LeetCode-in-Java

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:

• 1 <= n <= 105
• 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

Solution

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

public class Solution {
    public int[] minReverseOperations(int n, int p, int[] banned, int k) {
        int[] out = new int[n];
        Arrays.fill(out, -1);
        for (int node : banned) {
            out[node] = -2;
        }
        List<Integer> nodes = new ArrayList<>();
        nodes.add(p);
        int depth = 0;
        out[p] = depth;
        int step = k - 1;
        int[] nextNode2s = new int[n + 1];
        for (int i = 0; i < n + 1; i++) {
            nextNode2s[i] = i + 2;
        }
        while (!nodes.isEmpty()) {
            depth++;
            List<Integer> newNodes = new ArrayList<>();
            for (int node1 : nodes) {
                int loReverseStart = Math.max(node1 - step, 0);
                int hiReverseStart = Math.min(node1, n - k);
                int loNode2 = 2 * loReverseStart + k - 1 - node1;
                int hiNode2 = 2 * hiReverseStart + k - 1 - node1;
                int postHiNode2 = hiNode2 + 2;
                int node2 = loNode2;
                while (node2 <= hiNode2) {
                    int nextNode2 = nextNode2s[node2];
                    nextNode2s[node2] = postHiNode2;
                    if (node2 < n && out[node2] == -1) {
                        newNodes.add(node2);
                        out[node2] = depth;
                    }
                    node2 = nextNode2;
                }
            }
            nodes = newNodes;
        }
        for (int i = 0; i < n; i++) {
            if (out[i] == -2) {
                out[i] = -1;
            }
        }
        return out;
    }
}

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