Problem 1: Balanced Bracket Sequence

Function Description

The function isConvertibleData determines whether each string in a dataset can be transformed into a balanced bracket sequence.

Parameters:

• string dataset[n]: The dataset where each string contains characters ) and (.

Returns:

• int[n]: An array of integers where the ith integer is 1 if the corresponding string can be transformed into a balanced bracket sequence and 0 otherwise.

Constraints:

• 1 ≤ n ≤ 200,000
• 1 ≤ |dataset[i]| ≤ 100,000
• n × sum(|dataset[i]|) ≤ 200,000

Each string in dataset consists of characters ) and ( only.

Input Format

• The first line contains an integer, n, the number of elements in dataset.
• Each of the next n lines contains a string dataset[i].

Sample Input:

2
)(
(())

Sample Output:

1
1

Explanation:

• For the first string )(, the operation can rearrange the brackets to form (), which is a balanced bracket sequence. Hence, the result is 1.
• The second string ((())) is already balanced. Hence, the result is 1.

Problem 2: Image Processing

Function Description

Implement a prototype image processing service. The function getFinalImage performs transformations on a binary image matrix.

Parameters:

• int[n][n] image: The image to be processed.
• int rotation: The rotation parameter.
• int vertical_flip: The vertical flip parameter.
• int horizontal_flip: The horizontal flip parameter.

Returns:

• int[n][n]: The final image after applying the operations.

Constraints:

• 1 ≤ n ≤ 20
• image is a square matrix.
• image[i][j] is either 0 or 1.
• rotation is either 90, 180, or 270.
• horizontal_flip, vertical_flip are either 0 or 1.

Operations:

1. Rotate the image by 90, 180, or 270 degrees clockwise.
2. Flip the image vertically if vertical_flip = 1.
3. Flip the image horizontally if horizontal_flip = 1.

Sample Input:

n = 3, rotation = 270, vertical_flip = 0, horizontal_flip = 1
image = [[1, 0, 0], [0, 1, 1], [0, 0, 1]]

Sample Output:

[[1, 1, 0],
 [0, 1, 0],
 [0, 0, 1]]

Explanation:

• Rotating the image by 270 degrees results in:

[[0, 1, 0],
 [1, 0, 0],
 [1, 1, 1]]

• Vertical flip is skipped as vertical_flip = 0.
• Horizontal flip results in:

[[1, 1, 0],
 [0, 1, 0],
 [0, 0, 1]]

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