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algorithm:b-tree [2015/08/01 01:25]
will Basic visualisation.
algorithm:b-tree [2015/08/09 15:30] (current)
will improve insert viz
Line 4: Line 4:
 ======= Algorithm ======= ======= Algorithm =======
 <syntax js> <syntax js>
-// https://​github.com/​dsernst/​data-structures/​blob/​master/​sprint-two/​src/​bTree.js +function ​BTree(order) { 
-var BTree = function ​(order) { +    this.order = order; 
-  this.order = order; +    this.values = []; 
-  this.values = []; +    this.children = [];
-  this.children = [];+
 }; };
  
 BTree.prototype.insert = function (value) { BTree.prototype.insert = function (value) {
-  ​var destination ​= this.pickChild(value); +    ​var m_r = this.insertInternal(value); 
-  if (typeof ​destination ​=== "number") { +    // Handle root split case. 
-    ​this.insert.call(this.children[destination], value); +    ​if (typeof ​m_r === "object") { 
-  } else { +        // If the root(this) split into root,​median,​right copy this into 
-    this.values.push(value)+        // into a new `leftSplit` child, and make this into: 
-    this.sortNode()+        // leftSplit <- [median-> rightSplit 
-    if (this.isOverloaded()) { +        var leftSplit = new BTree(this.order); 
-      this.split();+        ​leftSplit.values ​= this.values
 +        ​leftSplit.children = this.children
 +        this.values = [m_r.median];​ 
 +        this.children = [leftSplit, m_r.rightSplit];
     }     }
-  } 
 }; };
  
-BTree.prototype.sortNode ​= function () { +BTree.prototype.insertInternal ​= function (value) { 
-  this.values.sort(function ​(a, b) {return ​a - b; });+ // Is a leaf node? 
 +    if (this.children.length === 0) { 
 +        return this.insertAndSplit(value); 
 +    } 
 +    else { 
 +        // Pick child to insert into. 
 +        for (var i=0c=this.values.length;​ i<=c; i++) { 
 +            if (i === c || value < this.values[i]) { 
 +                var m_r = this.children[i].insertInternal(value);​ 
 +                if (typeof m_r === "​object"​) { 
 +                    ​return ​this.insertAndSplit(m_r.median,​ m_r.rightSplit); 
 +                ​} 
 +                break; 
 +            } 
 +        } 
 +    } 
 +    return false;
 }; };
  
-BTree.prototype.isOverloaded ​= function () { +BTree.prototype.insertAndSplit ​= function (value, newRight) { 
-  ​return ​this.values.length === this.order;+    for (var i=0, c=this.values.length; i<=c; i++) { 
 +        if (i === c || value < this.values[i]) { 
 +            this.values.splice(i,​ 0, value); 
 +            if (this.children.length !== 0) { 
 +                this.children.splice(i+1,​ 0, newRight);​ 
 +            } 
 +            break; 
 +        } 
 +    } 
 +     
 +    if (this.values.length >= this.order) { 
 +        return this.split();​ 
 +    } 
 +    return false;
 }; };
  
 BTree.prototype.split = function () { BTree.prototype.split = function () {
-  ​var leftSplit ​= new BTree(this.order);​ +    // Splits a node into three: a this, a median value and a right node. 
-  var rightSplit = new BTree(this.order);+    ​var rightSplit ​= new BTree(this.order);​ 
 +    var splitIndex = Math.ceil(this.values.length / 2); 
 +    ​rightSplit.values ​this.values.splice(splitIndex);​ 
 +    var median = this.values.pop();​ 
 +    rightSplit.children = this.children.splice(splitIndex);
  
-  ​leftSplit.values = this.values.splice(0Math.ceil(this.values.length / 2) - 1); +    return {leftSplit:this, median:medianrightSplit:​rightSplit}
-  var median ​= this.values.splice(01)[0]+};
-  ​rightSplit.values = this.values.splice(0);+
  
-  ​for (var i = 0; i < this.children.length; i++) { +// Returns the BTree node and index containing `value` or null if not found. 
-    if (i + 1 <= this.children.length / 2) { +// currently hacked for deletion... 
-      this.children[i].parent = leftSplit+BTree.prototype.find = function (value, asStack) { 
-    } else { +    ​for (var i=0, c=this.values.length; i<=c; i++) { 
-      this.children[i].parent = rightSplit;+        if (i === c || value < this.values[i]) { 
 +            // Recurse and search the ordered child for `value`. 
 +            var foundNode = this.children[i].find(value, asStack)
 +            if (asStack && foundNode) foundNode.push([this,​ i]); 
 +            return foundNode;​ 
 +        ​} 
 +        ​else if (value === this.values[i]) ​
 +            if (asStack) return [[this, i]]; 
 +            return ​[this, i]; 
 +        }
     }     }
-  } +    return null
-  leftSplit.children = this.children.splice(0,​ this.children.length / 2)//TODO +};
-  ​rightSplit.children = this.children.splice(0);+
  
-  if (this.parent) { +BTree.prototype.findMin = function () { 
-    ​var parent = this.parent; +    ​if (this.children.length > 0) { 
-    leftSplit.parent = parent; +        var foundNode ​this.children[0].findMin(); 
-    ​rightSplit.parent = parent; +        ​foundNode.push([this0]); 
-    ​var destination ​parent.pickChild(leftSplit.values[0]); +        ​return foundNode
-    ​parent.children.splice(destination1, leftSplit, rightSplit); +    } 
-    ​parent.insert(median)+    ​else { 
-  } else { +        ​return [[this, ​0]]; 
-    ​this.values[0] = median; +    }
-    ​this.children = [leftSplitrightSplit]; +
-    ​leftSplit.parent = this; +
-    rightSplit.parent = this; +
-  ​}+
 }; };
  
-BTree.prototype.pickChild ​= function (value) { +BTree.prototype.remove ​= function (value) { 
-  var hasOpenSlots ​((this.children.length - 1- this.values.length0; +    var nodeStack ​= this.find(value, true)
-  if (this.children.length ​!== 0 && !hasOpenSlots) { +     
-    ​for (var destination ​= 0; destination < this.values.length; destination++{ +    if (!nodeStackreturn; 
-      if (value < this.values[destination]) { +    var nodeToRemove = nodeStack[0][0], indexToRemove = nodeStack[0][1]
-        ​break+     
-      }+    ​if (nodeToRemove.children.length ​=== 0) { 
 +        nodeToRemove.values.splice(indexToRemove,​ 1); 
 +        nodeStack.shift();​ 
 +        nodeToRemove.rebalance(nodeStack);​ 
 +    ​
 +    else { 
 +        // Find the min value > '​value'​. 
 +        var minStack = nodeToRemove.children[indexToRemove+1].findMin(); 
 +        ​var minNode ​minStack[0][0]; 
 +        // Replace '​value'​ with the next min value. 
 +        nodeToRemove.values[indexToRemove] = minNode.values.shift(); 
 +        // Rebalance the tree from the node the min value came from. 
 +        nodeStack[0][1]++; 
 +        extendArray(minStack,​ nodeStack); 
 +        ​minStack.shift()
 +        ​minNode.rebalance(minStack);​
     }     }
-    return destination;​ 
-  } 
-  return null; 
 }; };
  
-BTree.prototype.contains ​= function (value) { +BTree.prototype.rebalance ​= function (nodeStack) { 
-  var found = false; +    var parent, parentIndex
-  this.traverse(function (node) { +    ​if (nodeStack.length ​> 0) { 
-    ​for (var i = 0; i < node.values.length; i++){ +        ​parent ​nodeStack[0][0],​ parentIndex ​nodeStack[0][1];
-      ​found ​found || value === node.values[i];+
     }     }
-  ​}); +    var minValues = Math.floor(this.order/​2);​ 
-  ​return found+    if (this.values.length < minValues && parent) { 
-}+        // Rotate right? 
 +        var didRotate = false; 
 +        if (parentIndex > 0) { 
 +            var leftSibling = parent.children[parentIndex-1];​ 
 +            if (leftSibling.values.length > minValues) { 
 +                this.values.unshift(parent.values[parentIndex-1]);​ 
 +                parent.values[parentIndex-1] = leftSibling.values.pop();​ 
 +                if (leftSibling.children.length > 0) { 
 +                    this.children.unshift(leftSibling.children.pop());​ 
 +                ​} 
 +                 
 +                didRotate = true; 
 +            } 
 +        } 
 +        // Rotate left? 
 +        if (!didRotate && parentIndex < parent.children.length-1
 +            var rightSibling = parent.children[parentIndex+1]
 +            if (rightSibling.values.length > minValues) { 
 +                this.values.push(parent.values[parentIndex])
 +                ​parent.values[parentIndex] = rightSibling.values.shift();​ 
 +                if (rightSibling.children.length > 0) { 
 +                    this.children.push(rightSibling.children.shift());​ 
 +                ​} 
 +                didRotate = true; 
 +            } 
 +        } 
 +        // Merge siblings? 
 +        if (!didRotate) { 
 +            var mergeIndex;​ 
 +            if (leftSibling) { 
 +                rightSibling = this; 
 +                mergeIndex = parentIndex-1;​ 
 +            } 
 +            else { 
 +                leftSibling = this; 
 +                mergeIndex = parentIndex;​ 
 +            } 
 +            leftSibling.values.push(parent.values[mergeIndex]);​ 
 +            extendArray(leftSibling.values,​ rightSibling.values);​ 
 +            extendArray(leftSibling.children,​ rightSibling.children);​ 
 +            parent.values.splice(mergeIndex,​ 1); 
 +            parent.children.splice(mergeIndex+1,​ 1); 
 +            nodeStack.shift();​ 
 +            parent.rebalance(nodeStack);​ 
 +        } 
 +    } 
 +    else if (this.values.length === 0 && !parent) { 
 +        // Eliminate an empty root. 
 +        this.values = this.children[0].values;​ 
 +        this.children = this.children[0].children;​ 
 +    } 
 +};
  
-BTree.prototype.traverse ​= function (callback) { +BTree.prototype.forEach ​= function (callback) { 
-  ​callback(this)+    var numChildren = this.children.length
-  for (var i = 0; i < this.children.length; i++) { +    if (numChildren > 0) { 
-    this.traverse.call(this.children[i], callback);​ +        ​for (var i=0; i<numChildren; i++) { 
-  }+            this.children[i].forEach(callback);​ 
 +            if (i<​numChildren-1) { 
 +                callback(this.values[i]); 
 +            } 
 +        } 
 +    } 
 +    else { 
 +        // No children casejust pass all the values to `callback`. 
 +        this.values.forEach(callback);​ 
 +    }
 };</​syntax>​ };</​syntax>​
  
Line 98: Line 206:
 <syntax js> <syntax js>
 var btree = new BTree(3); var btree = new BTree(3);
-for (var i=0;​i<​10;​i++) { + 
-    btree.insert(Math.floor(Math.random()*100));​+function setup() { 
 +    // Make sure we don't add '​i'​ to the environment. 
 +    ​for (var i=0;​i<​10;​i++) { 
 +        btree.insert(Math.floor(Math.random()*100)); 
 +    } 
 +
 +setup(); 
 + 
 +function fixBTree(fixbtree) { 
 +    if (fixbtree && !(fixbtree instanceof BTree)) { 
 +        var mybtree = new BTree(fixbtree.order);​ 
 +        mybtree.values = fixbtree.values;​ 
 +        fixbtree.children.forEach(function (x) { 
 +            mybtree.children.push(fixBTree(x));​ 
 +        }); 
 +        return mybtree; 
 +    } 
 +    return fixbtree; 
 +
 + 
 +function preRun() { 
 +    btree = fixBTree(btree);​ 
 +
 + 
 +function extendArray(a,​ b) { 
 +    Array.prototype.push.apply(a,​ b);
 }</​syntax>​ }</​syntax>​
  
 ======= Tests ======= ======= Tests =======
 <syntax js> <syntax js>
-/Unit tests… +function insertTest(order,​ count) { 
-function ​testA() { +    var btree = new BTree(order);​ 
-    if (!ok) { + var inserted = []; 
-        ​throw "Not ok."+ var result = []; 
 +     
 +    for (var i=0;​i<​count;​i++) { 
 +        var x = Math.floor(Math.random()*100); 
 +        ​inserted.push(x);​ 
 +        btree.insert(x);​ 
 +    } 
 +     
 +    btree.forEach(function(x){result.push(x);​});​ 
 +    ​ 
 +    inserted.sort(function(a,​b){return a-b;}); 
 +     
 +    assertEqual(result.length,​ inserted.length);​ 
 +    for (var i=0; i<​result.length;​ i++) { 
 +        assertEqual(result[i],​ inserted[i]);​ 
 +    } 
 +
 + 
 +function testBasic() { 
 +    insertTest(3,​ 10); 
 +
 + 
 +function testHigherOrder() { 
 +    insertTest(7,​ 100); 
 +
 + 
 +function testDeletion() { 
 +    var btree = new BTree(3); 
 + var inserted = []; 
 + var toDelete = []; 
 + var result = []; 
 +     
 +    for (var i=0;​i<​20;​i++) { 
 +        var x = Math.floor(Math.random()*100);​ 
 +        ​if (Math.random()>​0.5) toDelete.push(x);​ 
 +        else inserted.push(x);​ 
 +        btree.insert(x);​ 
 +    } 
 +    for (var i=0;​i<​toDelete.length;​i++) { 
 +        ​btree.remove(toDelete[i]);​ 
 +    } 
 +     
 +    btree.forEach(function(x){result.push(x);​});​ 
 +    inserted.sort(function(a,​b){return a-b;}); 
 +     
 +    assertEqual(result.length,​ inserted.length);​ 
 +    for (var i=0; i<​result.length;​ i++) { 
 +        assertEqual(result[i],​ inserted[i]);​
     }     }
 } }
-*/ 
 </​syntax>​ </​syntax>​
  
Line 118: Line 297:
     "​title":"​B-tree",​     "​title":"​B-tree",​
     "​preRunSource":​ true,     "​preRunSource":​ true,
-    "​height":"​500px"​+    "​height":"​500px"​
 +    "​persistentGlobals":​ ["​btree"​]
 } }
 </​syntax>​ </​syntax>​
Line 144: Line 324:
             fill: rgb(249, 3, 104);             fill: rgb(249, 3, 104);
             stroke: blue;             stroke: blue;
 +        }
 +        g.new tspan {
 +            opacity: 0.5;
 +        }
 +        g.new .node-dot
 +        {
 +            stroke-dasharray:​5,​5;​
         }         }
         g.found rect.node-dot {         g.found rect.node-dot {
Line 157: Line 344:
             stroke: black;             stroke: black;
   marker-end:​ url(#​arrow);​   marker-end:​ url(#​arrow);​
 +        }
 +        tspan.index {
 +            fill: red;
         }         }
         input {         input {
Line 162: Line 352:
         }         }
     </​style>​     </​style>​
-<script src="http://​d3js.org/​d3.v3.min.js"></​script>​+<script src="algorithms-lib/​d3.v3.min.js"></​script>​
 </​head>​ </​head>​
  
