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| 1 | +/** |
| 2 | + * datastructures-js/binary-search-tree |
| 3 | + * @copyright 2020 Eyas Ranjous <eyas.ranjous@gmail.com> |
| 4 | + * @license MIT |
| 5 | + */ |
| 6 | + |
| 7 | +const BinarySearchTree = require('./binarySearchTree'); |
| 8 | +const AvlTreeNode = require('./avlTreeNode'); |
| 9 | + |
| 10 | +/** |
| 11 | + * @class AvlTree |
| 12 | + * @extends BinarySearchTree |
| 13 | + */ |
| 14 | +class AvlTree extends BinarySearchTree { |
| 15 | + /** |
| 16 | + * @private |
| 17 | + * applies the proper rotation on nodes after inserting a node |
| 18 | + * @param {AvlTreeNode} node |
| 19 | + */ |
| 20 | + balanceAfterInsert(key, node) { |
| 21 | + if (!node) return; |
| 22 | + |
| 23 | + node.updateHeight(); |
| 24 | + const balance = node.calculateBalance(); |
| 25 | + if (balance > 1) { |
| 26 | + if (key < node.getLeft().getKey()) { |
| 27 | + node.rotateRight(); |
| 28 | + } else { |
| 29 | + node.rotateLeftRight(); |
| 30 | + } |
| 31 | + } else if (balance < -1) { |
| 32 | + if (key > node.getRight().getKey()) { |
| 33 | + node.rotateLeft(); |
| 34 | + } else { |
| 35 | + node.rotateRightLeft(); |
| 36 | + } |
| 37 | + } |
| 38 | + if (node === this.rootNode && (balance < -1 || balance > 1)) { |
| 39 | + this.rootNode = node.getParent(); |
| 40 | + } |
| 41 | + } |
| 42 | + |
| 43 | + /** |
| 44 | + * @private |
| 45 | + * applies the proper rotation on nodes after removing a node |
| 46 | + * @param {AvlTreeNode} node |
| 47 | + */ |
| 48 | + balanceAfterRemove(node) { |
| 49 | + if (!node) return; |
| 50 | + |
| 51 | + node.updateHeight(); |
| 52 | + const balance = node.calculateBalance(); |
| 53 | + if (balance > 1) { |
| 54 | + if (node.getLeft().getLeft() !== null) { |
| 55 | + node.rotateRight(); |
| 56 | + } else if (node.getLeft().getRight() !== null) { |
| 57 | + node.rotateLeftRight(); |
| 58 | + } |
| 59 | + } else if (balance < -1) { |
| 60 | + if (node.getRight().getRight() !== null) { |
| 61 | + node.rotateLeft(); |
| 62 | + } else if (node.getRight().getLeft() !== null) { |
| 63 | + node.rotateRightLeft(); |
| 64 | + } |
| 65 | + } |
| 66 | + if (node === this.rootNode && (balance < -1 || balance > 1)) { |
| 67 | + this.rootNode = node.getParent(); |
| 68 | + } |
| 69 | + } |
| 70 | + |
| 71 | + /** |
| 72 | + * @public |
| 73 | + * |
| 74 | + * inserts a node with a key/value into tree |
| 75 | + * and maintains the tree balanced by applying the necessary rotations |
| 76 | + * |
| 77 | + * @param {number|string} key |
| 78 | + * @param {object} vaue |
| 79 | + * @return {AvlTreeNode} the inserted node |
| 80 | + */ |
| 81 | + insert(key, value, node = this.rootNode) { |
| 82 | + if (node === null) { |
| 83 | + this.rootNode = new AvlTreeNode(key, value); |
| 84 | + this.nodesCount += 1; |
| 85 | + return this.rootNode; |
| 86 | + } |
| 87 | + |
| 88 | + if (key < node.getKey() && node.getLeft() === null) { |
| 89 | + const newNode = new AvlTreeNode(key, value); |
| 90 | + node.setLeft(newNode); |
| 91 | + newNode.setParent(node); |
| 92 | + node.updateHeight(); |
| 93 | + this.nodesCount += 1; |
| 94 | + return newNode; |
| 95 | + } |
| 96 | + |
| 97 | + if (key > node.getKey() && node.getRight() === null) { |
| 98 | + const newNode = new AvlTreeNode(key, value); |
| 99 | + node.setRight(newNode); |
| 100 | + newNode.setParent(node); |
| 101 | + node.updateHeight(); |
| 102 | + this.nodesCount += 1; |
| 103 | + return newNode; |
| 104 | + } |
| 105 | + |
| 106 | + if (key === node.getKey()) { |
| 107 | + node.setValue(value); |
| 108 | + return node; |
| 109 | + } |
| 110 | + |
| 111 | + if (key < node.getKey()) { |
| 112 | + const newNode = this.insert(key, value, node.getLeft()); |
| 113 | + this.balanceAfterInsert(key, node); // back-tracking |
| 114 | + return newNode; |
| 115 | + } |
| 116 | + |
| 117 | + const newNode = this.insert(key, value, node.getRight()); |
| 118 | + this.balanceAfterInsert(key, node); // back-tracking |
| 119 | + return newNode; |
| 120 | + } |
| 121 | + |
| 122 | + remove(key, node = this.rootNode) { |
| 123 | + if (node === null) return false; |
| 124 | + |
| 125 | + if (key < node.getKey()) { |
| 126 | + const removed = this.remove(key, node.getLeft()); |
| 127 | + this.balanceAfterRemove(node); |
| 128 | + return removed; |
| 129 | + } |
| 130 | + |
| 131 | + if (key > node.getKey()) { |
| 132 | + const removed = this.remove(key, node.getRight()); |
| 133 | + this.balanceAfterRemove(node); |
| 134 | + return removed; |
| 135 | + } |
| 136 | + |
| 137 | + if (node.getLeft() === null && node.getRight() === null) { |
| 138 | + if (node.getParent() === null) { |
| 139 | + this.rootNode = null; |
| 140 | + } else if (key < node.getParent().getKey()) { |
| 141 | + node.getParent().setLeft(null); |
| 142 | + node.getParent().updateHeight(); |
| 143 | + } else { |
| 144 | + node.getParent().setRight(null); |
| 145 | + node.getParent().updateHeight(); |
| 146 | + } |
| 147 | + this.nodesCount -= 1; |
| 148 | + return true; |
| 149 | + } |
| 150 | + |
| 151 | + if (node.getRight() === null) { |
| 152 | + if (node.getParent() === null) { |
| 153 | + this.rootNode = node.getLeft(); |
| 154 | + } else if (key < node.getParent().getKey()) { |
| 155 | + node.getParent().setLeft(node.getLeft()); |
| 156 | + node.getParent().updateHeight(); |
| 157 | + } else { |
| 158 | + node.getParent().setRight(node.getLeft()); |
| 159 | + node.getParent().updateHeight(); |
| 160 | + } |
| 161 | + node.getLeft().setParent(node.getParent()); |
| 162 | + this.nodesCount -= 1; |
| 163 | + return true; |
| 164 | + } |
| 165 | + |
| 166 | + if (node.getLeft() === null) { |
| 167 | + if (node.getParent() === null) { |
| 168 | + this.rootNode = node.getRight(); |
| 169 | + } else if (key < node.getParent().getKey()) { |
| 170 | + node.getParent().setLeft(node.getRight()); |
| 171 | + node.getParent().updateHeight(); |
| 172 | + } else { |
| 173 | + node.getParent().setRight(node.getRight()); |
| 174 | + node.getParent().updateHeight(); |
| 175 | + } |
| 176 | + node.getRight().setParent(node.getParent()); |
| 177 | + this.nodesCount -= 1; |
| 178 | + return true; |
| 179 | + } |
| 180 | + |
| 181 | + const minRight = this.min(node.getRight()); |
| 182 | + node.setKey(minRight.getKey()); |
| 183 | + return this.remove(minRight.getKey(), minRight); |
| 184 | + } |
| 185 | +} |
| 186 | + |
| 187 | +module.exports = AvlTree; |
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