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AVL Tree balance on removal. Added remove specs. #51

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Feb 28, 2015
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AVL Tree balance on removal. Added remove specs. #51

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137 changes: 104 additions & 33 deletions src/data-structures/avl-tree.js
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Original file line number Diff line number Diff line change
Expand Up @@ -93,6 +93,76 @@
return true;
};

exports.AVLTree.prototype._getNodesToRestructureRemove =
function (traveledNodes) {
// z is last traveled node - imbalance found at z
var zIndex = traveledNodes.length;
zIndex -= 1;
var z = traveledNodes[zIndex];
// y should be child of z with larger height
// (cannot be ancestor of removed node)
var y;
if (z._left !== null && z._right !== null){
y = (z._left === y) ? z._right : z._left;
}else if (z._left !== null && z._right === null){
y = z._left;
}else if (z._right !== null && z._left === null){
y = z._right;
}
// x should be tallest child of y.
// If children same height, x should be child of y
// that has same orientation as z to y.
var x;
if (y._left !== null && y._right !== null){
if (y._left._height > y._right._height){
x = y._left;
}else if (y._left._height < y._right._height){
x = y._right;
}else if (y._left._height === y._right._height){
x = (z._left === y) ? y._left : y._right;
}
}else if (y._left !== null && y._right === null){
x = y._left;
}else if (y._right !== null && y._left === null){
x = y._right;
}
return [x, y, z];
};

exports.AVLTree.prototype._getNodesToRestructureInsert =
function (traveledNodes) {
// z is last traveled node - imbalance found at z
var zIndex = traveledNodes.length;
zIndex -= 1;
var z = traveledNodes[zIndex];
// y should be child of z with larger height
// (must be ancestor of inserted node)
// therefore, last traveled node is correct.
var yIndex = traveledNodes.length;
yIndex -= 2;
var y = traveledNodes[yIndex];
// x should be tallest child of y.
// If children same height, x should be ancestor
// of inserted node (in traveled path).
var x;
if (y._left !== null && y._right !== null){
if (y._left._height > y._right._height){
x = y._left;
}else if (y._left._height < y._right._height){
x = y._right;
}else if (y._left._height === y._right._height){
var xIndex = traveledNodes.length;
xIndex -= 3;
x = traveledNodes[xIndex];
}
}else if (y._left !== null && y._right === null){
x = y._left;
}else if (y._right !== null && y._left === null){
x = y._right;
}
return [x, y, z];
};

/**
* Maintains the height balance property by
* walking to root and checking for invalid height
Expand All @@ -102,21 +172,20 @@
* @public
* @method
* @param {Node} node Started node.
* @param {Boolean} isRemove Represents if method was called after remove.
*/
exports.AVLTree.prototype._maintainHeightBalanceProperty = function (node) {
exports.AVLTree.prototype._maintainHeightBalanceProperty =
function (node, isRemove) {
var current = node;
var path = []; //During restructure, use last 3 nodes traveled.
var traveledNodes = [];
while (current !== null){
path.push(current);
traveledNodes.push(current);
current._height = this._getHeightAtNode(current);
if (!this._isBalancedAtNode(current)){
if (path.length >= 3){
var nodesToRestructure = path.slice(0, 3);
var x = nodesToRestructure[0];
var y = nodesToRestructure[1];
var z = nodesToRestructure[2];
this._restructure(x, y, z);
}
var nodesToBeRestructured = (isRemove)
? this._getNodesToRestructureRemove(traveledNodes)
: this._getNodesToRestructureInsert(traveledNodes);
this._restructure(nodesToBeRestructured);
}
current = current._parent;
}
Expand All @@ -128,11 +197,13 @@
*
* @public
* @method
* @param {Node} x node with lowest height to be restructured.
* @param {Node} y parent of x parameter.
* @param {Node} z grandparent of x, largest height.
* @param {Array} nodesToBeRestructured
* array of nodes, in format, [x, y, z], to be restructured
*/
exports.AVLTree.prototype._restructure = function (x, y, z) {
exports.AVLTree.prototype._restructure = function (nodesToBeRestructured) {
var x = nodesToBeRestructured[0];
var y = nodesToBeRestructured[1];
var z = nodesToBeRestructured[2];
//Determine Rotation Pattern
if (z._right === y && y._right === x){
this._rightRight(x, y, z);
Expand Down Expand Up @@ -337,7 +408,7 @@
}
if (!current[insertKey]) {
current[insertKey] = new exports.Node(value, null, null, current);
this._maintainHeightBalanceProperty(current[insertKey]);
this._maintainHeightBalanceProperty(current[insertKey], false);
} else {
this.insert(value, current[insertKey]);
}
Expand Down Expand Up @@ -481,9 +552,11 @@
*/
exports.AVLTree.prototype._replaceChild =
function (parent, oldChild, newChild) {
if (!parent) {
if (parent === null) {
this._root = newChild;
this._root._parent = null;
if (this._root !== null){
this._root._parent = null;
}
} else {
if (parent._left === oldChild) {
parent._left = newChild;
Expand All @@ -501,33 +574,31 @@
* Average runtime complexity: O(log N).
*
* @public
* @param {Node} node to be removed
* @param {Number|String} value of node to be removed
* @returns {Boolean} True/false depending
* on whether the given node is removed.
*/
exports.AVLTree.prototype.remove = function (node) {
exports.AVLTree.prototype.remove = function (value) {
var node = this.find(value);
if (!node) {
return false;
}

