How to Solve Minimum Space Wasted From Packaging Problem
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Minimum Space Wasted From Packaging
You have n packages that you are trying to place in boxes, one package in each box. There are m suppliers that each produce boxes of different sizes (with infinite supply). A package can be placed in ...
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Understanding the Minimum Space Wasted From Packaging Problem
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Problem Statement
You have n packages that you are trying to place in boxes, one package in each box. There are m suppliers that each produce boxes of different sizes (with infinite supply). A package can be placed in a box if the size of the package is less than or equal to the size of the box. The package sizes are given as an integer array packages, where packages[i] is the size of the ith package. The suppliers are given as a 2D integer array boxes, where boxes[j] is an array of box sizes that the jth supplier produces. You want to choose a single supplier and use boxes from them such that the total wasted space is minimized. For each package in a box, we define the space wasted to be size of the box - size of the package. The total wasted space is the sum of the space wasted in all the boxes. For example, if you have to fit packages with sizes [2,3,5] and the supplier offers boxes of sizes [4,8], you can fit the packages of size-2 and size-3 into two boxes of size-4 and the package with size-5 into a box of size-8. This would result in a waste of (4-2) + (4-3) + (8-5) = 6. Return the minimum total wasted space by choosing the box supplier optimally, or -1 if it is impossible to fit all the packages inside boxes. Since the answer may be large, return it modulo 109 + 7.
Minimum Space Wasted From Packaging
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Examples
packages = [2,3,5], boxes = [[4,8],[2,8]]
6
It is optimal to choose the first supplier, using two size-4 boxes and one size-8 box. The total waste is (4-2) + (4-3) + (8-5) = 6.
packages = [2,3,5], boxes = [[1,4],[2,3],[3,4]]
-1
There is no box that the package of size 5 can fit in.
packages = [3,5,8,10,11,12], boxes = [[12],[11,9],[10,5,14]]
9
It is optimal to choose the third supplier, using two size-5 boxes, two size-10 boxes, and two size-14 boxes. The total waste is (5-3) + (5-5) + (10-8) + (10-10) + (14-11) + (14-12) = 9.
Constraints
n == packages.length
m == boxes.length
1 <= n <= 105
1 <= m <
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