P14672 [ICPC 2025 Seoul R] CPEquivalence

Given an integer array $x$ consisting of integers (namely, each item of $x$ is an integer), the Closest Position array (CP-array) $CP(x)$ is an array of length $|x|$ defined to be $$ CP(x)[i] = \max(\{j \mid j < i; x[j] \ge x[i]\} \cup \{-1\}) \text{ for all } 0 \le i < |x|, $$ where $x[i]$ denotes the $i$-th integer in $x$, and the length $|x|$ is the number of integers in $x$. In other words, $CP(x)[i]$ is the greatest index of $x$ that is smaller than $i$ and whose item at that index is greater than or equal to $x[i]$. For example, when $x = [64, 2, 5, 100, 100]$, its CP-array is $CP(x) = [-1, 0, 0, -1, 3]$, and $|x| = 5$. We say that two integer arrays $x$ and $y$ are CP-equivalent if $CP(x) = CP(y)$. It is obvious that two CP-equivalent integer arrays $x$ and $y$ have the same length. For example, two arrays $x = [64, 2, 5, 100, 100]$ and $y = [3, 1, 2, 4, 1]$ are CP-equivalent because their CP-arrays are the same as $[-1, 0, 0, -1, 3]$. For an integer array $x$, an integer $a$ and a non-negative integer $i < |x|$, a substitution operation on $x$ at position $i$ into $a$ returns the array $[x[0], x[1], \cdots, x[i-1], a, x[i+1], \cdots, x[|x|-1]]$. For an integer array $x$ and a non-negative integer $i < |x|$, a deletion operation on $x$ at position $i$ returns the array $[x[0], x[1], \cdots, x[i-1], x[i+1], \cdots, x[|x|-1]]$. Finally, for an integer array $x$, an integer $a$ and a non-negative integer $i \le |x|$, an insertion operation on $x$ at position $i$ returns the array $[x[0], x[1], \cdots, x[i-1], a, x[i], \cdots, x[|x|-1]]$. An edit operation on $x$ is one of an insertion, a deletion or a substitution at a single position. Given two integer arrays $x$ and $y$, compute the minimum number of edit operations on $y$ to obtain an array $y'$ satisfying $CP(x) = CP(y')$. For example, let $x = [64, 2, 5, 100, 100]$ and $y = [-5, -5, -5, -5]$. Consider the array $y' = [-5, -6, -5, -4, -5]$. Then, we have $CP(y') = [-1, 0, 0, -1, 3]$ and therefore $x$ and $y'$ are CP-equivalent. Then, we can obtain the integer array $y'$ applying two edit operations on $y$ and it is minimum.

Your program is to read from standard input. The input consists of three lines. The first line consists of two integers $n$ and $m$ ($1 \le n \le 40$; $1 \le m \le 40$) that indicate the length of $x$ and $y$, respectively. The second line consists of $n$ integers between $-1,000,000$ and $1,000,000$ (both inclusive), representing the array $x$. The third line consists of $m$ integers between $-1,000,000$ and $1,000,000$ (both inclusive), representing the array $y$.

Your program is to write to standard output. Print exactly one line containing the minimum number of edit operations on $y$ to obtain an integer array $y'$ satisfying $CP(x) = CP(y')$.