Frog 2

AtCoder

IDdp_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ stones, numbered $1, 2, \ldots, N$. For each $i$ ($1 \leq i \leq N$), the height of Stone $i$ is $h_i$. There is a frog who is initially on Stone $1$. He will repeat the following action some number of times to reach Stone $N$: * If the frog is currently on Stone $i$, jump to one of the following: Stone $i + 1, i + 2, \ldots, i + K$. Here, a cost of $|h_i - h_j|$ is incurred, where $j$ is the stone to land on. Find the minimum possible total cost incurred before the frog reaches Stone $N$. ## Constraints * All values in input are integers. * $2 \leq N \leq 10^5$ * $1 \leq K \leq 100$ * $1 \leq h_i \leq 10^4$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $h_1$ $h_2$ $\ldots$ $h_N$ [samples]

Samples

Input #1

5 3
10 30 40 50 20

Output #1

30

If we follow the path $1$ → $2$ → $5$, the total cost incurred would be $|10 - 30| + |30 - 20| = 30$.

Input #2

3 1
10 20 10

Output #2

20

If we follow the path $1$ → $2$ → $3$, the total cost incurred would be $|10 - 20| + |20 - 10| = 20$.

Input #3

2 100
10 10

Output #3

0

If we follow the path $1$ → $2$, the total cost incurred would be $|10 - 10| = 0$.

Input #4

10 4
40 10 20 70 80 10 20 70 80 60

Output #4

40

If we follow the path $1$ → $4$ → $8$ → $10$, the total cost incurred would be $|40 - 70| + |70 - 70| + |70 - 60| = 40$.

API Response (JSON)

{
  "problem": {
    "name": "Frog 2",
    "description": {
      "content": "There are $N$ stones, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), the height of Stone $i$ is $h_i$. There is a frog who is initially on Stone $1$. He will repeat the following action",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "dp_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ stones, numbered $1, 2, \\ldots, N$. For each $i$ ($1 \\leq i \\leq N$), the height of Stone $i$ is $h_i$.\nThere is a frog who is initially on Stone $1$. He will repeat the following action...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments