C - Rotate and Palindrome
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C - Rotate and Palindrome
Score : $300$ points
Problem Statement
You are given a string $S$ of length $N$. Let $S_i\ (1\leq i \leq N)$ be the $i$-th character of $S$ from the left.
You may perform the following two kinds of operations zero or more times in any order:
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Pay $A$ yen (the currency in Japan). Move the leftmost character of $S$ to the right end. In other words, change $S_1S_2\ldots S_N$ to $S_2\ldots S_NS_1$.
-
Pay $B$ yen. Choose an integer $i$ between $1$ and $N$, and replace $S_i$ with any lowercase English letter.
How many yen do you need to pay to make $S$ a palindrome?
What is a palindrome?
A string $T$ is a palindrome if and only if the $i$-th character from the left and the $i$-th character from the right are the same for all integers $i$ ($1 \le i \le |T|$), where $|T|$ is the length of $T$.Constraints
- $1\leq N \leq 5000$
- $1\leq A,B\leq 10^9$
- $S$ is a string of length $N$ consisting of lowercase English letters.
- All values in the input except for $S$ are integers.
Input
The input is given from Standard Input in the following format:
Output
Print the answer as an integer.
5 1 2
rrefa
3
First, pay $2$ yen to perform the operation of the second kind once: let $i=5$ to replace $S_5$ with e. $S$ is now rrefe.
Then, pay $1$ yen to perform the operation of the first kind once. $S$ is now refer, which is a palindrome.
Thus, you can make $S$ a palindrome for $3$ yen. Since you cannot make $S$ a palindrome for $2$ yen or less, $3$ is the answer.
8 1000000000 1000000000
bcdfcgaa
4000000000
Note that the answer may not fit into a $32$-bit integer type.