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#### GroceryStore

Find the shortest path in a weighted graph
Spoken language:

There is no food in your fridge and you are hungry. You want to go to a local store and buy some food. You have to hurry as some of the shops will close soon.

There are N squares in your neighborhood and M direct roads connecting them. The squares are numbered from 0 to N − 1. You are living in square 0 and can reach it in 0 seconds. The stores are located in the squares, one in each of them. You are given a map of the neighborhood in the form of four zero-indexed arrays A, B, C and D. Each of the arrays A, B, C contains M integers, while D contains N integers.

• For each I (0 ≤ I < M), the walking distance between squares A[I] and B[I] is C[I] seconds (in either direction).
• There can be multiple roads connecting the same pair of squares, or a road with both ends entering the same square.
• It is possible that some roads go through tunnels or over bridges (that is, the graph of squares and roads doesn't have to be planar).
• It is not guaranteed that you are able to reach all the squares.
• For each J (0 ≤ J < N), the shop at square J will close in D[J] seconds (if D[J] = −1, then the store is already closed);
it is possible to buy the food even if you reach the shop at the very last second, when it closes.

Write a function:

class Solution { public int solution(int[] A, int[] B, int[] C, int[] D); }

that, given arrays A, B, C and D, returns the minimum time (in seconds) needed to reach an open store. If it is impossible, it should return −1.

For example, given:

A[0] = 0 B[0] = 1 C[0] = 2 D[0] = -1 A[1] = 1 B[1] = 2 C[1] = 3 D[1] = 1 A[2] = 3 B[2] = 2 C[2] = 4 D[2] = 3 A[3] = 1 B[3] = 3 C[3] = 5 D[3] = 8 A[4] = 2 B[4] = 0 C[4] = 7 A[5] = 2 B[5] = 1 C[5] = 5

the function should return 7. To reach the closest open shop you should follow the path: 0 −> 1 −> 3.

However, if given, for example:

A[0] = 0 D[0] = -1 B[0] = 1 D[1] = 6 C[0] = 10 D[2] = 8

the function should return −1, as you will not be able to reach square 1 in less than 10 seconds, and you cannot reach square 2 at all.

Write an efficient algorithm for the following assumptions:

• N is an integer within the range [1..120];
• M is an integer within the range [0..N**2];
• each element of arrays A and B is an integer within the range [0..N - 1];
• each element of array C is an integer within the range [0..100,000];
• each element of array D is an integer within the range [−1..1,000,000,000].
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