2612 - Minimum Reverse Operations.

Hard

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 i^th 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.

• A subarray is a contiguous non-empty sequence of elements within an array.

• The values of ans[i] are independent for all i's.

• The reverse of an array is an array containing the values in reverse order.

Example 1:

Input: n = 4, p = 0, banned = 1,2, k = 4

Output: 0,-1,-1,1

Explanation:

In this case k = 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 is 0. 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 is 1.

Example 2:

Input: n = 5, p = 0, banned = 2,4, k = 3

Output: 0,-1,-1,-1,-1

Explanation:

In this case the 1 is initially at position 0, so the answer for that position is 0. 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.

Example 3:

Input: n = 4, p = 2, banned = 0,1,3, k = 1

Output: -1,-1,0,-1

Explanation: In this case we can only perform reverse operations of size 1.So the 1 never changes its position.

Constraints:

• <code>1 <= n <= 10⁵</code>

• 0 <= p <= n - 1

• 0 <= banned.length <= n - 1

• 0 <= banned[i] <= n - 1

• 1 <= k <= n

• banned[i] != p

• all values in banned are unique