2d-quadtree/js/bundle.js

Quadtree for games and simulations

(function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
var Quadtree = window.Quadtree = require('./quadtree.js');


var map = window.map = new Quadtree();

var object1 = window.object1 = {'x': 10, 'y': 10, 'height': 10, 'width': 10};
var object2 = window.object2 = {'x': 0, 'y': 0, 'height': 20, 'width': 20};
var object3 = window.object3 = {'x': 0, 'y': 0, 'height': 30, 'width': 30};
var object4 = window.object4 = {'x': 0, 'y': 0, 'height': 40, 'width': 40};
var object5 = window.object5 = {'x': 0, 'y': 0, 'height': 50, 'width': 50};

map.insert(object1);
map.insert(object2);
map.insert(object3);
map.insert(object4);
map.insert(object5);

console.log('-----------------------------------------------------------------------------');

console.log('Number of children: ' + map.getChildCount());
console.log('Number of orphans : ' + map.getOrphanCount());
console.log('Number of orphans and children: ' + map.getOrphanAndChildCount());
},{"./quadtree.js":2}],2:[function(require,module,exports){
'use strict';

var _ = require('underscore');

var DEFAULT_MAX_CHILDREN = 4,
    DEFAULT_DEPTH        = 4,
    DEFAULT_WIDTH        = 1000,
    DEFAULT_HEIGHT       = 1000,
    NORTH_WEST           = 1,
    NORTH_EAST           = 2,
    SOUTH_WEST           = 4,
    SOUTH_EAST           = 8;           

/**
 * Rectangles inserted into the quadtree are extended with this object literal
 */
var rectPrototype = {
  /**
   * Moves the rectangle in the quadtree to a new position (x, y)
   * @method
   * @param  {Number} x The x coordinate as defined by the quadtree coordinate system
   * @param  {Number} y The y coordinate as defined by the quadtree coordinate system
   */
  'move': function (x, y) {
  
    this.x = x;
    this.y = y;
    
    if (this.parent.orphans.indexOf(this) !== -1 || !isWithinBounds(this.parent, this)) {
      this.parent.remove(this);
      this.parent.insert(this);
    }

  },

  /**
   * Returns an array of the rectangles within the quadtree that intersect with this rectangle
   * @method
   * @return {Array} The rectangles that intersect with this rectangle
   */
  'getCollisions': function () {
    return this.parent.getCollisions(this);
  },

  /**
   * Comepletely removes this rectangle from the quadtree
   * @method
   */
  'remove': function () {
    this.parent.remove(this);
  }

};

/**
 * Quadtree contstructor function. Use to initialize the Quadtree. Also, whenever the quadtree splits,
 * this constructor is used to initialize the new nodes of the quadtree.
 * @constructor
 * @param {Object} options The only options of concern to you: width, height, maxChildren, depth
 */
function Quadtree (options) {
  
  options = options || {};

	this.maxChildren = options.maxChildren || DEFAULT_MAX_CHILDREN;
	this.depth       = options.depth       || DEFAULT_DEPTH;
  this.height      = options.height      || DEFAULT_HEIGHT;
  this.width       = options.width       || DEFAULT_WIDTH;
  this.halfHeight  = this.height / 2;
  this.halfWidth   = this.width  / 2;
  this.x           = options.x || 0;
  this.y           = options.y || 0;
  this.parent      = options.parent || null;
  this.children    = [];
  this.orphans     = [];
  this.isLeaf      = true;
  this.quadrant    = options.quadrant || (NORTH_WEST + NORTH_EAST + SOUTH_WEST + SOUTH_EAST);
}

/**
 * 
 * Inserts an object into the quadTree
 * @param  {Object} An arbitrary object with rectangle properties (x, y, width, height)
 */
Quadtree.prototype.insert = function (object) {

  var numberOfChildren = this.children.length;
  
  if (!hasRectProps(object)) {
    throw 'Inserting an object into the Quadtree requires a height, width, x, and y property'; 
  }
 
  if (!object.move) {
    _.extend(object, rectPrototype);
  }

  if (!isWithinBounds(this, object)) {
    if (this.parent) {
      this.parent.insert(object);
      return;
    } else {
      forceObjectWithinBounds(object, this);
    }
  }

  object.parent   = this;
  object.quadrant = undefined;

  // This quadTree does not contain quadTrees
  if (this.isLeaf) {
    
    this.children.push(object);
    setQuadrant(object, this);

    if (this.children.length > this.maxChildren && this.depth) {
      this.divide();
      return;
    }

  
  // This quadTree contains quadTrees
  // We should check if the object we are inserting can be completely contained within
  // one of these quadTrees.  If it can't, it must be an orphan.
  } else {

    for (var i = 0; i < numberOfChildren; i++) {
      if (isWithinBounds(this.children[i], object)) {
        this.children[i].insert(object);
        return;
      }
    }

    // Object does not fit within any of the sub-quadTrees.  It's an orphan.

    setQuadrant(object, this);
    this.orphans.push(object);

  }    

};

/**
 * Removes the object and potentially collapses the quadTree
 * @method remove
 * @param  {Object} Item that was inserted into the quadTree
 */
Quadtree.prototype.remove = function (object) {

  var parent    = object.parent,
      children  = parent.children,
      orphans   = parent.orphans,
      newParent = parent;

  if (_.contains(children, object)) {
    children.splice(children.indexOf(object), 1);
  } else if (_.contains(orphans, object)) {
    orphans.splice(orphans.indexOf(object), 1);
  } else {
    throw 'Object not found in quadTree when attempting to remove';
  }
  while (newParent.parent) {
    newParent = newParent.parent;
  }
  object.parent = newParent;
  parent.collapse();
};

/**
 * Partitions the quadTree into 4 equal sized quadTrees.
 * It also re-inserts all of the children that the leaf contained.
 */
Quadtree.prototype.divide = function () {

  var children      = this.children,
      quarterWidth  = this.width  / 4,
      quarterHeight = this.height / 4,
      options       = {
                        'depth' : this.depth - 1,
                        'width' : this.width  / 2,
                        'height': this.height / 2,
                        'parent': this
                      };

  this.isLeaf = false;

  this.children = [
    new Quadtree(_.extend(options, {
      'x'       : this.x - quarterWidth,
      'y'       : this.y - quarterHeight,
      'quadrant': NORTH_WEST
    })),
    new Quadtree(_.extend(options, {
      'x'       : this.x + quarterWidth,
      'y'       : this.y - quarterHeight,
      'quadrant': NORTH_EAST
    })),
    new Quadtree(_.extend(options, {
      'x'       : this.x - quarterWidth,
      'y'       : this.y + quarterHeight,
      'quadrant': SOUTH_WEST
    })),
    new Quadtree(_.extend(options, {
      'x'       : this.x + quarterWidth,
      'y'       : this.y + quarterHeight,
      'quadrant': SOUTH_EAST
    }))
  ];

  for (var i = 0, l = children.length; i < l; i++) {
    this.insert(children[i]);
  }

    
};

/**
 * Collapses the quadTree
 */
Quadtree.prototype.collapse = function () {

  if (this.parent) {
    if (this !== this.parent.children[0] && this !== this.parent.children[1] && this !== this.parent.children[2] && this !== this.parent.children[3]) {
      throw 'This was a bug that was fixed, but I am paranoid this will get hit so I left it...';
    }
  }
  
  if (this.parent && this.parent.canCollapse()) {
    this.parent.collapse();
    return; 
  }

  if (this.canCollapse() && !this.isLeaf) {

    var allChildrenAndOrphans = this.getOrphansAndChildren();

    this.children = [];
    this.orphans  = [];
    this.isLeaf   = true;

    for (var i = 0; i < allChildrenAndOrphans.length; i++) {
      this.insert(allChildrenAndOrphans[i]);
    }  

  }

};

/**
 * Helper method that determines if the quadtree should collapse
 */
Quadtree.prototype.canCollapse = function () {
  return this.getOrphanAndChildCount() <= this.maxChildren;
}

/**
 * getOrphanCount returns the number of orphans in the quadTree
 * @return {Array} number of orphans in the quadTree
 */
Quadtree.prototype.getOrphanCount = function () {
  
  var numberOfOrphans  = this.orphans.length,
      numberOfChildren = this.children.length, 
      count            = numberOfOrphans;

  if (this.isLeaf) {
    if (count !== 0) {
      throw 'Why does this leaf have orphans?!';
    }
    return count; // should be 0.
  } else {
    for (var i = 0; i < numberOfChildren; i++) {
      count += this.children[i].getOrphanCount();
    }
  }

  return count;

};

/**
 * Returns the number of children in the quadTree
 * @return {Number} The number of children in the quadTree
 */
Quadtree.prototype.getChildCount = function () {

  var count            = 0,
      numberOfChildren = this.children.length;

  if (!this.isLeaf) {
    for (var i = 0; i < numberOfChildren; i++) {
      count += this.children[i].getChildCount();
    }
  } else {
    count += numberOfChildren;
  }

  return count;

};

/**
 * getOrphanAndChildCount returns all rectangles that have been inserted into the quadtree
 * @return {Number} The number of all inserted objects in the quadtree
 */
Quadtree.prototype.getOrphanAndChildCount = function () {
  return this.getOrphanCount() + this.getChildCount();
};

/**
 * getOrphans return all the orphans of the quadTree
 * @return {Array} all the orphans of the quadTree
 */
Quadtree.prototype.getOrphans = function () {

  var orphans = [];

  if (!this.isLeaf) {
    
    orphans = this.orphans;

    for (var i = 0; i < this.children.length; i++) {
      orphans = orphans.concat(this.children[i].getOrphans());
    }

  }

  return orphans;

};

/**
 * getChildren returns an array of all the children of the quadTree
 * @return {Array} all the children of the quadTree
 */
Quadtree.prototype.getChildren = function () {
  
  var children = [];

  if (this.isLeaf) {
    return this.children;
  } else {
    for (var i = 0; i < this.children.length; i++) {
      children = children.concat(this.children[i].getChildren());
    }
  }

  return children;
};

/**
 * getOrphansAndChildren returns an array of all the children and orphans of the quadTree
 * @return {Array} all the children and orphans of the quadTree
 */
Quadtree.prototype.getOrphansAndChildren = function () {
  return this.getChildren().concat(this.getOrphans());
};

/**
 * getQuadtreeCount returns the number of divisions within the quadtree.
 * @return {Number} The number of divisions within the quadtree.
 */
Quadtree.prototype.getQuadtreeCount = function () {
  
  var count = this.children.length;
  
  if (this.isLeaf) {
    return 0;
  }

  for (var i = 0; i < this.children.length; i++) {
    count += this.children[i].getQuadtreeCount();
  }

  return count;

};

Quadtree.prototype.getEntireQuadtreesOrphansAndChildren = function () {
  
  var originalParent = this;

  while (originalParent.parent) {
    originalParent = originalParent.parent;
  }

  return originalParent.getOrphansAndChildren();

}

Quadtree.prototype.getParentOrphanComparisons = function () {
  
  var comparisonList  = [],
      orphans         = this.parent && this.parent.orphans;

  if (!orphans) {
    return comparisonList;
  }

  for (var i = 0; i < orphans.length; i++) {
    if ((orphans[i].quadrant & this.quadrant)) {
      comparisonList.push(orphans[i]);
    }
  }

  return comparisonList.concat(this.parent.getParentOrphanComparisons());
};

Quadtree.prototype.getCollisions = function (rect) {
  
  if (!hasRectProps(rect)) {
    throw 'Collsion must be a rect';
  }

  return getCollisions(this.getComparisons(rect), rect);

};

// This might be an area to optimized.  A rectangle that is an orphans of the parent-most quadtree
// that overlaps all quadrants will be the same as a brute force collision detector.
Quadtree.prototype.getOrphansAndChildrenInQuadrants = function (rect) {
  
  var orphansAndChildren = [],
      quadrant           = rect.quadrant;

  if (quadrant & NORTH_WEST) {
    orphansAndChildren = orphansAndChildren.concat(this.children[0].getOrphansAndChildren());
  }
  
  if (quadrant & NORTH_EAST) {
    orphansAndChildren = orphansAndChildren.concat(this.children[1].getOrphansAndChildren());
  }

  if (quadrant & SOUTH_WEST) {
    orphansAndChildren = orphansAndChildren.concat(this.children[2].getOrphansAndChildren());
  }

  if (quadrant & SOUTH_EAST) {
    orphansAndChildren = orphansAndChildren.concat(this.children[3].getOrphansAndChildren());
  }

  return orphansAndChildren;

};

Quadtree.prototype.getComparisons = function (rect) {

  if (!hasRectProps(rect)) {
    throw 'Collsion must be a rect';
  }

  if (!rect.quadrant) {
    throw 'Rect does not have a quadrant property';
  }

  var comparisonList          = rect.parent.isLeaf ? rect.parent.getChildren() : rect.parent.getOrphansAndChildrenInQuadrants(rect),
      directOrphans           = rect.parent.orphans,
      parentOrphanComparisons = rect.parent.getParentOrphanComparisons(rect); 

  for (var i = 0; i < directOrphans.length; i++) {
    if ((directOrphans[i].quadrant & rect.quadrant)) {
      comparisonList.push(directOrphans[i]);
    }
  }

  comparisonList = comparisonList.concat(parentOrphanComparisons);

  if (_.contains(comparisonList, rect)) {
    comparisonList.splice(comparisonList.indexOf(rect), 1);    
  }

  return comparisonList;

};

Quadtree.prototype.getBruteForceCollisions = function (rect) {
  
  if (!hasRectProps(rect)) {
    throw 'Collsion must be a rect';
  }

  var comparisonList,
      currentQuadTree = this;

  while (currentQuadTree.parent) {
    currentQuadTree = currentQuadTree.parent;
  }

  comparisonList = currentQuadTree.getOrphansAndChildren();

  if (_.contains(comparisonList, rect)) {
    comparisonList.splice(comparisonList.indexOf(rect), 1);    
  }

  return getCollisions(comparisonList, rect);

};

// Helper functions

/**
 * setQuadrant sets the overlapping quadrants (quadtrees) given an object
 * @param {Object} object   A rectangle that is inserted in the quadtree
 * @param {Object} quadtree A quadtree
 */
function setQuadrant (object, quadtree) {

  if (quadtree.isLeaf) {

    if (quadtree.parent) {
      object.quadrant = (isIntersecting(quadtree.parent.children[0], object) * NORTH_WEST) +
                        (isIntersecting(quadtree.parent.children[1], object) * NORTH_EAST) +
                        (isIntersecting(quadtree.parent.children[2], object) * SOUTH_WEST) +
                        (isIntersecting(quadtree.parent.children[3], object) * SOUTH_EAST);      
    } else {
      object.quadrant = 15;
    }

  } else {

    object.quadrant = (isIntersecting(quadtree.children[0], object) * NORTH_WEST) +
                      (isIntersecting(quadtree.children[1], object) * NORTH_EAST) +
                      (isIntersecting(quadtree.children[2], object) * SOUTH_WEST) +
                      (isIntersecting(quadtree.children[3], object) * SOUTH_EAST);
  
  }
}

/**
 * [hasRectProps determines if the object has the necessary properties to be considered a rectangle]
 * @param  {Object}  object [The object questioned for rect props]
 * @return {Boolean}        [True if it is a rectangle]
 */
function hasRectProps (object) {
  return typeof object.width !== 'undefined' && object.height !== 'undefined' && object.x !== 'undefined' && object.y !== 'undefined';
}

/**
 * [getBounds returns the bounds of a rectangle]
 * @param  {Object} r [x, y, width, height]
 * @return {Object}   [left, right, top, bottom]
 */
function getBounds (r) {
  return {
    'left'  : r.x - r.width  / 2,
    'right' : r.x + r.width  / 2,
    'top'   : r.y - r.height / 2,
    'bottom': r.y + r.height / 2
  };
}

/**
 * [isWithinBounds retuns true if rect2 is completely within rect1]
 * @param  {Object}  r1 [x, y, width, height]
 * @param  {Object}  r2 [x, y, width, height]
 * @return {Boolean}    [true if rect2 is completely within rect1]
 */
function isWithinBounds (r1, r2) {

  var r1Bounds = getBounds(r1),
      r2Bounds = getBounds(r2);
      
  return (r2Bounds.left   >= r1Bounds.left  &&
          r2Bounds.right  <= r1Bounds.right &&
          r2Bounds.top    >= r1Bounds.top   &&
          r2Bounds.bottom <= r1Bounds.bottom);
}

/**
 * [isIntersecting returns true if two rectangles intersect]
 * @param  {Object}  r1 [rectangle]
 * @param  {Object}  r2 [rectangle]
 * @return {Boolean}    [True if two rectangles isIntersecting]
 * @diagram
 *  
 *   * * * * * *
 *   *   r2    *
 *   *       * * * *
 *   * * * * * *   *
 *           *  r1 *
 *           * * * *
 *
 *  * * * * * * 
 *  *    r2   *
 *  *         *   * * * *
 *  * * * * * *   *  r1 *
 *                *     *
 *                * * * * 
 */
function isIntersecting (r1, r2) { 

  if (r1.radius && r2.radius) {
    return isIntersectingCircles(r1, r2);
  } else {
    return isIntersectingSquares(r1, r2);
  }

}

function isIntersectingSquares (r1, r2) {
  var r1Bounds = getBounds(r1),
      r2Bounds = getBounds(r2);
      
  return (r1Bounds.left   < r2Bounds.right  &&
          r1Bounds.right  > r2Bounds.left   &&
          r1Bounds.top    < r2Bounds.bottom &&
          r1Bounds.bottom > r2Bounds.top);

}

function isIntersectingCircles (c1, c2) {
  
  var dx       = c1.x - c2.x,
      dy       = c1.y - c2.y,
      distance = Math.sqrt(dx * dx + dy * dy);

  return distance < c1.radius + c2.radius;
}

function getCollisions (comparisonList, rect) {

  var collisionList = [];
  
  for (var i = 0; i < comparisonList.length; i++) {
    if (isIntersecting(comparisonList[i], rect)) {
      collisionList.push(comparisonList[i]);
    }
  }

  return collisionList;

}

/**
 * [forceObjectWithinBounds forces the inserted object into the quadtree bounds.
 * This makes the quadtree behave like pac-man when he goes into the opening on
 * the side of the map]
 * @param  {Object} object [This is the parent-most quadtree]
 * @param  {Object} rect   [The inserted rectangle]
 */
function forceObjectWithinBounds (object, rect) {

  var objectBounds    = getBounds(object),
      containerBounds = getBounds(rect),
      isTooFarLeft    = objectBounds.left   < containerBounds.left,
      isTooFarRight   = objectBounds.left   > containerBounds.right,
      isTooFarAbove   = objectBounds.top    < containerBounds.top,
      isTooFarBelow   = objectBounds.top    > containerBounds.bottom; 

  if (isTooFarLeft) {
    while (object.x < containerBounds.left) {
      object.x = containerBounds.right + object.x + rect.halfWidth;
    }
  }

  if (isTooFarRight) {
    while (object.x > containerBounds.right) {
      object.x = containerBounds.left + object.x - rect.halfWidth;
    }
  }

  if (isTooFarAbove) {
    while (object.y < containerBounds.top) {
      object.y = containerBounds.bottom + object.y + rect.halfHeight;
    }
  }
  
  if (isTooFarBelow) {
    while (object.y > containerBounds.bottom) {
      object.y = containerBounds.top + object.y - rect.halfHeight;
    }
  }  

}

module.exports = Quadtree;
},{"underscore":3}],3:[function(require,module,exports){
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//     (c) 2009-2015 Jeremy Ashkenas, DocumentCloud and Investigative Reporters & Editors
//     Underscore may be freely distributed under the MIT license.

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  // Related: http://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength
  // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094
  var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1;
  var getLength = property('length');
  var isArrayLike = function(collection) {
    var length = getLength(collection);
    return typeof length == 'number' && length >= 0 && length <= MAX_ARRAY_INDEX;
  };

  // Collection Functions
  // --------------------

  // The cornerstone, an `each` implementation, aka `forEach`.
  // Handles raw objects in addition to array-likes. Treats all
  // sparse array-likes as if they were dense.
  _.each = _.forEach = function(obj, iteratee, context) {
    iteratee = optimizeCb(iteratee, context);
    var i, length;
    if (isArrayLike(obj)) {
      for (i = 0, length = obj.length; i < length; i++) {
        iteratee(obj[i], i, obj);
      }
    } else {
      var keys = _.keys(obj);
      for (i = 0, length = keys.length; i < length; i++) {
        iteratee(obj[keys[i]], keys[i], obj);
      }
    }
    return obj;
  };

  // Return the results of applying the iteratee to each element.
  _.map = _.collect = function(obj, iteratee, context) {
    iteratee = cb(iteratee, context);
    var keys = !isArrayLike(obj) && _.keys(obj),
        length = (keys || obj).length,
        results = Array(length);
    for (var index = 0; index < length; index++) {
      var currentKey = keys ? keys[index] : index;
      results[index] = iteratee(obj[currentKey], currentKey, obj);
    }
    return results;
  };

