{ "data": { "question": { "questionId": "2726", "questionFrontendId": "2612", "categoryTitle": "Algorithms", "boundTopicId": 2198327, "title": "Minimum Reverse Operations", "titleSlug": "minimum-reverse-operations", "content": "
You are given an integer n
and an integer p
in the range [0, n - 1]
. Representing a 0-indexed array arr
of length n
where all positions are set to 0
's, except position p
which is set to 1
.
You are also given an integer array banned
containing some positions from the array. For the ith position in banned
, arr[banned[i]] = 0
, and banned[i] != p
.
You can perform multiple operations on arr
. In an operation, you can choose a subarray with size k
and reverse the subarray. However, the 1
in arr
should never go to any of the positions in banned
. In other words, after each operation arr[banned[i]]
remains 0
.
Return an array ans
where for each i
from [0, n - 1]
, ans[i]
is the minimum number of reverse operations needed to bring the 1
to position i
in arr, or -1
if it is impossible.
ans[i]
are independent for all i
's.\n
Example 1:
\n\n\nInput: n = 4, p = 0, banned = [1,2], k = 4\nOutput: [0,-1,-1,1]\nExplanation: In this case\n\nk = 4
so there is only one possible reverse operation we can perform, which is reversing the whole array. Initially, 1 is placed at position 0 so the amount of operations we need for position 0 is0
. We can never place a 1 on the banned positions, so the answer for positions 1 and 2 is-1
. Finally, with one reverse operation we can bring the 1 to index 3, so the answer for position 3 is1
. \n
Example 2:
\n\n\nInput: n = 5, p = 0, banned = [2,4], k = 3\nOutput: [0,-1,-1,-1,-1]\nExplanation: In this case the 1 is initially at position 0, so the answer for that position is\n\n0
. We can perform reverse operations of size 3. The 1 is currently located at position 0, so we need to reverse the subarray[0, 2]
for it to leave that position, but reversing that subarray makes position 2 have a 1, which shouldn't happen. So, we can't move the 1 from position 0, making the result for all the other positions-1
. \n
Example 3:
\n\n\nInput: n = 4, p = 2, banned = [0,1,3], k = 1\nOutput: [-1,-1,0,-1]\nExplanation: In this case we can only perform reverse operations of size 1. So the 1 never changes its position.\n\n\n
\n
Constraints:
\n\n1 <= n <= 105
0 <= p <= n - 1
0 <= banned.length <= n - 1
0 <= banned[i] <= n - 1
1 <= k <= n
banned[i] != p
banned
are unique 给你一个整数 n
和一个在范围 [0, n - 1]
以内的整数 p
,它们表示一个长度为 n
且下标从 0 开始的数组 arr
,数组中除了下标为 p
处是 1
以外,其他所有数都是 0
。
同时给你一个整数数组 banned
,它包含数组中的一些位置。banned
中第 i 个位置表示 arr[banned[i]] = 0
,题目保证 banned[i] != p
。
你可以对 arr
进行 若干次 操作。一次操作中,你选择大小为 k
的一个 子数组 ,并将它 翻转 。在任何一次翻转操作后,你都需要确保 arr
中唯一的 1
不会到达任何 banned
中的位置。换句话说,arr[banned[i]]
始终 保持 0
。
请你返回一个数组 ans
,对于 [0, n - 1]
之间的任意下标 i
,ans[i]
是将 1
放到位置 i
处的 最少 翻转操作次数,如果无法放到位置 i
处,此数为 -1
。
i
,ans[i]
相互之间独立计算。\n\n
示例 1:
\n\n\n输入:n = 4, p = 0, banned = [1,2], k = 4\n输出:[0,-1,-1,1]\n解释:k = 4,所以只有一种可行的翻转操作,就是将整个数组翻转。一开始
1 在位置 0 处,所以将它翻转到位置 0 处需要的操作数为 0 。\n我们不能将 1 翻转到 banned 中的位置,所以位置 1 和 2 处的答案都是 -1 。\n通过一次翻转操作,可以将 1 放到位置 3 处,所以位置 3 的答案是 1 。\n
\n\n示例 2:
\n\n\n输入:n = 5, p = 0, banned = [2,4], k = 3\n输出:[0,-1,-1,-1,-1]\n解释:这个例子中 1 一开始在位置 0 处,所以此下标的答案为 0 。\n翻转的子数组长度为 k = 3 ,1 此时在位置 0 处,所以我们可以翻转子数组 [0, 2],但翻转后的下标 2 在 banned 中,所以不能执行此操作。\n由于 1 没法离开位置 0 ,所以其他位置的答案都是 -1 。\n\n\n
示例 3:
\n\n\n输入:n = 4, p = 2, banned = [0,1,3], k = 1\n输出:[-1,-1,0,-1]\n解释:这个例子中,我们只能对长度为 1 的子数组执行翻转操作,所以 1 无法离开初始位置。\n\n\n
\n\n
提示:
\n\n1 <= n <= 105
0 <= p <= n - 1
0 <= banned.length <= n - 1
0 <= banned[i] <= n - 1
1 <= k <= n
banned[i] != p
banned
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