Pure Straight

AtCoder

IDarc126_d

Time2000ms

Memory256MB

Difficulty—

Given is a sequence of $N$ positive integers $A = (A_1, A_2, \ldots, A_N)$, where each $A_i$ is $1$, $2$, $\ldots$, or $K$. You can do the following operation on this sequence any number of times. * Swap two adjacent elements, that is, choose $i$ and $j$ such that $|i-j|=1$ and swap $A_i$ and $A_j$. Find the minimum number of operations needed to make $A$ satisfy the following condition. * $A$ contains $(1, 2, \ldots, K)$ as a contiguous subsequence, that is, there is a positive integer $n$ at most $N-K+1$ such that $A_n = 1$, $A_{n+1} = 2$, $\ldots$, and $A_{n+K-1} = K$. ## Constraints * $2\leq K\leq 16$ * $K \leq N\leq 200$ * $A_i$ is $1$, $2$, $\ldots$, or $K$. * $A$ contains at least one occurrence of each of $1, 2, \ldots, K$. ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

4 3
3 1 2 1

Output #1

2

One optimal sequence of operations is as follows.

*   Swap $A_1$ and $A_2$, changing $A$ to $(1,3,2,1)$.
*   Swap $A_2$ and $A_3$, changing $A$ to $(1,2,3,1)$.
*   Now we have $A_1 = 1$, $A_2 = 2$, $A_3 = 3$, satisfying the condition.

Input #2

5 5
4 1 5 2 3

Output #2

Input #3

8 4
4 2 3 2 4 2 1 4

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Pure Straight",
    "description": {
      "content": "Given is a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$, where each $A_i$ is $1$, $2$, $\\ldots$, or $K$. You can do the following operation on this sequence any number of times. * ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc126_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a sequence of $N$ positive integers $A = (A_1, A_2, \\ldots, A_N)$, where each $A_i$ is $1$, $2$, $\\ldots$, or $K$.\nYou can do the following operation on this sequence any number of times.\n\n* ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments