{ "data": { "question": { "questionId": "2018", "questionFrontendId": "1889", "categoryTitle": "Algorithms", "boundTopicId": 808708, "title": "Minimum Space Wasted From Packaging", "titleSlug": "minimum-space-wasted-from-packaging", "content": "
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.
[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
.
\n
Example 1:
\n\n\nInput: packages = [2,3,5], boxes = [[4,8],[2,8]]\nOutput: 6\nExplanation: It is optimal to choose the first supplier, using two size-4 boxes and one size-8 box.\nThe total waste is (4-2) + (4-3) + (8-5) = 6.\n\n\n
Example 2:
\n\n\nInput: packages = [2,3,5], boxes = [[1,4],[2,3],[3,4]]\nOutput: -1\nExplanation: There is no box that the package of size 5 can fit in.\n\n\n
Example 3:
\n\n\nInput: packages = [3,5,8,10,11,12], boxes = [[12],[11,9],[10,5,14]]\nOutput: 9\nExplanation: It is optimal to choose the third supplier, using two size-5 boxes, two size-10 boxes, and two size-14 boxes.\nThe total waste is (5-3) + (5-5) + (10-8) + (10-10) + (14-11) + (14-12) = 9.\n\n\n
\n
Constraints:
\n\nn == packages.length
m == boxes.length
1 <= n <= 105
1 <= m <= 105
1 <= packages[i] <= 105
1 <= boxes[j].length <= 105
1 <= boxes[j][k] <= 105
sum(boxes[j].length) <= 105
boxes[j]
are distinct.给你 n
个包裹,你需要把它们装在箱子里,每个箱子装一个包裹。总共有 m
个供应商提供 不同尺寸 的箱子(每个规格都有无数个箱子)。如果一个包裹的尺寸 小于等于 一个箱子的尺寸,那么这个包裹就可以放入这个箱子之中。
包裹的尺寸用一个整数数组 packages
表示,其中 packages[i]
是第 i
个包裹的尺寸。供应商用二维数组 boxes
表示,其中 boxes[j]
是第 j
个供应商提供的所有箱子尺寸的数组。
你想要选择 一个供应商 并只使用该供应商提供的箱子,使得 总浪费空间最小 。对于每个装了包裹的箱子,我们定义 浪费的 空间等于 箱子的尺寸 - 包裹的尺寸
。总浪费空间 为 所有 箱子中浪费空间的总和。
[4,8]
的箱子装下尺寸为 [2,3,5]
的包裹,你可以将尺寸为 2
和 3
的两个包裹装入两个尺寸为 4
的箱子中,同时把尺寸为 5
的包裹装入尺寸为 8
的箱子中。总浪费空间为 (4-2) + (4-3) + (8-5) = 6
。请你选择 最优 箱子供应商,使得 总浪费空间最小 。如果 无法 将所有包裹放入箱子中,请你返回 -1
。由于答案可能会 很大 ,请返回它对 109 + 7
取余 的结果。
\n\n
示例 1:
\n\n\n输入:packages = [2,3,5], boxes = [[4,8],[2,8]]\n输出:6\n解释:选择第一个供应商最优,用两个尺寸为 4 的箱子和一个尺寸为 8 的箱子。\n总浪费空间为 (4-2) + (4-3) + (8-5) = 6 。\n\n\n
示例 2:
\n\n\n输入:packages = [2,3,5], boxes = [[1,4],[2,3],[3,4]]\n输出:-1\n解释:没有箱子能装下尺寸为 5 的包裹。\n\n\n
示例 3:
\n\n\n输入:packages = [3,5,8,10,11,12], boxes = [[12],[11,9],[10,5,14]]\n输出:9\n解释:选择第三个供应商最优,用两个尺寸为 5 的箱子,两个尺寸为 10 的箱子和两个尺寸为 14 的箱子。\n总浪费空间为 (5-3) + (5-5) + (10-8) + (10-10) + (14-11) + (14-12) = 9 。\n\n\n
\n\n
提示:
\n\nn == packages.length
m == boxes.length
1 <= n <= 105
1 <= m <= 105
1 <= packages[i] <= 105
1 <= boxes[j].length <= 105
1 <= boxes[j][k] <= 105
sum(boxes[j].length) <= 105
boxes[j]
中的元素 互不相同 。\\u7248\\u672c\\uff1a \\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528 \\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n \\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\" \\u7248\\u672c\\uff1a \\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982\\uff1aarray<\\/a>, bisect<\\/a>, 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