|
| 1 | +package com.jwetherell.algorithms.data_structures; |
| 2 | + |
| 3 | +import java.util.ArrayList; |
| 4 | +import java.util.List; |
| 5 | + |
| 6 | +/** |
| 7 | + * Structure for storing rooted tree which allows to find lowest common ancestor. |
| 8 | + * <p> |
| 9 | + * @param <T> type of value stored in nodes. |
| 10 | + * <br> |
| 11 | + * @author Szymon Stankiewicz <dakurels@gmail.com> |
| 12 | + * @author Justin Wetherell <phishman3579@gmail.com> |
| 13 | + */ |
| 14 | +public class LowestCommonAncestor<T> { |
| 15 | + |
| 16 | + /** |
| 17 | + * Exception which can be thrown by lowestCommonAncestor function if two |
| 18 | + * nodes are in different trees. |
| 19 | + * |
| 20 | + */ |
| 21 | + public static class NodesNotInSameTreeException extends Exception { |
| 22 | + private static final long serialVersionUID = -5366787886097250564L; |
| 23 | + } |
| 24 | + |
| 25 | + /** |
| 26 | + * Finds lower common ancestor of two nodes. |
| 27 | + * |
| 28 | + * Complexity O(log n) where n is the height of the tree. |
| 29 | + * |
| 30 | + * @param node1 first node |
| 31 | + * @param node2 second node |
| 32 | + * @return lower common ancestor |
| 33 | + * @throws NodesNotInSameTreeException if nodes don't have common root |
| 34 | + */ |
| 35 | + public static <S> RootedTree<S> lowestCommonAncestor(RootedTree<S> node1, RootedTree<S> node2) throws NodesNotInSameTreeException { |
| 36 | + if (node1 == node2) |
| 37 | + return node1; |
| 38 | + else if (node1.depth < node2.depth) |
| 39 | + return lowestCommonAncestor(node2, node1); |
| 40 | + else if (node1.depth > node2.depth) { |
| 41 | + int diff = node1.depth - node2.depth; |
| 42 | + int jump = 0; |
| 43 | + while (diff > 0) { |
| 44 | + if (diff % 2 == 1) |
| 45 | + node1 = node1.ancestors.get(jump); |
| 46 | + jump++; |
| 47 | + diff /= 2; |
| 48 | + } |
| 49 | + return lowestCommonAncestor(node1, node2); |
| 50 | + } else { |
| 51 | + try { |
| 52 | + int step = 0; |
| 53 | + while (1<<(step+1) <= node1.depth) |
| 54 | + step++; |
| 55 | + while (step >= 0) { |
| 56 | + if(step < node1.ancestors.size() && node1.ancestors.get(step) != node2.ancestors.get(step)) { |
| 57 | + node1 = node1.ancestors.get(step); |
| 58 | + node2 = node2.ancestors.get(step); |
| 59 | + } |
| 60 | + step--; |
| 61 | + } |
| 62 | + return node1.ancestors.get(0); |
| 63 | + } catch (Exception e) { |
| 64 | + throw new NodesNotInSameTreeException(); |
| 65 | + } |
| 66 | + |
| 67 | + } |
| 68 | + } |
| 69 | + |
| 70 | + public static final class RootedTree<T> { |
| 71 | + |
| 72 | + private final List<RootedTree<T>> ancestors = new ArrayList<RootedTree<T>>(); |
| 73 | + private final List<RootedTree<T>> children = new ArrayList<RootedTree<T>>(); |
| 74 | + |
| 75 | + private T value = null; |
| 76 | + private int depth = 0; |
| 77 | + |
| 78 | + /** |
| 79 | + * Creates tree with root only. |
| 80 | + * |
| 81 | + */ |
| 82 | + public RootedTree() { } |
| 83 | + |
| 84 | + /** |
| 85 | + * Creates tree with root (storing value) only. |
| 86 | + * |
| 87 | + * @param value value to be stored in root |
| 88 | + */ |
| 89 | + public RootedTree(T value) { |
| 90 | + this.value = value; |
| 91 | + } |
| 92 | + |
| 93 | + private RootedTree(RootedTree<T> parent) { |
| 94 | + parent.children.add(this); |
| 95 | + this.ancestors.add(parent); |
| 96 | + this.depth = parent.depth + 1; |
| 97 | + int dist = 0; |
| 98 | + while (true) { |
| 99 | + try { |
| 100 | + this.ancestors.add(this.ancestors.get(dist).ancestors.get(dist)); |
| 101 | + dist++; |
| 102 | + } catch (Exception e){ |
| 103 | + break; |
| 104 | + } |
| 105 | + } |
| 106 | + } |
| 107 | + |
| 108 | + public RootedTree<T> setValue(T value) { |
| 109 | + this.value = value; |
| 110 | + return this; |
| 111 | + } |
| 112 | + |
| 113 | + /** |
| 114 | + * Creates new child for this node and returns it. |
| 115 | + * |
| 116 | + * Complexity O(log depth) |
| 117 | + * |
| 118 | + * @return added child |
| 119 | + */ |
| 120 | + public RootedTree<T> addChild() { |
| 121 | + return new RootedTree<T>(this); |
| 122 | + } |
| 123 | + |
| 124 | + /** |
| 125 | + * Creates new child (storing value) for this node and returns it. |
| 126 | + * |
| 127 | + * Complexity O(log depth) |
| 128 | + * |
| 129 | + * @param value value to be stored in new child |
| 130 | + * @return added child |
| 131 | + */ |
| 132 | + public RootedTree<T> addChild(T value) { |
| 133 | + return addChild().setValue(value); |
| 134 | + } |
| 135 | + |
| 136 | + /** |
| 137 | + * Returns value stored in node. |
| 138 | + * |
| 139 | + * @return node's value. |
| 140 | + */ |
| 141 | + public T getValue() { |
| 142 | + return value; |
| 143 | + } |
| 144 | + |
| 145 | + /** |
| 146 | + * Finds subtree with given value in the root. |
| 147 | + * |
| 148 | + * @param value value to be find |
| 149 | + * @return subtree with given value in the root |
| 150 | + */ |
| 151 | + public RootedTree<T> find(T value) { |
| 152 | + if (this.value == null) { |
| 153 | + if (value == null) |
| 154 | + return this; |
| 155 | + } else if (this.value.equals(value)) |
| 156 | + return this; |
| 157 | + for (RootedTree<T> child: children) { |
| 158 | + final RootedTree<T> res = child.find(value); |
| 159 | + if (res != null) |
| 160 | + return res; |
| 161 | + } |
| 162 | + return null; |
| 163 | + } |
| 164 | + |
| 165 | + /** |
| 166 | + * Returns true if tree contains a node with given value |
| 167 | + * |
| 168 | + * @param value to be checked |
| 169 | + * @return true if tree contains node with given value, false otherwise |
| 170 | + */ |
| 171 | + public boolean contains(T value) { |
| 172 | + return find(value) != null; |
| 173 | + } |
| 174 | + } |
| 175 | +} |
0 commit comments