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package g2601_2700.s2612_minimum_reverse_operations;

// #Hard #Array #Breadth_First_Search #Ordered_Set
// #2023_08_30_Time_19_ms_(100.00%)_Space_59_MB_(78.00%)

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 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 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;
    }
}