Wall

AtCoder

IDabc079_d

Time2000ms

Memory256MB

Difficulty—

Joisino the magical girl has decided to turn every single digit that exists on this world into $1$. Rewriting a digit $i$ with $j$ $(0≤i,j≤9)$ costs $c_{i,j}$ MP (Magic Points). She is now standing before a wall. The wall is divided into $HW$ squares in $H$ rows and $W$ columns, and at least one square contains a digit between $0$ and $9$ (inclusive). You are given $A_{i,j}$ that describes the square at the $i$\-th row from the top and $j$\-th column from the left, as follows: * If $A_{i,j}≠-1$, the square contains a digit $A_{i,j}$. * If $A_{i,j}=-1$, the square does not contain a digit. Find the minimum total amount of MP required to turn every digit on this wall into $1$ in the end. ## Constraints * $1≤H,W≤200$ * $1≤c_{i,j}≤10^3$ $(i≠j)$ * $c_{i,j}=0$ $(i=j)$ * $-1≤A_{i,j}≤9$ * All input values are integers. * There is at least one digit on the wall. ## Input Input is given from Standard Input in the following format: $H$ $W$ $c_{0,0}$ $...$ $c_{0,9}$ $:$ $c_{9,0}$ $...$ $c_{9,9}$ $A_{1,1}$ $...$ $A_{1,W}$ $:$ $A_{H,1}$ $...$ $A_{H,W}$ [samples]

Samples

Input #1

2 4
0 9 9 9 9 9 9 9 9 9
9 0 9 9 9 9 9 9 9 9
9 9 0 9 9 9 9 9 9 9
9 9 9 0 9 9 9 9 9 9
9 9 9 9 0 9 9 9 9 2
9 9 9 9 9 0 9 9 9 9
9 9 9 9 9 9 0 9 9 9
9 9 9 9 9 9 9 0 9 9
9 9 9 9 2 9 9 9 0 9
9 2 9 9 9 9 9 9 9 0
-1 -1 -1 -1
8 1 1 8

Output #1

12

To turn a single $8$ into $1$, it is optimal to first turn $8$ into $4$, then turn $4$ into $9$, and finally turn $9$ into $1$, costing $6$ MP.
The wall contains two $8$s, so the minimum total MP required is $6×2=12$.

Input #2

5 5
0 999 999 999 999 999 999 999 999 999
999 0 999 999 999 999 999 999 999 999
999 999 0 999 999 999 999 999 999 999
999 999 999 0 999 999 999 999 999 999
999 999 999 999 0 999 999 999 999 999
999 999 999 999 999 0 999 999 999 999
999 999 999 999 999 999 0 999 999 999
999 999 999 999 999 999 999 0 999 999
999 999 999 999 999 999 999 999 0 999
999 999 999 999 999 999 999 999 999 0
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

Output #2

0

Note that she may not need to change any digit.

Input #3

3 5
0 4 3 6 2 7 2 5 3 3
4 0 5 3 7 5 3 7 2 7
5 7 0 7 2 9 3 2 9 1
3 6 2 0 2 4 6 4 2 3
3 5 7 4 0 6 9 7 6 7
9 8 5 2 2 0 4 7 6 5
5 4 6 3 2 3 0 5 4 3
3 6 2 3 4 2 4 0 8 9
4 6 5 4 3 5 3 2 0 8
2 1 3 4 5 7 8 6 4 0
3 5 2 6 1
2 5 3 2 1
6 9 2 5 6

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Wall",
    "description": {
      "content": "Joisino the magical girl has decided to turn every single digit that exists on this world into $1$. Rewriting a digit $i$ with $j$ $(0≤i,j≤9)$ costs $c_{i,j}$ MP (Magic Points). She is now standing be",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc079_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Joisino the magical girl has decided to turn every single digit that exists on this world into $1$.\nRewriting a digit $i$ with $j$ $(0≤i,j≤9)$ costs $c_{i,j}$ MP (Magic Points).\nShe is now standing be...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments