Minimum Reverse Operations

arrayhash tablebreadth-first search

Problem Statement

You are given an integer n and an integer p representing an array arr of length n where all elements are set to 0's, except position p which is set to 1. You are also given an integer array banned containing restricted positions. Perform the following operation on arr :

Reverse a subarray with size k if the single 1 is not set to a position in banned .

Return an integer array answer with n results where the i ^th result is the minimum number of operations needed to bring the single 1 to position i in arr , or -1 if it is impossible.

Examples

Example 1

Input: n = 4, p = 0, banned = [1,2], k = 4
Output: [0,-1,-1,1]
Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0. 
 We can never place 1 on the banned positions, so the answer for positions 1 and 2 is -1. 
 Perform the operation of size 4 to reverse the whole array. 
 After a single operation 1 is at position 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]
Initially 1 is placed at position 0 so the number of operations we need for position 0 is 0. 
 We cannot perform the operation on the subarray positions [0, 2] because position 2 is in banned. 
 Because 1 cannot be set at position 2, it is impossible to set 1 at other positions in more operations.

Example 3

Input: n = 4, p = 2, banned = [0,1,3], k = 1
Output: [-1,-1,0,-1]
Perform operations of size 1 and 1 never changes its position.

Constraints

1 <= n <= 10 ^5

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

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicHash Table