Permutation Distance

AtCoder

IDabc283_f

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P=(P _ 1,P _ 2,\ldots,P _ N)$ of $(1,2,\ldots,N)$. Find the following value for all $i\ (1\leq i\leq N)$: * $D _ i=\displaystyle\min_{j\neq i}\left\lparen\left\lvert P _ i-P _ j\right\rvert+\left\lvert i-j\right\rvert\right\rparen$. What is a permutation? A permutation of $(1,2,\ldots,N)$ is a sequence that is obtained by rearranging $(1,2,\ldots,N)$. In other words, a sequence $A$ of length $N$ is a permutation of $(1,2,\ldots,N)$ if and only if each $i\ (1\leq i\leq N)$ occurs in $A$ exactly once. ## Constraints * $2 \leq N \leq 2\times10^5$ * $1 \leq P _ i \leq N\ (1\leq i\leq N)$ * $i\neq j\implies P _ i\neq P _ j$ * All values in the input 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

4
3 2 4 1

Output #1

2 2 3 3 

For example, for $i=1$,

*   if $j=2$, we have $\left\lvert P _ i-P _ j\right\rvert=1$ and $\left\lvert i-j\right\rvert=1$;
*   if $j=3$, we have $\left\lvert P _ i-P _ j\right\rvert=1$ and $\left\lvert i-j\right\rvert=2$;
*   if $j=4$, we have $\left\lvert P _ i-P _ j\right\rvert=2$ and $\left\lvert i-j\right\rvert=3$.

Thus, the value is minimum when $j=2$, where $\left\lvert P _ i-P _ j\right\rvert+\left\lvert i-j\right\rvert=2$, so $D _ 1=2$.

Input #2

7
1 2 3 4 5 6 7

Output #2

2 2 2 2 2 2 2

Input #3

16
12 10 7 14 8 3 11 13 2 5 6 16 4 1 15 9

Output #3

3 3 3 5 3 4 3 3 4 2 2 4 4 4 4 7

API Response (JSON)

{
  "problem": {
    "name": "Permutation Distance",
    "description": {
      "content": "You are given a permutation $P=(P _ 1,P _ 2,\\ldots,P _ N)$ of $(1,2,\\ldots,N)$. Find the following value for all $i\\ (1\\leq i\\leq N)$: *   $D _ i=\\displaystyle\\min_{j\\neq i}\\left\\lparen\\left\\lvert P ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc283_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a permutation $P=(P _ 1,P _ 2,\\ldots,P _ N)$ of $(1,2,\\ldots,N)$.\nFind the following value for all $i\\ (1\\leq i\\leq N)$:\n\n*   $D _ i=\\displaystyle\\min_{j\\neq i}\\left\\lparen\\left\\lvert P ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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