I solve it greedy in O(n) : if string s writing as s1 + s2 + s3 and s1,s3 is palindrome and s2[i]==s2[i+1] for any i :i is even then it is a draw else Alice win example string s=abbcca ,s=abeerrba ,s=abccba ,s=aabbcc here it is a draw here my submission :https://mirror.codeforces.com/contest/1728/submission/171626668

but I suggest to solve it using DP suppose we have string of length n : s[l],s[l+1],,,,,,,,s[r-1],s[r] we have four cases : p1 : Alice choose s[l] and Bob choose s[l+1] ,p1=solve(l+2,r) if p1==0 then you need to compare s[l] , s[l+1]

p2 : Alice choose s[l] and Bob choose s[r] ,p2=solve(l+1,r-1) if p2==0 then you need to compare s[l] , s[r]

p3 : Alice choose s[r] and Bob choose s[l] ,p3=solve(l+1,r-1) if p3==0 then you need to compare s[r] , s[l]

p4 : Alice choose s[r] and Bob choose s[r-1] ,p4=solve(l,r-2) if p4==0 then you need to compare s[r] , s[r-1]

then the ans[l][r] = max(min(p1,p2),min(p3,p4)) you should calculate any substring with length 2 before here my submission using DP : https://mirror.codeforces.com/contest/1728/submission/171633331