if (node._left && node._right) {
var min = this._findMin(node._right);
var temp = node.value;

node.value = min.value;
min.value = temp;
return this.remove(min);
} else {
if (node._parent !== null) {
if (node._left) {
this._replaceChild(node._parent, node, node._left);
} else if (node._right) {
this._replaceChild(node._parent, node, node._right);
} else {
this._replaceChild(node._parent, node, null);
}
}else {
this._root = null;
if (node._left) {
this._replaceChild(node._parent, node, node._left);
this._maintainHeightBalanceProperty(node._left, true);
} else if (node._right) {
this._replaceChild(node._parent, node, node._right);
this._maintainHeightBalanceProperty(node._right, true);
} else {
this._replaceChild(node._parent, node, null);
this._maintainHeightBalanceProperty(node._parent, true);
}
return true;
}
Expand Down Expand Up @@ -656,12 +727,12 @@
* @returns {Node} The lowest common ancestor of the two nodes or null.
*/
exports.AVLTree.prototype.lowestCommonAncestor =
function (firstNode, secondNode) {
function (firstNode, secondNode) {
return this._lowestCommonAncestor(firstNode, secondNode, this._root);
};

exports.AVLTree.prototype._lowestCommonAncestor =
function (firstNode, secondNode, current) {
function (firstNode, secondNode, current) {
var firstNodeInLeft = this._existsInSubtree(firstNode, current._left);
var secondNodeInLeft = this._existsInSubtree(secondNode, current._left);
var firstNodeInRight = this._existsInSubtree(firstNode, current._right);
Expand Down
38 changes: 38 additions & 0 deletions test/data-structures/avl-tree.spec.js
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Original file line number Diff line number Diff line change
Expand Up @@ -123,4 +123,42 @@ describe('AVL Tree', function () {
expect(avlTree._root._left._right._right.value).toBe(27);
expect(avlTree._root._left._right._right._height).toBe(1);
});
it('should remove nodes and balance properly (1)', function () {
var avlTree = new AVLTree();
avlTree.insert(30);
avlTree.insert(15);
avlTree.insert(60);
avlTree.insert(90);
avlTree.insert(100);
avlTree.remove(15);
// depth 1
expect(avlTree._root.value).toBe(90);
expect(avlTree._root._height).toBe(3);
// depth 2
expect(avlTree._root._left.value).toBe(30);
expect(avlTree._root._left._height).toBe(2);

expect(avlTree._root._right.value).toBe(100);
expect(avlTree._root._right._height).toBe(1);
// depth 3
expect(avlTree._root._left._right.value).toBe(60);
expect(avlTree._root._left._right._height).toBe(1);
});
it('should remove nodes and balance properly (2)', function () {
var avlTree = new AVLTree();
avlTree.insert(55);
avlTree.insert(25);
avlTree.insert(11);
avlTree.insert(1);
avlTree.remove(55);
// depth 1
expect(avlTree._root.value).toBe(11);
expect(avlTree._root._height).toBe(2);
// depth 2
expect(avlTree._root._left.value).toBe(1);
expect(avlTree._root._left._height).toBe(1);

expect(avlTree._root._right.value).toBe(25);
expect(avlTree._root._right._height).toBe(1);
});
});