -> Int

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

- it is empty;
- it has the form "
(U)" whereUis a valid bracket sequence;- it has the form "
VW" whereVandWare valid bracket sequences.

For example, the sequence "`(())()`" is a valid bracket expression, but "`((())(()`" is not.

Write a function:

Private Function solution(S As String, K As Integer) As Integer

`)()()(`" and K = 3, you can rotate the first and last brackets to get "`(()())`", which is a valid bracket sequence, so the function should return 6 (notice that you need to perform only two rotations in this instance, though).

`)))(((`" and K = 2, you can rotate the second and fifth brackets to get "`)()()(`", which has a substring "`()()`" that is a valid bracket sequence, so the function should return 4.

`)))(((`" and K = 0, you can't rotate any brackets, and since there is no valid bracket sequence with a positive length in string S, the function should return 0.

Assume that:

- string S contains only brackets: '
(' or ')';- N is an integer within the range [1..30,000];
- K is an integer within the range [0..N].

Complexity:

- expected worst-case time complexity is O(N);

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