Three Sequences

AtCoder

IDarc211_b

Time2000ms

Memory256MB

Difficulty—

You are given a triple of positive integers $(X,Y,Z)$ such that $X\leq Y\leq Z$. Output one triple of sequences of non-negative integers $(S_1,S_2,S_3)$ that satisfies all of the following conditions: * The lengths of $S_1,S_2,S_3$ are each between $1$ and $1000$, inclusive. * The length of a longest sequence that is both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_2$ is $X$. * The length of a longest sequence that is both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_3$ is $Y$. * The length of a longest sequence that is both a contiguous subsequence of $S_2$ and a contiguous subsequence of $S_3$ is $Z$. * $\max(\max(S_1),\max(S_2),\max(S_3))$ is minimized among all triples satisfying the above four conditions. It can be proved that under the constraints of this problem, a triple $(S_1,S_2,S_3)$ satisfying the conditions always exists. If there are multiple such triples, you may output any of them. ## Constraints * $1\leq X\leq Y\leq Z\leq 100$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $X$ $Y$ $Z$ [samples]

Samples

Input #1

4 5 5

Output #1

10 1 1 0 0 1 0 1 0 1 1
8 1 1 0 1 0 0 1 1
11 1 0 0 0 1 1 0 1 0 1 0

It can be verified that $S_1=(1,1,0,0,1,0,1,0,1,1),S_2=(1,1,0,1,0,0,1,1),S_3=(1,0,0,0,1,1,0,1,0,1,0)$ satisfies the conditions as follows:

*   The lengths of $S_1,S_2,S_3$ are $10,8,11$, respectively, all of which are between $1$ and $1000$, inclusive.
*   The longest sequences that are both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_2$ are $(1,0,0,1)$ and $(1,0,1,0)$, with length $X=4$.
*   The longest sequences that are both a contiguous subsequence of $S_1$ and a contiguous subsequence of $S_3$ are $(1,0,1,0,1)$ and $(0,1,0,1,0)$, with length $Y=5$.
*   The longest sequence that is both a contiguous subsequence of $S_2$ and a contiguous subsequence of $S_3$ is $(1,1,0,1,0)$, with length $Z=5$.
*   $\max(\max(S_1),\max(S_2),\max(S_3))=1$, and it can be shown that it is impossible to satisfy the above four conditions with $\max(\max(S_1),\max(S_2),\max(S_3))=0$, so this is minimal.

API Response (JSON)

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  "problem": {
    "name": "Three Sequences",
    "description": {
      "content": "You are given a triple of positive integers $(X,Y,Z)$ such that $X\\leq Y\\leq Z$. Output one triple of sequences of non-negative integers $(S_1,S_2,S_3)$ that satisfies all of the following conditions:",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
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    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc211_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a triple of positive integers $(X,Y,Z)$ such that $X\\leq Y\\leq Z$.\nOutput one triple of sequences of non-negative integers $(S_1,S_2,S_3)$ that satisfies all of the following conditions:...",
      "is_translate": false,
      "language": "English"
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