 <​body>​ <​body>​
   <div style="​padding:​2px"​ id="​buttons">​   <div style="​padding:​2px"​ id="​buttons">​
-    <button onclick="​random()">​Random</​button>​ <button onclick="​insert()">​Insert</​button>​ <button onclick="​bstRemove()">​Remove</​button>​ <button onclick="​find()">​Find</​button>​ <input id="​input"​ value="​26">​+    <button onclick="​random()">​Random</​button>​ <button onclick="​insert()">​Insert</​button>​ <button onclick="​btreeRemove()">​Remove</​button>​ <button onclick="​find()">​Find</​button>​ <input id="​input"​ value="​26">​
   </​div>​   </​div>​
 <div id="​visualisation"></​div>​ <div id="​visualisation"></​div>​
Line 200: Line 390:
 } }
     ​     ​
-function ​buildTree(currentminNodefoundNodetreeData, duration) { +function ​d3Node(node) { 
-//    var height ​Math.min(50020*(1+treeDepth(treeData)));+    if (!node) return node; 
 +    if (!node._d3Node) { 
 +        node._d3Node = {node:​node};​ 
 +    } 
 +    return node._d3Node;​ 
 +
 + 
 +function inTree(treenode) { 
 +    if (tree===node) return true; 
 +    for (var i=0; i<​tree.children.length;​ i++) { 
 +        if (inTree(tree.children[i]node)) { 
 +            return true; 
 +        } 
 +    } 
 +    return false; 
 +
 + 
 +function buildTree(xbtree, duration) { 
 +    var current = thisInTopFunction(x,​ btree.split) || thisInTopFunction(x,​ btree.insertInternal) || thisInTopFunction(x,​ btree.insert) || thisInTopFunction(x,​ btree.find);​ 
 +    var foundNode = varInTopFunction(x,​ "​foundNode"​) || (x.returnedFrom === btree.find? x.returnedValue : null); 
 +    if (foundNode && foundNode.length === 2 && foundNode[0].length === 2) foundNode = foundNode[0][0];​ 
 +    else if (foundNode && foundNode.length === 2) foundNode = foundNode[0];​ 
 +    var minNode;// = x.lookupInScope("​min"​) || varInTopFunction(x,​ "​rightMin"​) || (x.returnedFrom === bst.findMin?​ x.returnedValue : null); 
 +    ​var ​index x.lookupInScope("​i"​);​ 
 +    var m_r = varInTopFunction(x"​m_r"​);​ 
 +    var rightSplit = x.lookupInScope("​rightSplit"​);​ 
 +    var splitSibling = current; 
 +    if (!rightSplit && x.returnedValue
 +        rightSplit = x.returnedValue.rightSplit;​ 
 +        splitSibling = x.returnedValue.leftSplit;​ 
 +    } 
 +    if (!rightSplit && m_r
 +        rightSplit = m_r.rightSplit;​ 
 +        splitSibling = m_r.leftSplit;​ 
 +    } 
 +    if (inTree(btree,​ rightSplit)) { 
 +        rightSplit = null; 
 +    } 
 +     
 +    foundNode = d3Node(foundNode);​ 
 +    minNode = d3Node(minNode);​ 
 +    rightSplit = d3Node(rightSplit);​ 
 +    splitSibling = d3Node(splitSibling);​ 
 +    current = d3Node(current);​ 
 +    ​
     ​     ​
     // size of the diagram     // size of the diagram
Line 208: Line 442:
         .nodeSize([60,​ 40])         .nodeSize([60,​ 40])
         .children(function(d) {         .children(function(d) {
-            ​// Add dummy nodes to ensure a binary looking tree+            ​var d3Children = d.node.children.map(d3Node);​ 
-            ​//if (d.left || d.right) { +            var currentChildIndex = d3Children.indexOf(splitSibling);​ 
-            //​ return [d.left? d.left : {}d.right? d.right : {}]+            if (currentChildIndex !== -1 && rightSplit && d3Children.indexOf(rightSplit) === -1) { 
-            ​//+                ​d3Children.splice(currentChildIndex+10, rightSplit)
-            return ​d.children;+            } 
 +            return ​d3Children;
         })         })
     .separation(function(a,​ b) {     .separation(function(a,​ b) {
-          ​return (a.parent == b.parent ? 1 : 1.5);+            ​return (a.parent == b.parent ? 1.1 : 1.3);
         });         });
  
-    var nodes = tree.nodes(treeData);+    var nodes = tree.nodes(d3Node(btree));
     var links = tree.links(nodes);​     var links = tree.links(nodes);​
-    ​ 
-    // Filter to remove dummy nodes. 
-    //nodes = nodes.filter(function(d) {return d.hasOwnProperty("​data"​) && d.data !== undefined;​});​ 
-    //links = links.filter(function(d) {return d.target.hasOwnProperty("​data"​);​});​ 
  
     // Edges between nodes as a <path class="​link"​ />     // Edges between nodes as a <path class="​link"​ />
Line 235: Line 466:
     linkNodes.transition().duration(duration)     linkNodes.transition().duration(duration)
     .attr("​d",​ function(a) {return "​M"​+a.source.x+","​+a.source.y+"​L"​+a.target.x+","​+a.target.y;​});​     .attr("​d",​ function(a) {return "​M"​+a.source.x+","​+a.source.y+"​L"​+a.target.x+","​+a.target.y;​});​
 +    linkNodes.attr("​visibility",​ function(d){return (d.target===rightSplit)?"​hidden":"​visible"​});​
  
