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| 1 | 1 | package g3301_3400.s3327_check_if_dfs_strings_are_palindromes; | 
| 2 | 2 | 
 | 
| 3 |  | -// #Hard #2024_10_21_Time_244_ms_(100.00%)_Space_96.3_MB_(100.00%) | 
|  | 3 | +// #Hard #Array #String #Hash_Table #Tree #Hash_Function #Depth_First_Search | 
|  | 4 | +// #2024_10_22_Time_159_ms_(90.40%)_Space_93.9_MB_(80.80%) | 
| 4 | 5 | 
 | 
| 5 | 6 | import java.util.ArrayList; | 
|  | 7 | +import java.util.List; | 
| 6 | 8 | 
 | 
| 7 | 9 | public class Solution { | 
| 8 |  | -    private StringBuilder dfsString; | 
|  | 10 | +    private final List<List<Integer>> e = new ArrayList<>(); | 
|  | 11 | +    private final StringBuilder stringBuilder = new StringBuilder(); | 
|  | 12 | +    private String s; | 
|  | 13 | +    private int now; | 
|  | 14 | +    private int n; | 
|  | 15 | +    private int[] l; | 
|  | 16 | +    private int[] r; | 
|  | 17 | +    private int[] p; | 
|  | 18 | +    private char[] c; | 
| 9 | 19 | 
 | 
| 10 |  | -    private int[] fillManacher(String s) { | 
| 11 |  | -        int n = s.length(); | 
| 12 |  | -        s = "$" + s + "@"; | 
| 13 |  | -        int[] p = new int[n + 2]; | 
| 14 |  | -        int center = 0; | 
| 15 |  | -        int right = 0; | 
| 16 |  | -        for (int i = 1; i <= n; i++) { | 
| 17 |  | -            int mirror = 2 * center - i; | 
| 18 |  | -            if (i < right) { | 
| 19 |  | -                p[i] = Math.min(right - i, p[mirror]); | 
| 20 |  | -            } | 
| 21 |  | -            while (s.charAt(i + p[i]) == s.charAt(i - p[i])) { | 
| 22 |  | -                p[i]++; | 
| 23 |  | -            } | 
| 24 |  | -            if (i + p[i] > right) { | 
| 25 |  | -                center = i; | 
| 26 |  | -                right = i + p[i]; | 
| 27 |  | -            } | 
|  | 20 | +    private void dfs(int x) { | 
|  | 21 | +        l[x] = now + 1; | 
|  | 22 | +        for (int v : e.get(x)) { | 
|  | 23 | +            dfs(v); | 
| 28 | 24 |         } | 
| 29 |  | -        return p; | 
|  | 25 | +        stringBuilder.append(s.charAt(x)); | 
|  | 26 | +        r[x] = ++now; | 
| 30 | 27 |     } | 
| 31 | 28 | 
 | 
| 32 |  | -    private int[] manacher() { | 
| 33 |  | -        StringBuilder temp = new StringBuilder(); | 
| 34 |  | -        for (int i = 0; i < dfsString.length(); i++) { | 
| 35 |  | -            temp.append("#"); | 
| 36 |  | -            temp.append(dfsString.charAt(i)); | 
|  | 29 | +    private void manacher() { | 
|  | 30 | +        c[0] = '~'; | 
|  | 31 | +        c[1] = '#'; | 
|  | 32 | +        for (int i = 1; i <= n; ++i) { | 
|  | 33 | +            c[2 * i + 1] = '#'; | 
|  | 34 | +            c[2 * i] = stringBuilder.charAt(i - 1); | 
| 37 | 35 |         } | 
| 38 |  | -        temp.append("#"); | 
| 39 |  | -        return fillManacher(String.valueOf(temp)); | 
| 40 |  | -        // return Arrays.copyOfRange(arr, 1, arr.length - 1); | 
| 41 |  | -    } | 
| 42 |  | - | 
| 43 |  | -    private void dfs( | 
| 44 |  | -            int node, int parent, ArrayList<ArrayList<Integer>> adj, int[][] range, String s) { | 
| 45 |  | -        int start = dfsString.length(); | 
| 46 |  | - | 
