{ "data": { "question": { "questionId": "2952", "questionFrontendId": "2809", "categoryTitle": "Algorithms", "boundTopicId": 2372351, "title": "Minimum Time to Make Array Sum At Most x", "titleSlug": "minimum-time-to-make-array-sum-at-most-x", "content": "
You are given two 0-indexed integer arrays nums1
and nums2
of equal length. Every second, for all indices 0 <= i < nums1.length
, value of nums1[i]
is incremented by nums2[i]
. After this is done, you can do the following operation:
0 <= i < nums1.length
and make nums1[i] = 0
.You are also given an integer x
.
Return the minimum time in which you can make the sum of all elements of nums1
to be less than or equal to x
, or -1
if this is not possible.
\n
Example 1:
\n\n\nInput: nums1 = [1,2,3], nums2 = [1,2,3], x = 4\nOutput: 3\nExplanation: \nFor the 1st second, we apply the operation on i = 0. Therefore nums1 = [0,2+2,3+3] = [0,4,6]. \nFor the 2nd second, we apply the operation on i = 1. Therefore nums1 = [0+1,0,6+3] = [1,0,9]. \nFor the 3rd second, we apply the operation on i = 2. Therefore nums1 = [1+1,0+2,0] = [2,2,0]. \nNow sum of nums1 = 4. It can be shown that these operations are optimal, so we return 3.\n\n\n\n
Example 2:
\n\n\nInput: nums1 = [1,2,3], nums2 = [3,3,3], x = 4\nOutput: -1\nExplanation: It can be shown that the sum of nums1 will always be greater than x, no matter which operations are performed.\n\n\n
\n
Constraints:
\n\n1 <= nums1.length <= 103
1 <= nums1[i] <= 103
0 <= nums2[i] <= 103
nums1.length == nums2.length
0 <= x <= 106
给你两个长度相等下标从 0 开始的整数数组 nums1
和 nums2
。每一秒,对于所有下标 0 <= i < nums1.length
,nums1[i]
的值都增加 nums2[i]
。操作 完成后 ,你可以进行如下操作:
0 <= i < nums1.length
的下标 i
,并使 nums1[i] = 0
。同时给你一个整数 x
。
请你返回使 nums1
中所有元素之和 小于等于 x
所需要的 最少 时间,如果无法实现,那么返回 -1
。
\n\n
示例 1:
\n\n\n输入:nums1 = [1,2,3], nums2 = [1,2,3], x = 4\n输出:3\n解释:\n第 1 秒,我们对 i = 0 进行操作,得到 nums1 = [0,2+2,3+3] = [0,4,6] 。\n第 2 秒,我们对 i = 1 进行操作,得到 nums1 = [0+1,0,6+3] = [1,0,9] 。\n第 3 秒,我们对 i = 2 进行操作,得到 nums1 = [1+1,0+2,0] = [2,2,0] 。\n现在 nums1 的和为 4 。不存在更少次数的操作,所以我们返回 3 。\n\n\n
示例 2:
\n\n\n输入:nums1 = [1,2,3], nums2 = [3,3,3], x = 4\n输出:-1\n解释:不管如何操作,nums1 的和总是会超过 x 。\n\n\n
\n\n
提示:
\n\n1 <= nums1.length <= 103
1 <= nums1[i] <= 103
0 <= nums2[i] <= 103
nums1.length == nums2.length
0 <= x <= 106
i
, we only need to set nums1[i]
to 0
at most once. (If we have to set it twice, we can simply remove the earlier set and all the operations “shift left” by 1
.)i1, i2, ..., ik
and set nums1[i1], nums1[i2], ..., nums1[ik]
to 0
, it’s always optimal to set them in the order of nums2[i1] <= nums2[i2] <= ... <= nums2[ik]
(the larger the increase is, the later we should set it to 0
).nums2
(in non-decreasing order). Let dp[i][j]
represent the maximum total value that can be reduced if we do j
operations on the first i
elements. Then we have dp[i][0] = 0
(for all i = 0, 1, ..., n
) and dp[i][j] = max(dp[i - 1][j], dp[i - 1][j - 1] + nums2[i - 1] * j + nums1[i - 1])
(for 1 <= i <= n
and 1 <= j <= i
).t
, such that 0 <= t <= n
and sum(nums1) + sum(nums2) * t - dp[n][t] <= x
, or -1
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