Frog 3

AtCoder

IDdp_z

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 $h_i$. Here, $h_1 < h_2 < \cdots < h_N$ holds. 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 $i + 1, i + 2, \ldots, N$. Here, a cost of $(h_j - h_i)^2 + C$ 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. * $2 \leq N \leq 2 \times 10^5$ * $1 \leq C \leq 10^{12}$ * $1 \leq h_1 < h_2 < \cdots < h_N \leq 10^6$ ## Input Input is given from Standard Input in the following format: $N$ $C$ $h_1$ $h_2$ $\ldots$ $h_N$ [samples]

Samples

Input #1

5 6
1 2 3 4 5

Output #1

20

If we follow the path $1$ → $3$ → $5$, the total cost incurred would be $((3 - 1)^2 + 6) + ((5 - 3)^2 + 6) = 20$.

Input #2

2 1000000000000
500000 1000000

Output #2

1250000000000

The answer may not fit into a 32-bit integer type.

Input #3

8 5
1 3 4 5 10 11 12 13

Output #3

62

If we follow the path $1$ → $2$ → $4$ → $5$ → $8$, the total cost incurred would be $((3 - 1)^2 + 5) + ((5 - 3)^2 + 5) + ((10 - 5)^2 + 5) + ((13 - 10)^2 + 5) = 62$.

API Response (JSON)

{
  "problem": {
    "name": "Frog 3",
    "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 $h_i$. Here, $h_1 < h_2 < \\cdots < h_N$ holds. There is a frog who is initially on Stone ",
      "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_z"
  },
  "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 $h_i$. Here, $h_1 < h_2 < \\cdots < h_N$ holds.\nThere is a frog who is initially on Stone ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments