290 lines
7.5 KiB
Java
290 lines
7.5 KiB
Java
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import java.util.*;
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// LinkCut tree with path queries. Query complexity is O(log(n)) amortized.
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// Based on Daniel Sleator's implementation http://www.codeforces.com/contest/117/submission/860934
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public class LinkCutTree {
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// Modify the following 5 methods to implement your custom operations on the tree.
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// This example implements Add/Sum operations. Operations like Add/Max, 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 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 * segmentLength;
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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 getNeutralValue() {
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return 0;
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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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public static class Node {
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int nodeValue;
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int subTreeValue;
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int delta; // delta affects nodeValue, subTreeValue, left.delta and right.delta
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int size;
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boolean revert;
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Node left;
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Node right;
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Node parent;
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Node(int value) {
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nodeValue = value;
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subTreeValue = value;
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delta = getNeutralDelta();
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size = 1;
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}
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// tests whether x is a root of a splay tree
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boolean isRoot() {
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return parent == null || (parent.left != this && parent.right != this);
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}
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void push() {
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if (revert) {
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revert = false;
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Node t = left;
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left = right;
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right = t;
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if (left != null)
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left.revert = !left.revert;
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if (right != null)
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right.revert = !right.revert;
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}
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nodeValue = joinValueWithDelta(nodeValue, delta);
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subTreeValue = joinValueWithDelta(subTreeValue, deltaEffectOnSegment(delta, size));
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if (left != null)
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left.delta = joinDeltas(left.delta, delta);
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if (right != null)
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right.delta = joinDeltas(right.delta, delta);
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delta = getNeutralDelta();
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}
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void update() {
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subTreeValue = queryOperation(queryOperation(getSubTreeValue(left), joinValueWithDelta(nodeValue, delta)), getSubTreeValue(right));
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size = 1 + getSize(left) + getSize(right);
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}
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}
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static int getSize(Node root) {
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return root == null ? 0 : root.size;
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}
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static int getSubTreeValue(Node root) {
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return root == null ? getNeutralValue() : joinValueWithDelta(root.subTreeValue, deltaEffectOnSegment(root.delta, root.size));
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}
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static void connect(Node ch, Node p, Boolean isLeftChild) {
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if (ch != null)
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ch.parent = p;
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if (isLeftChild != null) {
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if (isLeftChild)
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p.left = ch;
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else
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p.right = ch;
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}
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}
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// rotates edge (x, x.parent)
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// g g
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// / /
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// p x
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// / \ -> / \
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// x p.r x.l p
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// / \ / \
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// x.l x.r x.r p.r
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static void rotate(Node x) {
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Node p = x.parent;
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Node g = p.parent;
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boolean isRootP = p.isRoot();
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boolean leftChildX = (x == p.left);
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// create 3 edges: (x.r(l),p), (p,x), (x,g)
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connect(leftChildX ? x.right : x.left, p, leftChildX);
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connect(p, x, !leftChildX);
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connect(x, g, isRootP ? null : p == g.left);
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p.update();
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}
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// brings x to the root, balancing tree
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//
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// zig-zig case
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// g x
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// / \ p / \
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// p g.r rot(p) / \ rot(x) x.l p
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// / \ --> x g --> / \
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// x p.r / \ / \ x.r g
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// / \ x.l x.r p.r g.r / \
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// x.l x.r p.r g.r
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//
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// zig-zag case
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// g g
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// / \ / \ x
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// p g.r rot(x) x g.r rot(x) / \
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// / \ --> / \ --> p g
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// p.l x p x.r / \ / \
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// / \ / \ p.l x.l x.r g.r
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// x.l x.r p.l x.l
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static void splay(Node x) {
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while (!x.isRoot()) {
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Node p = x.parent;
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Node g = p.parent;
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if (!p.isRoot())
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g.push();
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p.push();
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x.push();
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if (!p.isRoot())
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rotate((x == p.left) == (p == g.left) ? p/*zig-zig*/ : x/*zig-zag*/);
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rotate(x);
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}
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x.push();
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x.update();
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}
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// makes node x the root of the virtual tree, and also x becomes the leftmost node in its splay tree
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static Node expose(Node x) {
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Node last = null;
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for (Node y = x; y != null; y = y.parent) {
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splay(y);
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y.left = last;
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last = y;
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}
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splay(x);
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return last;
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}
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public static void makeRoot(Node x) {
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expose(x);
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x.revert = !x.revert;
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}
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public static boolean connected(Node x, Node y) {
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if (x == y)
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return true;
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expose(x);
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// now x.parent is null
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expose(y);
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return x.parent != null;
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}
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public static void link(Node x, Node y) {
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if (connected(x, y))
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throw new RuntimeException("error: x and y are already connected");
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makeRoot(x);
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x.parent = y;
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}
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public static void cut(Node x, Node y) {
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makeRoot(x);
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expose(y);
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// check that exposed path consists of a single edge (y,x)
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if (y.right != x || x.left != null)
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throw new RuntimeException("error: no edge (x,y)");
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y.right.parent = null;
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y.right = null;
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}
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public static int query(Node from, Node to) {
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makeRoot(from);
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expose(to);
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return getSubTreeValue(to);
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}
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public static void modify(Node from, Node to, int delta) {
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makeRoot(from);
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expose(to);
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to.delta = joinDeltas(to.delta, 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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for (int step = 0; step < 1_000; step++) {
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int n = rnd.nextInt(50) + 1;
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boolean[][] g = new boolean[n][n];
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int[] val = new int[n];
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Node[] nodes = new Node[n];
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for (int i = 0; i < n; i++)
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nodes[i] = new Node(0);
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for (int query = 0; query < 2_000; query++) {
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int cmd = rnd.nextInt(10);
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int u = rnd.nextInt(n);
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int v = rnd.nextInt(n);
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Node x = nodes[u];
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Node y = nodes[v];
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if (cmd == 0) {
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makeRoot(x);
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expose(y);
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if (y.right == x && x.left == null && x.right == null) {
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cut(x, y);
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g[u][v] = g[v][u] = false;
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}
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} else if (cmd == 1) {
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if (connected(x, y)) {
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List<Integer> path = new ArrayList<>();
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getPathFromAtoB(g, u, v, -1, path);
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int res = getNeutralValue();
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for (int i : path)
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res = queryOperation(res, val[i]);
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if (query(x, y) != res)
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throw new RuntimeException();
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}
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} else if (cmd == 2) {
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if (connected(x, y)) {
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List<Integer> path = new ArrayList<>();
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getPathFromAtoB(g, u, v, -1, path);
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int delta = rnd.nextInt(100) + 1;
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for (int i : path)
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val[i] = joinValueWithDelta(val[i], delta);
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modify(x, y, delta);
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}
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} else {
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if (!connected(x, y)) {
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link(x, y);
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g[u][v] = g[v][u] = true;
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}
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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 boolean getPathFromAtoB(boolean[][] tree, int u, int v, int p, List<Integer> path) {
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path.add(u);
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if (u == v)
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return true;
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for (int i = 0; i < tree.length; i++)
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if (i != p && tree[u][i] && getPathFromAtoB(tree, i, v, u, 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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