  // Create a reducing function iterating left or right.
  function createReduce(dir) {
    // Optimized iterator function as using arguments.length
    // in the main function will deoptimize the, see #1991.
    function iterator(obj, iteratee, memo, keys, index, length) {
      for (; index >= 0 && index < length; index += dir) {
        var currentKey = keys ? keys[index] : index;
        memo = iteratee(memo, obj[currentKey], currentKey, obj);
      }
      return memo;
    }

    return function(obj, iteratee, memo, context) {
      iteratee = optimizeCb(iteratee, context, 4);
      var keys = !isArrayLike(obj) && _.keys(obj),
          length = (keys || obj).length,
          index = dir > 0 ? 0 : length - 1;
      // Determine the initial value if none is provided.
      if (arguments.length < 3) {
        memo = obj[keys ? keys[index] : index];
        index += dir;
      }
      return iterator(obj, iteratee, memo, keys, index, length);
    };
  }

  // **Reduce** builds up a single result from a list of values, aka `inject`,
  // or `foldl`.
  _.reduce = _.foldl = _.inject = createReduce(1);

  // The right-associative version of reduce, also known as `foldr`.
  _.reduceRight = _.foldr = createReduce(-1);

  // Return the first value which passes a truth test. Aliased as `detect`.
  _.find = _.detect = function(obj, predicate, context) {
    var key;
    if (isArrayLike(obj)) {
      key = _.findIndex(obj, predicate, context);
    } else {
      key = _.findKey(obj, predicate, context);
    }
    if (key !== void 0 && key !== -1) return obj[key];
  };

  // Return all the elements that pass a truth test.
  // Aliased as `select`.
  _.filter = _.select = function(obj, predicate, context) {
    var results = [];
    predicate = cb(predicate, context);
    _.each(obj, function(value, index, list) {
      if (predicate(value, index, list)) results.push(value);
    });
    return results;
  };

  // Return all the elements for which a truth test fails.
  _.reject = function(obj, predicate, context) {
    return _.filter(obj, _.negate(cb(predicate)), context);
  };

  // Determine whether all of the elements match a truth test.
  // Aliased as `all`.
  _.every = _.all = function(obj, predicate, context) {
    predicate = cb(predicate, context);
    var keys = !isArrayLike(obj) && _.keys(obj),
        length = (keys || obj).length;
    for (var index = 0; index < length; index++) {
      var currentKey = keys ? keys[index] : index;
      if (!predicate(obj[currentKey], currentKey, obj)) return false;
    }
    return true;
  };

  // Determine if at least one element in the object matches a truth test.
  // Aliased as `any`.
  _.some = _.any = function(obj, predicate, context) {
    predicate = cb(predicate, context);
    var keys = !isArrayLike(obj) && _.keys(obj),
        length = (keys || obj).length;
    for (var index = 0; index < length; index++) {
      var currentKey = keys ? keys[index] : index;
      if (predicate(obj[currentKey], currentKey, obj)) return true;
    }
    return false;
  };

  // Determine if the array or object contains a given item (using `===`).
  // Aliased as `includes` and `include`.
  _.contains = _.includes = _.include = function(obj, item, fromIndex, guard) {
    if (!isArrayLike(obj)) obj = _.values(obj);
    if (typeof fromIndex != 'number' || guard) fromIndex = 0;
    return _.indexOf(obj, item, fromIndex) >= 0;
  };

  // Invoke a method (with arguments) on every item in a collection.
  _.invoke = function(obj, method) {
    var args = slice.call(arguments, 2);
    var isFunc = _.isFunction(method);
    return _.map(obj, function(value) {
      var func = isFunc ? method : value[method];
      return func == null ? func : func.apply(value, args);
    });
  };

  // Convenience version of a common use case of `map`: fetching a property.
  _.pluck = function(obj, key) {
    return _.map(obj, _.property(key));
  };

  // Convenience version of a common use case of `filter`: selecting only objects
  // containing specific `key:value` pairs.
  _.where = function(obj, attrs) {
    return _.filter(obj, _.matcher(attrs));
  };

  // Convenience version of a common use case of `find`: getting the first object
  // containing specific `key:value` pairs.
  _.findWhere = function(obj, attrs) {
    return _.find(obj, _.matcher(attrs));
  };

  // Return the maximum element (or element-based computation).
  _.max = function(obj, iteratee, context) {
    var result = -Infinity, lastComputed = -Infinity,
        value, computed;
    if (iteratee == null && obj != null) {
      obj = isArrayLike(obj) ? obj : _.values(obj);
      for (var i = 0, length = obj.length; i < length; i++) {
        value = obj[i];
        if (value > result) {
          result = value;
        }
      }
    } else {
      iteratee = cb(iteratee, context);
      _.each(obj, function(value, index, list) {
        computed = iteratee(value, index, list);
        if (computed > lastComputed || computed === -Infinity && result === -Infinity) {
          result = value;
          lastComputed = computed;
        }
      });
    }
    return result;
  };

  // Return the minimum element (or element-based computation).
  _.min = function(obj, iteratee, context) {
    var result = Infinity, lastComputed = Infinity,
        value, computed;
    if (iteratee == null && obj != null) {
      obj = isArrayLike(obj) ? obj : _.values(obj);
      for (var i = 0, length = obj.length; i < length; i++) {
        value = obj[i];
        if (value < result) {
          result = value;
        }
      }
    } else {
      iteratee = cb(iteratee, context);
      _.each(obj, function(value, index, list) {
        computed = iteratee(value, index, list);
        if (computed < lastComputed || computed === Infinity && result === Infinity) {
          result = value;
          lastComputed = computed;
        }
      });
    }
    return result;
  };

