Hieroglyphs Batch Compilation commands

A team of researchers is studying the similarities between sequences of hieroglyphs. They represent each hieroglyph with a non-negative integer. To perform their study, they use the following concepts about sequences.

For a fixed sequence $A$, a sequence $S$ is called a subsequence of $A$ if and only if $S$ can be obtained by removing some elements (possibly none) from $A$.

The table below shows some examples of subsequences of a sequence $A = [3, 2, 1, 2]$.

Subsequence	How it can be obtained from $A$
[3, 2, 1, 2]	No elements are removed.
[2, 1, 2]	[<s>3</s>, 2, 1, 2]
[3, 2, 2]	[3, 2, <s>1</s>, 2]
[3, 2]	[3, <s>2</s>, <s>1</s>, 2] or [3, 2, <s>1</s>, <s>2</s>]
[3]	[3, <s>2</s>, <s>1</s>, <s>2</s>]
[ ]	[<s>3</s>, <s>2</s>, <s>1</s>, <s>2</s>]

On the other hand, $[3, 3]$ or $[1, 3]$ are not subsequences of $A$.

Consider two sequences of hieroglyphs, $A$ and $B$. A sequence $S$ is called a common subsequence of $A$ and $B$ if and only if $S$ is a subsequence of both $A$ and $B$. Moreover, we say that a sequence $U$ is a universal common subsequence of $A$ and $B$ if and only if the following two conditions are met:

• $U$ is a common subsequence of $A$ and $B$.
• Every common subsequence of $A$ and $B$ is also a subsequence of $U$.

It can be shown that any two sequences $A$ and $B$ have at most one universal common subsequence.

The researchers have found two sequences of hieroglyphs $A$ and $B$. Sequence $A$ consists of $N$ hieroglyphs and sequence $B$ consists of $M$ hieroglyphs. Help the researchers compute a universal common subsequence of sequences $A$ and $B$, or determine that such a sequence does not exist.

Implementation details

You should implement the following procedure.

std::vector<int> ucs(std::vector<int> A, std::vector<int> B)

• $A$: array of length $N$ describing the first sequence.
• $B$: array of length $M$ describing the second sequence.
• If there exists a universal common subsequence of $A$ and $B$, the procedure should return an array containing this sequence. Otherwise, the procedure should return $[-1]$ (an array of length $1$, whose only element is $-1$).
• This procedure is called exactly once for each test case.

Constraints

• $1 \leq N \leq 100\,000$
• $1 \leq M \leq 100\,000$
• $0 \leq A[i] \leq 200\,000$ for each $i$ such that $0 \leq i < N$
• $0 \leq B[j] \leq 200\,000$ for each $j$ such that $0 \leq j < M$

Subtasks

Subtask	Score	Additional Constraints
1	$3$	$N = M$; each of $A$ and $B$ consists of $N$ distinct integers between $0$ and $N-1$ (inclusive)
2	$15$	For any integer $k$, (the number of elements of $A$ equal to $k$) plus (the number of elements of $B$ equal to $k$) is at most $3$.
3	$10$	$A[i] \leq 1$ for each $i$ such that $0 \leq i < N$; $B[j] \leq 1$ for each $j$ such that $0 \leq j < M$
4	$16$	There exists a universal common subsequence of $A$ and $B$.
5	$14$	$N \leq 3000$; $M \leq 3000$
6	$42$	No additional constraints.

Examples

Example 1

Consider the following call.

ucs([0, 0, 1, 0, 1, 2], [2, 0, 1, 0, 2])

Here, the common subsequences of $A$ and $B$ are the following: $[\ ]$, $[0]$, $[1]$, $[2]$, $[0, 0]$, $[0, 1]$, $[0, 2]$, $[1, 0]$, $[1, 2]$, $[0, 0, 2]$, $[0, 1, 0]$, $[0, 1, 2]$, $[1, 0, 2]$ and $[0, 1, 0, 2]$.

Since $[0, 1, 0, 2]$ is a common subsequence of $A$ and $B$, and all common subsequences of $A$ and $B$ are subsequences of $[0, 1, 0, 2]$, the procedure should return $[0, 1, 0, 2]$.

Example 2

Consider the following call.

ucs([0, 0, 2], [1, 1])

Here, the only common subsequence of $A$ and $B$ is the empty sequence $[\ ]$. It follows that the procedure should return an empty array $[\ ]$.

Example 3

Consider the following call.

ucs([0, 1, 0], [1, 0, 1])

Here, the common subsequences of $A$ and $B$ are $[\ ], [0], [1], [0, 1]$ and $[1, 0]$. It can be shown that a universal common subsequence does not exist. Therefore, the procedure should return $[-1]$.

Sample Grader

Input format:

N  M
A[0]  A[1]  ...  A[N-1]
B[0]  B[1]  ...  B[M-1]

Output format:

T
R[0]  R[1]  ...  R[T-1]

Here, $R$ is the array returned by ucs and $T$ is its length.