Insertion Sort 2

AtCoder

IDarc162_b

Time2000ms

Memory256MB

Difficulty—

A permutation $P=(P_1,P_2,\ldots,P_N)$ of $(1,2,\ldots,N)$ is given. Determine whether it is possible to rearrange $P$ in ascending order by performing the following operation at most $2\times 10^3$ times, and if possible, show one such sequence of operations. * Choose integers $i$ and $j$ such that $1\leq i \leq N-1,0 \leq j \leq N-2$. Let $Q = (Q_1, Q_2,\ldots,Q_{N-2})$ be the sequence obtained by removing $(P_i,P_{i+1})$ from $P$. Replace $P$ with $(Q_1,\ldots,Q_j, P_i, P_{i+1}, Q_{j+1},\ldots,Q_{N-2})$. ## Constraints * $2 \leq N \leq 10^3$ * $P$ is a permutation of $(1,2,\ldots,N)$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $P_1$ $P_2$ $\ldots$ $P_N$ [samples]

Samples

Input #1

5
1 4 2 3 5

Output #1

Yes
1
3 1

Perform the operation with $i=3,j=1$.
Then, $Q=(P_1,P_2,P_5)=(1,4,5)$, so you get $P=(Q_1,P_3,P_4,Q_2,Q_3) = (1,2,3,4,5)$.
Thus, $P$ can be rearranged in ascending order with one operation.

Input #2

2
2 1

Output #2

No

It can be proved that $P$ cannot be rearranged in ascending order within $2\times 10^3$ operations.

Input #3

4
3 4 1 2

Output #3

Yes
3
3 0
1 2
3 0

There is no need to minimize the number of operations.

API Response (JSON)

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    "name": "Insertion Sort 2",
    "description": {
      "content": "A permutation $P=(P_1,P_2,\\ldots,P_N)$ of $(1,2,\\ldots,N)$ is given. Determine whether it is possible to rearrange $P$ in ascending order by performing the following operation at most $2\\times 10^3$ t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc162_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "A permutation $P=(P_1,P_2,\\ldots,P_N)$ of $(1,2,\\ldots,N)$ is given.\nDetermine whether it is possible to rearrange $P$ in ascending order by performing the following operation at most $2\\times 10^3$ t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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