  // Shuffle a collection, using the modern version of the
  // [Fisher-Yates shuffle](http://en.wikipedia.org/wiki/Fisher–Yates_shuffle).
  _.shuffle = function(obj) {
    var set = isArrayLike(obj) ? obj : _.values(obj);
    var length = set.length;
    var shuffled = Array(length);
    for (var index = 0, rand; index < length; index++) {
      rand = _.random(0, index);
      if (rand !== index) shuffled[index] = shuffled[rand];
      shuffled[rand] = set[index];
    }
    return shuffled;
  };

  // Sample **n** random values from a collection.
  // If **n** is not specified, returns a single random element.
  // The internal `guard` argument allows it to work with `map`.
  _.sample = function(obj, n, guard) {
    if (n == null || guard) {
      if (!isArrayLike(obj)) obj = _.values(obj);
      return obj[_.random(obj.length - 1)];
    }
    return _.shuffle(obj).slice(0, Math.max(0, n));
  };

  // Sort the object's values by a criterion produced by an iteratee.
  _.sortBy = function(obj, iteratee, context) {
    iteratee = cb(iteratee, context);
    return _.pluck(_.map(obj, function(value, index, list) {
      return {
        value: value,
        index: index,
        criteria: iteratee(value, index, list)
      };
    }).sort(function(left, right) {
      var a = left.criteria;
      var b = right.criteria;
      if (a !== b) {
        if (a > b || a === void 0) return 1;
        if (a < b || b === void 0) return -1;
      }
      return left.index - right.index;
    }), 'value');
  };

  // An internal function used for aggregate "group by" operations.
  var group = function(behavior) {
    return function(obj, iteratee, context) {
      var result = {};
      iteratee = cb(iteratee, context);
      _.each(obj, function(value, index) {
        var key = iteratee(value, index, obj);
        behavior(result, value, key);
      });
      return result;
    };
  };

  // Groups the object's values by a criterion. Pass either a string attribute
  // to group by, or a function that returns the criterion.
  _.groupBy = group(function(result, value, key) {
    if (_.has(result, key)) result[key].push(value); else result[key] = [value];
  });

  // Indexes the object's values by a criterion, similar to `groupBy`, but for
  // when you know that your index values will be unique.
  _.indexBy = group(function(result, value, key) {
    result[key] = value;
  });

  // Counts instances of an object that group by a certain criterion. Pass
  // either a string attribute to count by, or a function that returns the
  // criterion.
  _.countBy = group(function(result, value, key) {
    if (_.has(result, key)) result[key]++; else result[key] = 1;
  });

  // Safely create a real, live array from anything iterable.
  _.toArray = function(obj) {
    if (!obj) return [];
    if (_.isArray(obj)) return slice.call(obj);
    if (isArrayLike(obj)) return _.map(obj, _.identity);
    return _.values(obj);
  };

  // Return the number of elements in an object.
  _.size = function(obj) {
    if (obj == null) return 0;
    return isArrayLike(obj) ? obj.length : _.keys(obj).length;
  };

  // Split a collection into two arrays: one whose elements all satisfy the given
  // predicate, and one whose elements all do not satisfy the predicate.
  _.partition = function(obj, predicate, context) {
    predicate = cb(predicate, context);
    var pass = [], fail = [];
    _.each(obj, function(value, key, obj) {
      (predicate(value, key, obj) ? pass : fail).push(value);
    });
    return [pass, fail];
  };

  // Array Functions
  // ---------------

  // Get the first element of an array. Passing **n** will return the first N
  // values in the array. Aliased as `head` and `take`. The **guard** check
  // allows it to work with `_.map`.
  _.first = _.head = _.take = function(array, n, guard) {
    if (array == null) return void 0;
    if (n == null || guard) return array[0];
    return _.initial(array, array.length - n);
  };

  // Returns everything but the last entry of the array. Especially useful on
  // the arguments object. Passing **n** will return all the values in
  // the array, excluding the last N.
  _.initial = function(array, n, guard) {
    return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n)));
  };

  // Get the last element of an array. Passing **n** will return the last N
  // values in the array.
  _.last = function(array, n, guard) {
    if (array == null) return void 0;
    if (n == null || guard) return array[array.length - 1];
    return _.rest(array, Math.max(0, array.length - n));
  };

  // Returns everything but the first entry of the array. Aliased as `tail` and `drop`.
  // Especially useful on the arguments object. Passing an **n** will return
  // the rest N values in the array.
  _.rest = _.tail = _.drop = function(array, n, guard) {
    return slice.call(array, n == null || guard ? 1 : n);
  };

  // Trim out all falsy values from an array.
  _.compact = function(array) {
    return _.filter(array, _.identity);
  };

  // Internal implementation of a recursive `flatten` function.
  var flatten = function(input, shallow, strict, startIndex) {
    var output = [], idx = 0;
    for (var i = startIndex || 0, length = getLength(input); i < length; i++) {
      var value = input[i];
      if (isArrayLike(value) && (_.isArray(value) || _.isArguments(value))) {
        //flatten current level of array or arguments object
        if (!shallow) value = flatten(value, shallow, strict);
        var j = 0, len = value.length;
        output.length += len;
        while (j < len) {
          output[idx++] = value[j++];
        }
      } else if (!strict) {
        output[idx++] = value;
      }
    }
    return output;
  };

  // Flatten out an array, either recursively (by default), or just one level.
  _.flatten = function(array, shallow) {
    return flatten(array, shallow, false);
  };

