{ "data": { "question": { "questionId": "3831", "questionFrontendId": "3524", "categoryTitle": "Algorithms", "boundTopicId": 3654653, "title": "Find X Value of Array I", "titleSlug": "find-x-value-of-array-i", "content": "
You are given an array of positive integers nums
, and a positive integer k
.
You are allowed to perform an operation once on nums
, where in each operation you can remove any non-overlapping prefix and suffix from nums
such that nums
remains non-empty.
You need to find the x-value of nums
, which is the number of ways to perform this operation so that the product of the remaining elements leaves a remainder of x
when divided by k
.
Return an array result
of size k
where result[x]
is the x-value of nums
for 0 <= x <= k - 1
.
A prefix of an array is a subarray that starts from the beginning of the array and extends to any point within it.
\n\nA suffix of an array is a subarray that starts at any point within the array and extends to the end of the array.
\n\nNote that the prefix and suffix to be chosen for the operation can be empty.
\n\n\n
Example 1:
\n\nInput: nums = [1,2,3,4,5], k = 3
\n\nOutput: [9,2,4]
\n\nExplanation:
\n\nx = 0
, the possible operations include all possible ways to remove non-overlapping prefix/suffix that do not remove nums[2] == 3
.x = 1
, the possible operations are:\n\t[2, 3, 4, 5]
. nums
becomes [1]
.[1, 2, 3]
and the suffix [5]
. nums
becomes [4]
.x = 2
, the possible operations are:\n\t[3, 4, 5]
. nums
becomes [1, 2]
.[1]
and the suffix [3, 4, 5]
. nums
becomes [2]
.[1, 2, 3]
and the empty suffix. nums
becomes [4, 5]
.[1, 2, 3, 4]
and the empty suffix. nums
becomes [5]
.Example 2:
\n\nInput: nums = [1,2,4,8,16,32], k = 4
\n\nOutput: [18,1,2,0]
\n\nExplanation:
\n\nx = 0
, the only operations that do not result in x = 0
are:\n\n\t[4, 8, 16, 32]
. nums
becomes [1, 2]
.[2, 4, 8, 16, 32]
. nums
becomes [1]
.[1]
and the suffix [4, 8, 16, 32]
. nums
becomes [2]
.x = 1
, the only possible operation is:\n\t[2, 4, 8, 16, 32]
. nums
becomes [1]
.x = 2
, the possible operations are:\n\t[4, 8, 16, 32]
. nums
becomes [1, 2]
.[1]
and the suffix [4, 8, 16, 32]
. nums
becomes [2]
.x = 3
, there is no possible way to perform the operation.Example 3:
\n\nInput: nums = [1,1,2,1,1], k = 2
\n\nOutput: [9,6]
\n\n
Constraints:
\n\n1 <= nums[i] <= 109
1 <= nums.length <= 105
1 <= k <= 5
给你一个由 正 整数组成的数组 nums
,以及一个 正 整数 k
。
你可以对 nums
执行 一次 操作,该操作中可以移除任意 不重叠 的前缀和后缀,使得 nums
仍然 非空 。
你需要找出 nums
的 x 值,即在执行操作后,剩余元素的 乘积 除以 k
后的 余数 为 x
的操作数量。
返回一个大小为 k
的数组 result
,其中 result[x]
表示对于 0 <= x <= k - 1
,nums
的 x 值。
数组的 前缀 指从数组起始位置开始到数组中任意位置的一段连续子数组。
\n\n数组的 后缀 是指从数组中任意位置开始到数组末尾的一段连续子数组。
\n\n子数组 是数组中一段连续的元素序列。
\n\n注意,在操作中选择的前缀和后缀可以是 空的 。
\n\n\n\n
示例 1:
\n\n输入: nums = [1,2,3,4,5], k = 3
\n\n输出: [9,2,4]
\n\n解释:
\n\nx = 0
,可行的操作包括所有不会移除 nums[2] == 3
的前后缀移除方式。x = 1
,可行操作包括:\n\t[2, 3, 4, 5]
,nums
变为 [1]
。[1, 2, 3]
和后缀 [5]
,nums
变为 [4]
。x = 2
,可行操作包括:\n\t[3, 4, 5]
,nums
变为 [1, 2]
。[1]
和后缀 [3, 4, 5]
,nums
变为 [2]
。[1, 2, 3]
和空后缀,nums
变为 [4, 5]
。[1, 2, 3, 4]
和空后缀,nums
变为 [5]
。示例 2:
\n\n输入: nums = [1,2,4,8,16,32], k = 4
\n\n输出: [18,1,2,0]
\n\n解释:
\n\nx = 0
,唯一 不 得到 x = 0
的操作有:\n\n\t[4, 8, 16, 32]
,nums
变为 [1, 2]
。[2, 4, 8, 16, 32]
,nums
变为 [1]
。[1]
和后缀 [4, 8, 16, 32]
,nums
变为 [2]
。x = 1
,唯一的操作是:\n\t[2, 4, 8, 16, 32]
,nums
变为 [1]
。x = 2
,可行操作包括:\n\t[4, 8, 16, 32]
,nums
变为 [1, 2]
。[1]
和后缀 [4, 8, 16, 32]
,nums
变为 [2]
。x = 3
,没有可行的操作。示例 3:
\n\n输入: nums = [1,1,2,1,1], k = 2
\n\n输出: [9,6]
\n\n\n
提示:
\n\n1 <= nums[i] <= 109
1 <= nums.length <= 105
1 <= k <= 5
dp[i][r]
as the count of subarrays ending at index i
whose product modulo k
equals r
.",
"Compute dp[i][r]
for each index i
in nums
and sum over all indices to get the final counts for each remainder."
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