Shader Loader

A game's shaders are rendered using two GPUs: a and b. There is a string s, which represents that for the i^th shader, a GPU is used.

• If shader[i] = 'a', then GPU a is used for the i^th shader.
• If shader[i] = 'b', then GPU b is used for the i^th shader.

The idleness of this dual GPU system is defined as the maximum number of shaders for which the same GPU is used consecutively.
For example, for the string shader = "aabbba", for the first 2 seconds, GPU a is used, then for the next 3 seconds, GPU b is used, then for 1 second, GPU a is used. Hence, the idleness of the system is 3.

To reduce the idleness of the system, the following operation can be used at most switchCount times:

• Select any index i of the string shader. If shader[i] = 'a', then change it to shader[i] = 'b' and vice versa.

Find the minimum possible idleness of the system that can be achieved by applying the operations optimally.

Example:
It is given that shader = "aabbbaaaa" and switchCount = 2.

One optimal solution is:

• Switch shader[4] (1-based index) to get shader = "aababaaaa".
• Switch shader[7] (1-based index) to get shader = "aabababaa".

Now shader = "aabababaa", and the system has an idleness of 2.

Substring Removal

Given a string, seq, that consists of the characters 'A' and 'B' only, in one move, delete either an "AB" or a "BB" substring and concatenate the remaining substrings.

Find the minimum possible length of the remaining string after performing any number of moves.

Note: A substring is a contiguous subsequence of a string.

Example:
seq = "BABBA"

Using 0-based indexing, the following moves are optimal:

• Delete the substring "AB" starting at index 1:
"BABBA" → "BBA"

• Delete the substring "BB" starting at index 0:
"BBA" → "A"

There are no more moves, so the minimum possible length of the remaining string is 1.