  // Return a version of the array that does not contain the specified value(s).
  _.without = function(array) {
    return _.difference(array, slice.call(arguments, 1));
  };

  // Produce a duplicate-free version of the array. If the array has already
  // been sorted, you have the option of using a faster algorithm.
  // Aliased as `unique`.
  _.uniq = _.unique = function(array, isSorted, iteratee, context) {
    if (!_.isBoolean(isSorted)) {
      context = iteratee;
      iteratee = isSorted;
      isSorted = false;
    }
    if (iteratee != null) iteratee = cb(iteratee, context);
    var result = [];
    var seen = [];
    for (var i = 0, length = getLength(array); i < length; i++) {
      var value = array[i],
          computed = iteratee ? iteratee(value, i, array) : value;
      if (isSorted) {
        if (!i || seen !== computed) result.push(value);
        seen = computed;
      } else if (iteratee) {
        if (!_.contains(seen, computed)) {
          seen.push(computed);
          result.push(value);
        }
      } else if (!_.contains(result, value)) {
        result.push(value);
      }
    }
    return result;
  };

  // Produce an array that contains the union: each distinct element from all of
  // the passed-in arrays.
  _.union = function() {
    return _.uniq(flatten(arguments, true, true));
  };

  // Produce an array that contains every item shared between all the
  // passed-in arrays.
  _.intersection = function(array) {
    var result = [];
    var argsLength = arguments.length;
    for (var i = 0, length = getLength(array); i < length; i++) {
      var item = array[i];
      if (_.contains(result, item)) continue;
      for (var j = 1; j < argsLength; j++) {
        if (!_.contains(arguments[j], item)) break;
      }
      if (j === argsLength) result.push(item);
    }
    return result;
  };

  // Take the difference between one array and a number of other arrays.
  // Only the elements present in just the first array will remain.
  _.difference = function(array) {
    var rest = flatten(arguments, true, true, 1);
    return _.filter(array, function(value){
      return !_.contains(rest, value);
    });
  };

  // Zip together multiple lists into a single array -- elements that share
  // an index go together.
  _.zip = function() {
    return _.unzip(arguments);
  };

  // Complement of _.zip. Unzip accepts an array of arrays and groups
  // each array's elements on shared indices
  _.unzip = function(array) {
    var length = array && _.max(array, getLength).length || 0;
    var result = Array(length);

    for (var index = 0; index < length; index++) {
      result[index] = _.pluck(array, index);
    }
    return result;
  };

  // Converts lists into objects. Pass either a single array of `[key, value]`
  // pairs, or two parallel arrays of the same length -- one of keys, and one of
  // the corresponding values.
  _.object = function(list, values) {
    var result = {};
    for (var i = 0, length = getLength(list); i < length; i++) {
      if (values) {
        result[list[i]] = values[i];
      } else {
        result[list[i][0]] = list[i][1];
      }
    }
    return result;
  };

  // Generator function to create the findIndex and findLastIndex functions
  function createPredicateIndexFinder(dir) {
    return function(array, predicate, context) {
      predicate = cb(predicate, context);
      var length = getLength(array);
      var index = dir > 0 ? 0 : length - 1;
      for (; index >= 0 && index < length; index += dir) {
        if (predicate(array[index], index, array)) return index;
      }
      return -1;
    };
  }

  // Returns the first index on an array-like that passes a predicate test
  _.findIndex = createPredicateIndexFinder(1);
  _.findLastIndex = createPredicateIndexFinder(-1);

  // Use a comparator function to figure out the smallest index at which
  // an object should be inserted so as to maintain order. Uses binary search.
  _.sortedIndex = function(array, obj, iteratee, context) {
    iteratee = cb(iteratee, context, 1);
    var value = iteratee(obj);
    var low = 0, high = getLength(array);
    while (low < high) {
      var mid = Math.floor((low + high) / 2);
      if (iteratee(array[mid]) < value) low = mid + 1; else high = mid;
    }
    return low;
  };

  // Generator function to create the indexOf and lastIndexOf functions
  function createIndexFinder(dir, predicateFind, sortedIndex) {
    return function(array, item, idx) {
      var i = 0, length = getLength(array);
      if (typeof idx == 'number') {
        if (dir > 0) {
            i = idx >= 0 ? idx : Math.max(idx + length, i);
        } else {
            length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1;
        }
      } else if (sortedIndex && idx && length) {
        idx = sortedIndex(array, item);
        return array[idx] === item ? idx : -1;
      }
      if (item !== item) {
        idx = predicateFind(slice.call(array, i, length), _.isNaN);
        return idx >= 0 ? idx + i : -1;
      }
      for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) {
        if (array[idx] === item) return idx;
      }
      return -1;
    };
  }

  // Return the position of the first occurrence of an item in an array,
  // or -1 if the item is not included in the array.
  // If the array is large and already in sort order, pass `true`
  // for **isSorted** to use binary search.
  _.indexOf = createIndexFinder(1, _.findIndex, _.sortedIndex);
  _.lastIndexOf = createIndexFinder(-1, _.findLastIndex);

  // Generate an integer Array containing an arithmetic progression. A port of
  // the native Python `range()` function. See
  // [the Python documentation](http://docs.python.org/library/functions.html#range).
  _.range = function(start, stop, step) {
    if (stop == null) {
      stop = start || 0;
      start = 0;
    }
    step = step || 1;

    var length = Math.max(Math.ceil((stop - start) / step), 0);
    var range = Array(length);

    for (var idx = 0; idx < length; idx++, start += step) {
      range[idx] = start;
    }

    return range;
  };

