[ABC272F] Two Strings

ID: 1168

传统题

2000ms

1024MiB

尝试: 1

已通过: 1

难度: 6

上传者:

Hydro

Score : $500$ points

Problem Statement

You are given strings $S$ and $T$ of length $N$ each, consisting of lowercase English letters.

For a string $X$ and an integer $i$ , let $f(X,i)$ be the string obtained by performing on $X$ the following operation $i$ times:

Remove the first character of $X$ and append the same character to the end of $X$ .

Find the number of integer pairs $(i,j)$ satisfying $0 \le i,j \le N-1$ such that $f(S,i)$ is lexicographically smaller than or equal to $f(T,j)$ .

What is the lexicographical order?

Simply put, the lexicographical order is the order in which the words are arranged in a dictionary. Let us define it formally by describing an algorithm of finding the ordering of two distinct strings $S$ and $T$ consisting of lowercase English letters.

Here, we denote "the $i$ -th character of a string $S$ " by $S_i$ . Also, we write $S \lt T$ and $S \gt T$ if $S$ is lexicographically smaller and larger than $T$ , respectively.

Let $L$ be the smallest of the lengths of $S$ and $T$ . For $i=1,2,\dots,L$ , we check if $S_i$ equals $T_i$ .
If there is an $i$ such that $S_i \neq T_i$ , let $j$ be the smallest such $i$ . Comparing $S_j$ and $T_j$ , we terminate the algorithm by determining that $S \lt T$ if $S_j$ is smaller than $T_j$ in the alphabetical order, and that $S \gt T$ otherwise.
If there is no $i$ such that $S_i \neq T_i$ , comparing the lengths of $S$ and $T$ , we terminate the algorithm by determining that $S \lt T$ if $S$ is shorter than $T$ , and that $S \gt T$ otherwise.

Constraints

$1 \le N \le 2 \times 10^5$
$S$ and $T$ are strings of length $N$ each, consisting of lowercase English letters.
$N$ is an integer.

Input

The input is given from Standard Input in the following format:

$N$

$S$

$T$

Output

Print the answer.

3
adb
cab

There are $4$ pairs of $(i, j)$ satisfying the conditions: $(0,0),(0,2),(2,0)$ , and $(2,2)$ .

$(i,j)=(1,2)$ does not satisfy the conditions because $f(S,i)=$ dba and $f(T,j)=$ bca.

10
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#ABC272F. [ABC272F] Two Strings

Problem Statement

Constraints

Input

Output

状态

开发

支持

#ABC272F. [ABC272F] Two Strings

[ABC272F] Two Strings

Problem Statement

Constraints

Input

Output

状态

开发

支持

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