| 47 |  | -        for (int neigh : adj.get(node)) { | 
| 48 |  | -            if (neigh == parent) { | 
| 49 |  | -                continue; | 
|  | 36 | +        for (int i = 1, mid = 0, r = 0; i <= 2 * n + 1; ++i) { | 
|  | 37 | +            if (i <= r) p[i] = Math.min(p[(mid << 1) - i], r - i + 1); | 
|  | 38 | +            while (c[i - p[i]] == c[i + p[i]]) ++p[i]; | 
|  | 39 | +            if (p[i] + i > r) { | 
|  | 40 | +                r = p[i] + i - 1; | 
|  | 41 | +                mid = i; | 
| 50 | 42 |             } | 
| 51 |  | -            dfs(neigh, node, adj, range, s); | 
| 52 | 43 |         } | 
| 53 |  | -        dfsString.append(s.charAt(node)); | 
| 54 |  | -        int end = dfsString.length() - 1; | 
| 55 |  | -        range[node] = new int[] {start, end}; | 
| 56 | 44 |     } | 
| 57 | 45 | 
 | 
| 58 | 46 |     public boolean[] findAnswer(int[] parent, String s) { | 
| 59 |  | -        dfsString = new StringBuilder(); | 
| 60 |  | -        int n = parent.length; | 
| 61 |  | -        ArrayList<ArrayList<Integer>> adj = new ArrayList<>(); | 
| 62 |  | -        for (int i = 0; i < n; i++) { | 
| 63 |  | -            adj.add(new ArrayList<>()); | 
|  | 47 | +        n = parent.length; | 
|  | 48 | +        this.s = s; | 
|  | 49 | +        for (int i = 0; i < n; ++i) { | 
|  | 50 | +            e.add(new ArrayList<>()); | 
| 64 | 51 |         } | 
| 65 |  | -        for (int i = 0; i < n; i++) { | 
| 66 |  | -            if (parent[i] == -1) { | 
| 67 |  | -                continue; | 
| 68 |  | -            } | 
| 69 |  | -            adj.get(parent[i]).add(i); | 
|  | 52 | +        for (int i = 1; i < n; ++i) { | 
|  | 53 | +            e.get(parent[i]).add(i); | 
| 70 | 54 |         } | 
| 71 |  | -        int[][] range = new int[n][2]; | 
| 72 |  | -        dfs(0, -1, adj, range, s); | 
| 73 |  | -        int[] manacherArr = manacher(); | 
|  | 55 | +        l = new int[n]; | 
|  | 56 | +        r = new int[n]; | 
|  | 57 | +        dfs(0); | 
|  | 58 | +        c = new char[2 * n + 10]; | 
|  | 59 | +        p = new int[2 * n + 10]; | 
|  | 60 | +        manacher(); | 
| 74 | 61 |         boolean[] ans = new boolean[n]; | 
| 75 |  | -        for (int i = 0; i < n; i++) { | 
| 76 |  | -            int[] currRange = range[i]; | 
| 77 |  | -            int length = currRange[1] - currRange[0] + 1; | 
| 78 |  | -            // +2 because the string has $# in the starting and in the end | 
| 79 |  | -            int palindromeStart = 2 * currRange[0] + 2; | 
| 80 |  | -            int palindromeEnd = 2 * currRange[1] + 2; | 
| 81 |  | -            int center = (palindromeStart + palindromeEnd) / 2; | 
| 82 |  | -            // represents the palindrome length having center at center. | 
| 83 |  | -            int palindromeLength = manacherArr[center]; | 
| 84 |  | -            ans[i] = palindromeLength >= length; | 
|  | 62 | +        for (int i = 0; i < n; ++i) { | 
|  | 63 | +            int mid = (2 * r[i] - 2 * l[i] + 1) / 2 + 2 * l[i]; | 
|  | 64 | +            ans[i] = p[mid] - 1 >= r[i] - l[i] + 1; | 
| 85 | 65 |         } | 
| 86 | 66 |         return ans; | 
| 87 | 67 |     } | 
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