Problem:


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 8s, 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



Sample input:
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:
12

Submission status: Runtime Error

Solution code:
def calculate_magic_to_one_route(target, matrix, original_cost=0):
    if target == -1:
        return 0
    min_magic = matrix[target][1]
    if original_cost > 0 and min_magic > original_cost:
        # print("return: dump")
        return min_magic
    # print("start: {0} (cost: {1}) to 1".format(target, min_magic))
    for i in range(1, len(matrix)):
        # print("try: ", i)
        if target == i:
            continue
        cost = matrix[target][i]
        if cost < min_magic:
            # print("nowcost", min_magic, "subcost: ", cost,
            #       "origin cost", original_cost)
            original_cost = min(min_magic, cost+original_cost)
            subcost = calculate_magic_to_one_route(i, matrix,
                                                   original_cost=original_cost)
            if cost + subcost < min_magic:
                min_magic = cost + subcost
        # else:
            # print("contitune")
    # print("final cost: ", min_magic)
    return min_magic


if __name__ == '__main__':
    H, W = [int(x) for x in input().split()]
    c_mat = []
    for i in range(10):
        c_mat.append([int(x) for x in input().split()])
    A_mat = []
    for i in range(H):
        A_mat.append([int(x) for x in input().split()])
    total_cost = []
    for a_mat in A_mat:
        # print("start ", a_mat)
        # print([calculate_magic_to_one_route(x, c_mat)[0] for x in a_mat])
        total_cost += [calculate_magic_to_one_route(x, c_mat)
                       for x in a_mat]
    print(sum(total_cost))

Submission status: Runtime Error

Solution code:
import networkx as nx
import itertools 

def majic_power(c):
	graph = nx.DiGraph()
	graph.add_nodes_from(range(10))
	for s,t in itertools.product(range(10), range(10)):
		if s != t:
			graph.add_edge(s,t, weight=c[s][t])
	return [nx.dijkstra_path_length(graph, i, 1) for i in range(10)]

def wall(A, c):
	power = majic_power(c)
	cost = 0
	for i,j in itertools.product(range(H), range(W)):
		if A[i][j] == -1 or A[i][j] == 1:
			pass
		else:
			cost += power[A[i][j]]
	print(cost)

items = list(map(int, input().split()))
H = items[0]
W = items[1]
c = list()
A = list()
for i in range(10):
	c_i = list(map(int, input().split()))
	c.append(c_i)
for i in range(H):
	A_i = list(map(int, input().split()))
	A.append(A_i)

wall(A, c)

Submission status: Runtime Error

Solution code:
import networkx as nx
import itertools 

def majic_graph(c):
	graph = nx.DiGraph()
	graph.add_nodes_from(range(10))
	for s,t in itertools.product(range(10), range(10)):
		if s != t:
			graph.add_edge(s,t, weight=c[s][t])
	return graph

def wall(A, c):
	majic = majic_graph(c)
	cost = 0
	for i,j in itertools.product(range(H), range(W)):
		if A[i][j] == -1 or A[i][j] == 1:
			pass
		else:
			cost += nx.dijkstra_path_length(majic, A[i][j], 1)
	print(cost)

items = list(map(int, input().split()))
H = items[0]
W = items[1]
c = list()
A = list()
for i in range(10):
	c_i = list(map(int, input().split()))
	c.append(c_i)
for i in range(H):
	A_i = list(map(int, input().split()))
	A.append(A_i)

wall(A, c)

Submission status: Runtime Error

Solution code:
# -*- coding: utf-8 -*-
H, W = map(int, raw_input().split())
c = [[0 for i in range(10)] for j in range(10)]
A = [[0 for i in range(W)] for j in range(H)]
for i in range(10):
    n = map(int, raw_input().split())
    for j in range(10):
        c[i][j] = n[j]
for i in range(H):
    n = map(int, raw_input().split())
    for j in range(W):
        A[i][j] = n[j]
def getDistance(start):
    if start == 1:
        return 0
    d = [1000 for i in range(10)]
    d[start] = 0
    prev = [-1 for i in range(10)]
    Q = set()
    for i in range(10):
        Q.add(i)
    while len(Q) != 0:
        min = 1000
        for i in range(10):
            if d[i] < min and i in Q:
                min = d[i]
                u = i
        Q.remove(u)
        for v in range(10):
            if d[v] > d[u] + c[u][v]:
                d[v] = d[u] + c[u][v]
                prev[v] = u
    return(d[1])



if __name__ == '__main__':
    D = [0 for i in range(10)]
    for i in range(10):
        D[i] = getDistance(i)
    ans = 0
    for i in range(H):
        for j in range(W):
            if A[i][j] != -1:
                ans += D[A[i][j]]
    print(ans)