     // nodes     // nodes
Line 249: Line 481:
     newNodes.append("​rect"​)     newNodes.append("​rect"​)
         .attr("​class",​ "​node-dot"​)         .attr("​class",​ "​node-dot"​)
-        .attr("​rx", ​15+        .attr("​rx", ​5
-        .attr("​ry", ​15)+        .attr("​ry", ​5)
         .attr("​width",​ 0)         .attr("​width",​ 0)
         .attr("​height",​ 0); // Start small.         .attr("​height",​ 0); // Start small.
Line 259: Line 491:
     ​     ​
     var nodesUpdate = nodes.transition().duration(duration);​     var nodesUpdate = nodes.transition().duration(duration);​
-    ​/*nodes.classed("​current",​ function(d) {return d===current;}); +    nodes.classed("​current",​ function(d) {return d===current;​});​
-    nodes.classed("​min",​ function(d) {return d===minNode;});+
     nodes.classed("​found",​ function(d) {return d===foundNode;​});​     nodes.classed("​found",​ function(d) {return d===foundNode;​});​
 +    nodes.classed("​new",​ function(d) {return d===rightSplit;​});​
 +    /​*nodes.classed("​min",​ function(d) {return d===minNode;​});​
     ​     ​
     // Animate setting of current data from minNode.     // Animate setting of current data from minNode.
Line 293: Line 526:
      .attr("​transform",​ "​translate(-30,​-15)"​);​      .attr("​transform",​ "​translate(-30,​-15)"​);​
     ​     ​
-    ​nodes.select("​text"​+    ​function zipData(values, node{ 
-        .text(function(d) { +        ​var z = []; 
-            ​return d.values? d.values.join(",": "?"​;+        values.forEach(function(x){ 
 +            ​z.push([x,node]);
         });         });
 +        return z;
 +    }
 +    ​
 +    // Create the text for each node out of '​tspans'​.
 +    var nodeText = nodes.select("​text"​);​
 +    var spans = nodeText.selectAll("​tspan"​)
 +    .data(function(nodeD) {
 +        return zipData(nodeD.node.values,​ nodeD.node);​
 +          });
 +    spans.enter().append("​tspan"​);​
 +    spans.text(function(d,​ i) {
 +            return d[0] + (d[1].values.length>​i+1?​ ","​ : ""​);​
 +          });
 +    spans.classed("​index",​ function(d, i) {return d[1]===current && i===index;​});​
 +   ​ spans.exit().remove();​
     ​     ​
     // Centre.     // Centre.
     layoutRoot.transition().duration(duration)     layoutRoot.transition().duration(duration)
-    .attr("​transform",​ "​translate("​ + (400/2-treeData.x+0.5) + ",​20.5)"​);​+    .attr("​transform",​ "​translate("​ + (348/2-d3Node(btree).x+0.5) + ",​20.5)"​);​
     ​     ​
     var nodesExit = nodes.exit().transition().duration(duration);​     var nodesExit = nodes.exit().transition().duration(duration);​
Line 320: Line 569:
 } }
     ​     ​
-function ​bstRemove() {+function ​btreeRemove() {
     var data = document.getElementById('​input'​).value;​     var data = document.getElementById('​input'​).value;​
     data = parseInt(data);​     data = parseInt(data);​
Line 333: Line 582:
     var data = document.getElementById('​input'​).value;​     var data = document.getElementById('​input'​).value;​
     data = parseInt(data);​     data = parseInt(data);​
-    runScript("​foundNode = bst.find("​+ data +"​)"​);​+    runScript("​foundNode = btree.find("​+ data +"​)"​);​
 } }
  
Line 364: Line 613:
     if (x) {     if (x) {
         var btree = x.lookupInScope("​btree"​);​         var btree = x.lookupInScope("​btree"​);​
-        ​var insertNode;//​ = thisInTopFunction(x, bst.insert|| /​*thisInTopFunction(x,​ bst.remove) ||*/ thisInTopFunction(x,​ bst.find); +        ​if (btree{ 
-        var foundNode;//​ = varInTopFunction(x, "​foundNode"​) || (x.returnedFrom === bst.find? x.returnedValue : null) +            ​buildTree(x, btreeduration); 
-        var minNode;// = x.lookupInScope("​min"​) || varInTopFunction(x"​rightMin"​) || (x.returnedFrom === bst.findMin?​ x.returnedValue : null); +        ​}
-        ​buildTree(insertNode,​ minNode, foundNode, btree, duration);+
     }     }
     ​     ​
algorithm/b-tree.1438417508.txt.gz · Last modified: 2015/08/01 01:25 by will