119 lines
3.0 KiB
Java
119 lines
3.0 KiB
Java
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import java.util.*;
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import java.util.stream.Stream;
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// Answering LCA queries in O(1) with O(n) preprocessing
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public class LcaSchieberVishkin {
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int[] parent;
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int[] preOrder;
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int[] I;
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int[] head;
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int[] A;
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int time;
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void dfs1(List<Integer>[] tree, int u, int p) {
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parent[u] = p;
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I[u] = preOrder[u] = time++;
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for (int v : tree[u]) {
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if (v == p) continue;
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dfs1(tree, v, u);
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if (Integer.lowestOneBit(I[v]) > Integer.lowestOneBit(I[u])) {
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I[u] = I[v];
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}
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}
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head[I[u]] = u;
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}
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void dfs2(List<Integer>[] tree, int u, int p, int up) {
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A[u] = up | Integer.lowestOneBit(I[u]);
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for (int v : tree[u]) {
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if (v == p) continue;
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dfs2(tree, v, u, A[u]);
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}
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}
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public LcaSchieberVishkin(List<Integer>[] tree, int root) {
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int n = tree.length;
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preOrder = new int[n];
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I = new int[n];
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head = new int[n];
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A = new int[n];
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parent = new int[n];
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dfs1(tree, root, -1);
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dfs2(tree, root, -1, 0);
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}
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int enterIntoStrip(int x, int hz) {
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if (Integer.lowestOneBit(I[x]) == hz)
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return x;
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int hw = Integer.highestOneBit(A[x] & (hz - 1));
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return parent[head[I[x] & (~hw + 1) | hw]];
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}
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public int lca(int x, int y) {
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int hb = I[x] == I[y] ? Integer.lowestOneBit(I[x]) : Integer.highestOneBit(I[x] ^ I[y]);
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int hz = Integer.lowestOneBit(A[x] & A[y] & (~hb + 1));
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int ex = enterIntoStrip(x, hz);
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int ey = enterIntoStrip(y, hz);
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return preOrder[ex] < preOrder[ey] ? ex : ey;
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}
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// Random test
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public static void main(String[] args) {
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Random rnd = new Random(1);
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for (int step = 0; step < 1000; step++) {
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int n = rnd.nextInt(50) + 1;
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List<Integer>[] tree = getRandomTree(n, rnd);
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int[] depth = new int[n];
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Arrays.fill(depth, -1);
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int root = rnd.nextInt(n);
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calcDepth(tree, depth, root, 0);
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LcaSchieberVishkin q = new LcaSchieberVishkin(tree, root);
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for (int i = 0; i < 1000; i++) {
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int a = rnd.nextInt(n);
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int b = rnd.nextInt(n);
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List<Integer> path = new ArrayList<>();
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getPathFromAtoB(tree, a, b, -1, path);
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int res1 = q.lca(a, b);
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int res2 = a;
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for (int u : path)
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if (depth[res2] > depth[u])
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res2 = u;
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if (res1 != res2)
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throw new RuntimeException();
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}
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}
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System.out.println("Test passed");
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}
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static List<Integer>[] getRandomTree(int n, Random rnd) {
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List<Integer>[] t = Stream.generate(ArrayList::new).limit(n).toArray(List[]::new);
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int[] p = new int[n];
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for (int i = 0, j; i < n; j = rnd.nextInt(i + 1), p[i] = p[j], p[j] = i, i++) ; // random permutation
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for (int i = 1; i < n; i++) {
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int parent = p[rnd.nextInt(i)];
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t[parent].add(p[i]);
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t[p[i]].add(parent);
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}
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return t;
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}
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static void calcDepth(List<Integer>[] tree, int[] depth, int u, int d) {
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depth[u] = d;
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for (int v : tree[u])
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if (depth[v] == -1)
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calcDepth(tree, depth, v, d + 1);
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}
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static boolean getPathFromAtoB(List<Integer>[] tree, int a, int b, int p, List<Integer> path) {
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path.add(a);
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if (a == b)
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return true;
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for (int u : tree[a])
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if (u != p && getPathFromAtoB(tree, u, b, a, path))
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return true;
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path.remove(path.size() - 1);
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return false;
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}
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}
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