Find Permutation

AtCoder

IDabc291_e

Time2000ms

Memory256MB

Difficulty—

There is a length-$N$ sequence $A=(A_1,\ldots,A_N)$ that is a permutation of $1,\ldots,N$. While you do not know $A$, you know that $A_{X_i}<A_{Y_i}$ for $M$ pairs of integers $(X_i,Y_i)$. Can $A$ be uniquely determined? If it is possible, find $A$. ## Constraints * $2 \leq N \leq 2\times 10^5$ * $1 \leq M \leq 2\times 10^5$ * $1\leq X_i,Y_i \leq N$ * All values in the input are integers. * There is an $A$ consistent with the input. ## Input The input is given from Standard Input in the following format: $N$ $M$ $X_1$ $Y_1$ $\vdots$ $X_M$ $Y_M$ [samples]

Samples

Input #1

3 2
3 1
2 3

Output #1

Yes
3 1 2

We can uniquely determine that $A=(3,1,2)$.

Input #2

3 2
3 1
3 2

Output #2

No

Two sequences $(2,3,1)$ and $(3,2,1)$ can be $A$.

Input #3

Output #3

Yes
1 2 3 4

API Response (JSON)

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  "problem": {
    "name": "Find Permutation",
    "description": {
      "content": "There is a length-$N$ sequence $A=(A_1,\\ldots,A_N)$ that is a permutation of $1,\\ldots,N$. While you do not know $A$, you know that $A_{X_i}<A_{Y_i}$ for $M$ pairs of integers $(X_i,Y_i)$. Can $A$ be ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc291_e"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a length-$N$ sequence $A=(A_1,\\ldots,A_N)$ that is a permutation of $1,\\ldots,N$.\nWhile you do not know $A$, you know that $A_{X_i}<A_{Y_i}$ for $M$ pairs of integers $(X_i,Y_i)$.\nCan $A$ be ...",
      "is_translate": false,
      "language": "English"
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}

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