313 lines
8.7 KiB
Java
313 lines
8.7 KiB
Java
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import java.util.*;
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import java.util.stream.Stream;
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public class HeavyLight2 {
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// true - values on vertices, false - values on edges
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static boolean VALUES_ON_VERTICES = true;
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// Modify the following 6 methods to implement your custom operations on the tree.
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// This example implements Add/Max operations. Operations like Add/Sum, Set/Max can also be implemented.
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static int modifyOperation(int x, int y) {
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return x + y;
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}
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// query (or combine) operation
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static int queryOperation(int leftValue, int rightValue) {
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return Math.max(leftValue, rightValue);
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}
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static int deltaEffectOnSegment(int delta, int segmentLength) {
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if (delta == getNeutralDelta()) return getNeutralDelta();
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// Here you must write a fast equivalent of following slow code:
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// int result = delta;
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// for (int i = 1; i < segmentLength; i++) result = queryOperation(result, delta);
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// return result;
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return delta;
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}
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static int getNeutralDelta() {
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return 0;
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}
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static int getInitValue() {
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return 0;
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}
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static int getNeutralValue() {
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return Integer.MIN_VALUE;
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}
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// generic code
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static int joinValueWithDelta(int value, int delta) {
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if (delta == getNeutralDelta()) return value;
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return modifyOperation(value, delta);
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}
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static int joinDeltas(int delta1, int delta2) {
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if (delta1 == getNeutralDelta()) return delta2;
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if (delta2 == getNeutralDelta()) return delta1;
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return modifyOperation(delta1, delta2);
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}
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int[][] value;
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int[][] delta; // delta[i] affects value[i], delta[2*i+1] and delta[2*i+2]
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int[][] len;
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List<Integer>[] tree;
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int[] size;
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int[] parent;
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int[] tin;
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int[] tout;
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int time;
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int[] path;
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int[] pathSize;
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int[] pathPos;
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int[] pathRoot;
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int pathCount;
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public HeavyLight2(List<Integer>[] tree) {
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this.tree = tree;
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int n = tree.length;
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size = new int[n];
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parent = new int[n];
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tin = new int[n];
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tout = new int[n];
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calcSizeParentTinTout(0, -1);
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path = new int[n];
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pathSize = new int[n];
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pathPos = new int[n];
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pathRoot = new int[n];
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buildPaths(0, newPath(0));
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value = new int[pathCount][];
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delta = new int[pathCount][];
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len = new int[pathCount][];
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for (int i = 0; i < pathCount; i++) {
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int m = pathSize[i];
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value[i] = new int[2 * m];
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for (int j = 0; j < m; j++)
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value[i][j + m] = getInitValue();
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for (int j = 2 * m - 1; j > 1; j -= 2)
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value[i][j >> 1] = queryOperation(value[i][j], value[i][j ^ 1]);
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delta[i] = new int[2 * m];
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Arrays.fill(delta[i], getNeutralDelta());
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len[i] = new int[2 * m];
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Arrays.fill(len[i], m, 2 * m, 1);
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for (int j = 2 * m - 1; j > 1; j -= 2)
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len[i][j >> 1] = len[i][j] + len[i][j ^ 1];
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}
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}
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void calcSizeParentTinTout(int u, int p) {
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tin[u] = time++;
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parent[u] = p;
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size[u] = 1;
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for (int v : tree[u])
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if (v != p) {
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calcSizeParentTinTout(v, u);
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size[u] += size[v];
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}
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tout[u] = time++;
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}
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int newPath(int u) {
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pathRoot[pathCount] = u;
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return pathCount++;
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}
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void buildPaths(int u, int path) {
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this.path[u] = path;
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pathPos[u] = pathSize[path]++;
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for (int v : tree[u]) {
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if (v != parent[u])
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buildPaths(v, 2 * size[v] >= size[u] ? path : newPath(v));
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}
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}
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void pushDelta(int path, int i) {
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int d = 0;
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for (; (i >> d) > 0; d++)
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;
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for (d -= 2; d >= 0; d--) {
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int x = i >> d;
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value[path][x >> 1] = joinValueWithDelta0(path, x >> 1);
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delta[path][x] = joinDeltas(delta[path][x], delta[path][x >> 1]);
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delta[path][x ^ 1] = joinDeltas(delta[path][x ^ 1], delta[path][x >> 1]);
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delta[path][x >> 1] = getNeutralDelta();
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}
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}
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int joinValueWithDelta0(int path, int i) {
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return joinValueWithDelta(value[path][i], deltaEffectOnSegment(delta[path][i], len[path][i]));
