String game problem game theory

#1

i am not able to think how this can be solved, need some help to proceed in this

#2

Hint :

This game can be easily reduced to the game of nim. Each segment of consecutive same letters(for eg. “aaa”), can be considered as a pile of game of nim. For a single string, we can just take xor of the piles we defined earlier.

#3

but what their can be new blocks formed after removing of subtring

for ex:-

bbaaabb
if we remove aaa the the block size for b will be 4

#4

we will make two arrays suffix xor of piles ( i.e. consecutive same letters ) and prefix xor of plies and then we will see by removing any piles if we can make the xor equal to zero then B will win else A will win … Got it?

#5

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#6

sir i have doubt in string game ques of game theory ,what is sufixx xor ,prefix xor of piles,how to divide string ,take xor of what??