tree.js

function Tree(value) {
  this.parent = null;
  this.children = [];
  this.value = value || null;
};

Tree.prototype.addChild = function(value) {
  var child;

  if (value.constructor === Tree) {
    child = value;
  } else {
    child = new Tree(value);
  }

  child.parent = this;
  this.children.push(child);
};

Tree.prototype.contains = function(value) {
  if (this.value === value) return true;

  for (var i = 0; i < this.children.length; i++) {
    if (this.children[i].contains(value)) {
      return true;
    }
  }

  return false;
};

Tree.prototype.removeChild = function(value) {
  for (var i = 0; i < this.children.length; i++) {
    if (this.children[i].value === value) {
      var child = this.children.splice(i, 1);
      child.parent = null;
    }
  }
};

Tree.prototype.removeFromParent = function() {
  this.parent.removeChild(this.value);
};

Tree.prototype.isLeaf = function() {
  return this.children.length === 0;
};

Tree.prototype.isRoot = function() {
  return this.parent === null;
};