Problem Brief

Find Minimum Idleness

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

If shader[i] = "a" then the GPU a is used for the ith shader.

If shader[i] = "b" then the GPU b is used in the ith 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 = "aalbbbaa", 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.

In order 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.

Function Description

Complete the function findMinimumIdleness in the editor.

findMinimumIdleness has the following parameters:

String shader: a string representing the GPUs used
int switchCount: the maximum number of switches allowed

Returns

int: the minimum possible idleness of the system

1Example 1

Input

shader = "aabbbbaaaa", switchCount = 2

Output

Explanation

It is given that shader = "aabbbbaaaa" 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 with shader = "aabababaa", the system has an idleness of 2.

Constraints

Limits and guarantees your solution can rely on.

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