Non-Overlapping Swaps

AtCoder

IDwtf22_day1_b

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P=(P_1,P_2,\cdots,P_N)$ of $(1,2,\cdots,N)$. Find one sequence of integer pairs $((l_1,r_1),(l_2,r_2),\cdots,(l_k,r_k))$ that satisfies all of the following conditions. * The length $k$ of the sequence satisfies $0 \leq k \leq N-1$. * $1 \leq l_i \leq r_i \leq N$ ($1 \leq i \leq k$). * For each $1 \leq i \leq k-1$, it holds that $r_{i+1} \leq l_i$ or $r_i \leq l_{i+1}$. * Performing the following $k$ operations sorts $P$ in ascending order. * The $i$\-th operation: swap the values of $P_{l_i}$ and $P_{r_i}$. If $l_i=r_i$, do nothing. It can be proved that such a sequence always exists under the constraints of this problem. Process $T$ test cases for each input file. ## Constraints * $1 \leq T \leq 250000$ * $1 \leq N \leq 250000$ * $P=(P_1,P_2,\cdots,P_N)$ is a permutation of $(1,2,\cdots,N)$. * The sum of $N$ for each input file is at most $250000$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $case_1$ $case_2$ $\vdots$ $case_T$ Each test case $case_i$ is in the following format: $N$ $P_1$ $P_2$ $\cdots$ $P_N$ [samples]

Samples

Input #1

Output #1

2
2 3
1 2
3
1 4
1 1
2 3
0

Let us explain the first test case.
The sample output satisfies all of the conditions. For example, the fourth condition can be verified as follows: $P=(2,3,1)\to$(swap $P_2,P_3$)$\to(2,1,3)\to$(swap $P_1,P_2$)$\to(1,2,3)$．
The following output, on the other hand, is not correct:

2
1 2
1 3

This is because the third condition is not satisfied.

API Response (JSON)

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    "name": "Non-Overlapping Swaps",
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      "content": "You are given a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$. Find one sequence of integer pairs $((l_1,r_1),(l_2,r_2),\\cdots,(l_k,r_k))$ that satisfies all of the following conditions. *",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "wtf22_day1_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation $P=(P_1,P_2,\\cdots,P_N)$ of $(1,2,\\cdots,N)$.\nFind one sequence of integer pairs $((l_1,r_1),(l_2,r_2),\\cdots,(l_k,r_k))$ that satisfies all of the following conditions.\n\n*...",
      "is_translate": false,
      "language": "English"
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Full JSON Raw Segments