  // Function (ahem) Functions
  // ------------------

  // Determines whether to execute a function as a constructor
  // or a normal function with the provided arguments
  var executeBound = function(sourceFunc, boundFunc, context, callingContext, args) {
    if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args);
    var self = baseCreate(sourceFunc.prototype);
    var result = sourceFunc.apply(self, args);
    if (_.isObject(result)) return result;
    return self;
  };

  // Create a function bound to a given object (assigning `this`, and arguments,
  // optionally). Delegates to **ECMAScript 5**'s native `Function.bind` if
  // available.
  _.bind = function(func, context) {
    if (nativeBind && func.bind === nativeBind) return nativeBind.apply(func, slice.call(arguments, 1));
    if (!_.isFunction(func)) throw new TypeError('Bind must be called on a function');
    var args = slice.call(arguments, 2);
    var bound = function() {
      return executeBound(func, bound, context, this, args.concat(slice.call(arguments)));
    };
    return bound;
  };

  // Partially apply a function by creating a version that has had some of its
  // arguments pre-filled, without changing its dynamic `this` context. _ acts
  // as a placeholder, allowing any combination of arguments to be pre-filled.
  _.partial = function(func) {
    var boundArgs = slice.call(arguments, 1);
    var bound = function() {
      var position = 0, length = boundArgs.length;
      var args = Array(length);
      for (var i = 0; i < length; i++) {
        args[i] = boundArgs[i] === _ ? arguments[position++] : boundArgs[i];
      }
      while (position < arguments.length) args.push(arguments[position++]);
      return executeBound(func, bound, this, this, args);
    };
    return bound;
  };

  // Bind a number of an object's methods to that object. Remaining arguments
  // are the method names to be bound. Useful for ensuring that all callbacks
  // defined on an object belong to it.
  _.bindAll = function(obj) {
    var i, length = arguments.length, key;
    if (length <= 1) throw new Error('bindAll must be passed function names');
    for (i = 1; i < length; i++) {
      key = arguments[i];
      obj[key] = _.bind(obj[key], obj);
    }
    return obj;
  };

  // Memoize an expensive function by storing its results.
  _.memoize = function(func, hasher) {
    var memoize = function(key) {
      var cache = memoize.cache;
      var address = '' + (hasher ? hasher.apply(this, arguments) : key);
      if (!_.has(cache, address)) cache[address] = func.apply(this, arguments);
      return cache[address];
    };
    memoize.cache = {};
    return memoize;
  };

  // Delays a function for the given number of milliseconds, and then calls
  // it with the arguments supplied.
  _.delay = function(func, wait) {
    var args = slice.call(arguments, 2);
    return setTimeout(function(){
      return func.apply(null, args);
    }, wait);
  };

  // Defers a function, scheduling it to run after the current call stack has
  // cleared.
  _.defer = _.partial(_.delay, _, 1);

  // Returns a function, that, when invoked, will only be triggered at most once
  // during a given window of time. Normally, the throttled function will run
  // as much as it can, without ever going more than once per `wait` duration;
  // but if you'd like to disable the execution on the leading edge, pass
  // `{leading: false}`. To disable execution on the trailing edge, ditto.
  _.throttle = function(func, wait, options) {
    var context, args, result;
    var timeout = null;
    var previous = 0;
    if (!options) options = {};
    var later = function() {
      previous = options.leading === false ? 0 : _.now();
      timeout = null;
      result = func.apply(context, args);
      if (!timeout) context = args = null;
    };
    return function() {
      var now = _.now();
      if (!previous && options.leading === false) previous = now;
      var remaining = wait - (now - previous);
      context = this;
      args = arguments;
      if (remaining <= 0 || remaining > wait) {
        if (timeout) {
          clearTimeout(timeout);
          timeout = null;
        }
        previous = now;
        result = func.apply(context, args);
        if (!timeout) context = args = null;
      } else if (!timeout && options.trailing !== false) {
        timeout = setTimeout(later, remaining);
      }
      return result;
    };
  };

  // Returns a function, that, as long as it continues to be invoked, will not
  // be triggered. The function will be called after it stops being called for
  // N milliseconds. If `immediate` is passed, trigger the function on the
  // leading edge, instead of the trailing.
  _.debounce = function(func, wait, immediate) {
    var timeout, args, context, timestamp, result;

    var later = function() {
      var last = _.now() - timestamp;

      if (last < wait && last >= 0) {
        timeout = setTimeout(later, wait - last);
      } else {
        timeout = null;
        if (!immediate) {
          result = func.apply(context, args);
          if (!timeout) context = args = null;
        }
      }
    };

    return function() {
      context = this;
      args = arguments;
      timestamp = _.now();
      var callNow = immediate && !timeout;
      if (!timeout) timeout = setTimeout(later, wait);
      if (callNow) {
        result = func.apply(context, args);
        context = args = null;
      }

      return result;
    };
  };

  // Returns the first function passed as an argument to the second,
  // allowing you to adjust arguments, run code before and after, and
  // conditionally execute the original function.
  _.wrap = function(func, wrapper) {
    return _.partial(wrapper, func);
  };

  // Returns a negated version of the passed-in predicate.
  _.negate = function(predicate) {
    return function() {
      return !predicate.apply(this, arguments);
    };
  };

  // Returns a function that is the composition of a list of functions, each
  // consuming the return value of the function that follows.
  _.compose = fu