Sneaking

AtCoder

IDzone2021_e

Time2000ms

Memory256MB

Difficulty—

On a two-dimensional plane, you are now at coordinate $(1, 1)$ and want to get to $(R, C)$, the coordinates of the UFO. When you are at $(r, c)$, you can make the following four kinds of moves: * Move from $(r, c)$ to $(r, c + 1)$ at the cost of $A_{r, c}$. You can make this move when $c < C$. * Move from $(r, c)$ to $(r, c - 1)$ at the cost of $A_{r, c - 1}$. You can make this move when $c > 1$. * Move from $(r, c)$ to $(r + 1, c)$ at the cost of $B_{r, c}$. You can make this move when $r < R$. * Choose an integer $i$ such that $1 ≤ i < r$ and move from $(r, c)$ to $(r - i, c)$ at the cost of $1 + i$. Find the minimum cost needed to move from $(1, 1)$ to $(R, C)$. ## Constraints * All values in input are integers. * $2 ≤ R, C ≤ 500$ * $0 ≤ A_{i,j} < 10^3$ * $0 ≤ B_{i,j} < 10^3$ ## Input Input is given from Standard Input in the following format: $R$ $C$ $A_{1,1}$ $\cdots$ $A_{1,C-1}$ $\vdots$ $A_{R,1}$ $\cdots$ $A_{R,C-1}$ $B_{1,1}$ $\cdots$ $B_{1,C}$ $\vdots$ $B_{R-1,1}$ $\cdots$ $B_{R-1,C}$ [samples]

Samples

Input #1

Output #1

9

You can achieve the cost of $9$ as follows:

*   Move from $(1, 1)$ to $(2, 1)$ at the cost of $1$.
*   Move from $(2, 1)$ to $(3, 1)$ at the cost of $1$.
*   Move from $(3, 1)$ to $(3, 2)$ at the cost of $1$.
*   Move from $(3, 2)$ to $(1, 2)$ at the cost of $3$.
*   Move from $(1, 2)$ to $(1, 3)$ at the cost of $1$.
*   Move from $(1, 3)$ to $(2, 3)$ at the cost of $1$.
*   Move from $(2, 3)$ to $(3, 3)$ at the cost of $1$.

Input #2

7 11
42 77 94 76 40 66 43 28 66 23
27 34 41 31 83 13 64 69 81 82
23 81 0 22 39 51 4 37 84 43
62 37 82 86 26 67 45 78 85 2
79 18 72 62 68 84 69 88 19 48
0 27 21 51 71 13 87 45 39 11
74 57 32 0 97 41 87 96 17 98
69 58 76 32 51 16 38 68 86 82 64
53 47 33 7 51 75 43 14 96 86 70
80 58 12 76 94 50 59 2 1 54 25
14 14 62 28 12 43 15 70 65 44 41
56 50 50 54 53 34 16 3 2 59 88
27 85 50 79 48 86 27 81 78 78 64

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Sneaking",
    "description": {
      "content": "On a two-dimensional plane, you are now at coordinate $(1, 1)$ and want to get to $(R, C)$, the coordinates of the UFO.   When you are at $(r, c)$, you can make the following four kinds of moves: *  ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "zone2021_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On a two-dimensional plane, you are now at coordinate $(1, 1)$ and want to get to $(R, C)$, the coordinates of the UFO.  \nWhen you are at $(r, c)$, you can make the following four kinds of moves:\n\n*  ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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