Maximum Candies You Can Get from Boxes

Hard

You have n boxes labeled from 0 to n - 1. You receive four arrays: status, candies, keys, and containedBoxes where:

status[i] is 1 if the i th box is open and 0 if the i th box is closed,
candies[i] is the number of candies in the i th box,
keys[i] is a list of the labels of the boxes you can open after opening the i th box.
containedBoxes[i] is a list of the boxes you found inside the i th box.

You receive an integer array initialBoxes that has the labels of the boxes you initially have. You can take all the candies in any open box and you can use the keys in it to open new boxes and you also can use the boxes you determine in it.

Produce the maximum number of candies you can get following the rules above.

Example 1

Input: status = [1,0,1,0], candies = [7,5,4,100], keys = [[],[],[1],[]], containedBoxes = [[1,2],[3],[],[]], initialBoxes = [0]

Output: 16

Explanation: You will be initially given box 0. You will determine 7 candies in it and boxes 1 and 2.

Box 1 is closed and you do not have a key for it so you will open box 2. You will determine 4 candies and a key to box 1 in box 2.

In box 1, you will determine 5 candies and box 3 but you will not determine a key to box 3 so box 3 will remain closed.

Total number of candies collected = 7 + 4 + 5 = 16 candy.

Example 2

Input: status = [1,0,0,0,0,0], candies = [1,1,1,1,1,1], keys = [[1,2,3,4,5],[],[],[],[],[]], containedBoxes = [[1,2,3,4,5],[],[],[],[],[]], initialBoxes = [0]

Output: 6

Explanation: You have initially box 0. Opening it you can determine boxes 1,2,3,4 and 5 and their keys.

The total number of candies will be 6.

Constraints

n == status.length == candies.length == keys.length == containedBoxes.length
1 <= n <= 1000
status[i] is either 0 or 1.
1 <= candies[i] <= 1000
0 <= keys[i].length <= n
0 <= keys[i][j] < n
All values of keys[i] are unique.
0 <= containedBoxes[i].length <= n
0 <= containedBoxes[i][j] < n
All values of containedBoxes[i] are unique.
Each box is contained in one box at most.
0 <= initialBoxes.length <= n
0 <= initialBoxes[i] < n

Did this problem appear in one of your interviews?

Responses stay private.

Constraints

Did this problem appear in one of your interviews?

Acceptance rate: 0%