Nice explaination!

Can you also provide a explaination for problem C? Why can't we use the sqrt function to solve that question?

hey i didn't understand what you are trying to say.

I think The problem Statement is correct But Confusing

See for N=1

All the isomorphic string are a,b,c,d,e,............,z(smallest one is a)

for N=2

aa,bb,cc,dd,ee,ff,gg,..........,zz(with first and second value equal. All isomorphic to each other and the smallest one is aa)

ab,ac,ad,......,az,ba,bc,bd,.....bz,ca,cb,cd,....,cz,...........................zz (with first and second value different. All isomorphic to each other and the smallest one is ab)

So for N=3

aaa(smallest with all value same)

aab(smallest with first two same and last one different)

aba(smallest with first and last same and middle one different)

abb(smallest with last two same)

abc(smallest with all three different)

So this is what is required finding ALL smallest isomorphic strings(normal) of length N

And All the method told in this comment section works

The editorial solution is here: https://img.atcoder.jp/panasonic2020/editorial.pdf but in Japanese.

Define for signed integers $$$k$$$, the $$$k$$$-overlap from string $$$s$$$ to $$$t$$$, as the string $$$s_0 s_1\ldots s_{m-1}$$$ and $$$t_0t_1\ldots t_{n-1}$$$ "aligned at" the indices $$$s_0$$$ and $$$t_k$$$. This is actually the $$$-k$$$ overlap, and the $$$+k$$$ overlap is defined by aligning $$$s_k$$$ and $$$t_0$$$. You can think of starting off with $$$s$$$ and $$$t$$$ left-aligned, and then $$$+k$$$ means slide $$$s$$$ to the left, while $$$-k$$$ means slide $$$s$$$ to the right. We say the overlap is "good" if $$$s_0=t_k, s_1=t_{k+1}$$$, $$$s_2=t_{k+2}$$$ etc. for all valid indices. It only takes one mismatch to make the overlap bad. And note that if the magnitude $$$|k|$$$ is large enough, then the overlap is trivially good (because there is no overlap at all).

Looking at the code, they are building arrays ab, ac, and bc, which you can think of as:

$$$ab[k]$$$ = true means the $$$k$$$-overlap from string $$$a$$$ to $$$b$$$ is bad

and similarly for ac and bc (actually they do a translation by +50,000 so that ab[-k] is defined).

Lastly to get the answer, they try out various overlaps (in the last double loop, they are unfortunately using letters $$$i$$$, $$$j$$$ in the way that I use $$$k$$$). Precisely, a good superstring for $$$a,b$$$ and $$$c$$$ must simultaneously have a good overlap for pairs $$$(a,b)$$$, $$$(a,c)$$$, and $$$(b,c)$$$. But the reason we don't have to do a triple loop over all possible overlaps $$$k_1,k_2,k_3$$$, is that once you fix an overlap for any of the two pairs, like $$$a,b$$$ and $$$a,c$$$, then you are forced to use a certain overlap for the last pair $$$b,c$$$. In other worsd, $$$k_3$$$ for pair $$$(b,c)$$$ is some formula depending on $$$k_1$$$ and $$$k_2$$$.

For N=3 aaa aab aba abb abc For N=4 aaaa aaab aaba aabb aabc abaa abab abac abba abbb abbc abca abcb abcc abcd