100793: [AtCoder]ABC079 D - Wall
Description
Score : $400$ points
Problem Statement
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:
$H$ $W$ $c_{0,0}$ $...$ $c_{0,9}$ $:$ $c_{9,0}$ $...$ $c_{9,9}$ $A_{1,1}$ $...$ $A_{1,W}$ $:$ $A_{H,1}$ $...$ $A_{H,W}$
Output
Print the minimum total amount of MP required to turn every digit on the wall into $1$ in the end.
Sample 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
Sample 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 $6×2=12$.
Sample 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
Sample Output 2
0
Note that she may not need to change any digit.
Sample 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
Sample Output 3
47