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66 lines
1.4 KiB
Java
66 lines
1.4 KiB
Java
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*log(n)) preprocessing
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public class LcaSparseTable {
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int len;
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int[][] up;
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int[] tin;
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int[] tout;
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int time;
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void dfs(List<Integer>[] tree, int u, int p) {
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tin[u] = time++;
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up[0][u] = p;
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for (int i = 1; i < len; i++)
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up[i][u] = up[i - 1][up[i - 1][u]];
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for (int v : tree[u])
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if (v != p)
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dfs(tree, v, u);
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tout[u] = time++;
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}
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public LcaSparseTable(List<Integer>[] tree, int root) {
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int n = tree.length;
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len = 1;
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while ((1 << len) <= n) ++len;
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up = new int[len][n];
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tin = new int[n];
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tout = new int[n];
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dfs(tree, root, root);
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}
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boolean isParent(int parent, int child) {
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return tin[parent] <= tin[child] && tout[child] <= tout[parent];
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}
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public int lca(int a, int b) {
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if (isParent(a, b))
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return a;
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if (isParent(b, a))
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return b;
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for (int i = len - 1; i >= 0; i--)
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if (!isParent(up[i][a], b))
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a = up[i][a];
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return up[0][a];
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}
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// Usage example
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public static void main(String[] args) {
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List<Integer>[] tree = Stream.generate(ArrayList::new).limit(5).toArray(List[]::new);
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tree[0].add(1);
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tree[1].add(0);
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tree[1].add(2);
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tree[2].add(1);
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tree[3].add(1);
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tree[1].add(3);
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tree[0].add(4);
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tree[4].add(0);
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LcaSparseTable t = new LcaSparseTable(tree, 0);
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System.out.println(1 == t.lca(3, 2));
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System.out.println(0 == t.lca(2, 4));
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}
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}
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