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}
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int queryPath(int path, int from, int to) {
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from += value[path].length >> 1;
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to += value[path].length >> 1;
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pushDelta(path, from);
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pushDelta(path, to);
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int res = getNeutralValue();
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for (; from <= to; from = (from + 1) >> 1, to = (to - 1) >> 1) {
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if ((from & 1) != 0)
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res = queryOperation(res, joinValueWithDelta0(path, from));
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if ((to & 1) == 0)
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res = queryOperation(res, joinValueWithDelta0(path, to));
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}
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return res;
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}
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void modifyPath(int path, int from, int to, int delta) {
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from += value[path].length >> 1;
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to += value[path].length >> 1;
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pushDelta(path, from);
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pushDelta(path, to);
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int ta = -1;
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int tb = -1;
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for (; from <= to; from = (from + 1) >> 1, to = (to - 1) >> 1) {
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if ((from & 1) != 0) {
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this.delta[path][from] = joinDeltas(this.delta[path][from], delta);
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if (ta == -1)
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ta = from;
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}
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if ((to & 1) == 0) {
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this.delta[path][to] = joinDeltas(this.delta[path][to], delta);
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if (tb == -1)
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tb = to;
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}
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}
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for (int i = ta; i > 1; i >>= 1)
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value[path][i >> 1] = queryOperation(joinValueWithDelta0(path, i), joinValueWithDelta0(path, i ^ 1));
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for (int i = tb; i > 1; i >>= 1)
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value[path][i >> 1] = queryOperation(joinValueWithDelta0(path, i), joinValueWithDelta0(path, i ^ 1));
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}
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boolean isAncestor(int p, int ch) {
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return tin[p] <= tin[ch] && tout[ch] <= tout[p];
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}
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public int query(int a, int b) {
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int res = getNeutralValue();
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for (int root; !isAncestor(root = pathRoot[path[a]], b); a = parent[root])
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res = queryOperation(res, queryPath(path[a], 0, pathPos[a]));
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for (int root; !isAncestor(root = pathRoot[path[b]], a); b = parent[root])
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res = queryOperation(res, queryPath(path[b], 0, pathPos[b]));
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if (!VALUES_ON_VERTICES && a == b)
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return res;
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return queryOperation(
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res,
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queryPath(path[a], Math.min(pathPos[a], pathPos[b]) + (VALUES_ON_VERTICES ? 0 : 1),
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Math.max(pathPos[a], pathPos[b])));
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}
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public void modify(int a, int b, int delta) {
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for (int root; !isAncestor(root = pathRoot[path[a]], b); a = parent[root])
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modifyPath(path[a], 0, pathPos[a], delta);
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for (int root; !isAncestor(root = pathRoot[path[b]], a); b = parent[root])
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modifyPath(path[b], 0, pathPos[b], delta);
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if (!VALUES_ON_VERTICES && a == b)
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return;
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modifyPath(path[a], Math.min(pathPos[a], pathPos[b]) + (VALUES_ON_VERTICES ? 0 : 1),
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Math.max(pathPos[a], pathPos[b]), delta);
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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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VALUES_ON_VERTICES = true;
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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[] x = new int[n];
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Arrays.fill(x, getInitValue());
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HeavyLight2 hl = new HeavyLight2(tree);
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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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if (rnd.nextBoolean()) {
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int delta = rnd.nextInt(50) - 100;
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hl.modify(a, b, delta);
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for (int u : path)
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x[u] = joinValueWithDelta(x[u], delta);
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} else {
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int res1 = hl.query(a, b);
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int res2 = getNeutralValue();
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for (int u : path)
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res2 = queryOperation(res2, x[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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}
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VALUES_ON_VERTICES = false;
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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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Map<Long, Integer> x = new HashMap<>();
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for (int u = 0; u < tree.length; u++)
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for (int v : tree[u])
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x.put(edge(u, v), getInitValue());
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HeavyLight2 hl = new HeavyLight2(tree);
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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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if (rnd.nextBoolean()) {
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int delta = rnd.nextInt(50) - 100;
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hl.modify(a, b, delta);
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for (int j = 0; j + 1 < path.size(); j++) {
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long key = edge(path.get(j), path.get(j + 1));
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x.put(key, joinValueWithDelta(x.get(key), delta));
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}
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} else {
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int res1 = hl.query(a, b);
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int res2 = getNeutralValue();
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for (int j = 0; j + 1 < path.size(); j++) {
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long key = edge(path.get(j), path.get(j + 1));
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res2 = queryOperation(res2, x.get(key));
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}
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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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}
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System.out.println("Test passed");
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}
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static long edge(int u, int v) {
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return ((long) Math.min(u, v) << 16) + Math.max(u, v);
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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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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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}
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