Range Minimum Queries

AtCoder

IDarc098_c

Time2000ms

Memory256MB

Difficulty—

You are given an integer sequence $A$ of length $N$ and an integer $K$. You will perform the following operation on this sequence $Q$ times: * Choose a contiguous subsequence of length $K$, then remove the smallest element among the $K$ elements contained in the chosen subsequence (if there are multiple such elements, choose one of them as you like). Let $X$ and $Y$ be the values of the largest and smallest element removed in the $Q$ operations. You would like $X-Y$ to be as small as possible. Find the smallest possible value of $X-Y$ when the $Q$ operations are performed optimally. ## Constraints * $1 \leq N \leq 2000$ * $1 \leq K \leq N$ * $1 \leq Q \leq N-K+1$ * $1 \leq A_i \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ $Q$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

5 3 2
4 3 1 5 2

Output #1

1

In the first operation, whichever contiguous subsequence of length $3$ we choose, the minimum element in it is $1$. Thus, the first operation removes $A_3=1$ and now we have $A=(4,3,5,2)$. In the second operation, it is optimal to choose $(A_2,A_3,A_4)=(3,5,2)$ as the contiguous subsequence of length $3$ and remove $A_4=2$. In this case, the largest element removed is $2$, and the smallest is $1$, so their difference is $2-1=1$.

Input #2

10 1 6
1 1 2 3 5 8 13 21 34 55

Output #2

Input #3

11 7 5
24979445 861648772 623690081 433933447 476190629 262703497 211047202 971407775 628894325 731963982 822804784

Output #3

451211184

API Response (JSON)

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    "name": "Range Minimum Queries",
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    "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": "arc098_c"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence $A$ of length $N$ and an integer $K$. You will perform the following operation on this sequence $Q$ times:\n\n*   Choose a contiguous subsequence of length $K$, then re...",
      "is_translate": false,
      "language": "English"
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Full JSON Raw Segments