User Tools

Site Tools


Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
algorithm:b-tree [2015/08/04 01:15]
will Initial start of deletion code.
algorithm:b-tree [2015/08/09 15:30] (current)
will improve insert viz
Line 7: Line 7:
     this.order = order;     this.order = order;
     this.values = [];     this.values = [];
-    this.children2 ​= [];+    this.children ​= [];
 }; };
  
Line 14: Line 14:
     // Handle root split case.     // Handle root split case.
     if (typeof m_r === "​object"​) {     if (typeof m_r === "​object"​) {
 +        // If the root(this) split into root,​median,​right copy this into
 +        // into a new `leftSplit` child, and make this into:
 +        // leftSplit <- [median] -> rightSplit
         var leftSplit = new BTree(this.order);​         var leftSplit = new BTree(this.order);​
         leftSplit.values = this.values;​         leftSplit.values = this.values;​
-        leftSplit.children2 ​= this.children2+        leftSplit.children ​= this.children
-        this.values = [m_r[0]]; +        this.values = [m_r.median]; 
-        this.children2 ​= [leftSplit, m_r[1]];+        this.children ​= [leftSplit, m_r.rightSplit];
     }     }
 }; };
Line 24: Line 27:
 BTree.prototype.insertInternal = function (value) { BTree.prototype.insertInternal = function (value) {
  // Is a leaf node?  // Is a leaf node?
-    if (this.children2.length === 0) {+    if (this.children.length === 0) {
         return this.insertAndSplit(value);​         return this.insertAndSplit(value);​
     }     }
Line 31: Line 34:
         for (var i=0, c=this.values.length;​ i<=c; i++) {         for (var i=0, c=this.values.length;​ i<=c; i++) {
             if (i === c || value < this.values[i]) {             if (i === c || value < this.values[i]) {
-                var m_r = this.children2[i].insertInternal(value);​+                var m_r = this.children[i].insertInternal(value);​
                 if (typeof m_r === "​object"​) {                 if (typeof m_r === "​object"​) {
-                    return this.insertAndSplit(m_r[0], m_r[1]);+                    return this.insertAndSplit(m_r.median, m_r.rightSplit);
                 }                 }
                 break;                 break;
Line 46: Line 49:
         if (i === c || value < this.values[i]) {         if (i === c || value < this.values[i]) {
             this.values.splice(i,​ 0, value);             this.values.splice(i,​ 0, value);
-            if (this.children2.length !== 0) { +            if (this.children.length !== 0) { 
-                this.children2.splice(i+1,​ 0, newRight);+                this.children.splice(i+1,​ 0, newRight);
             }             }
             break;             break;
Line 65: Line 68:
     rightSplit.values = this.values.splice(splitIndex);​     rightSplit.values = this.values.splice(splitIndex);​
     var median = this.values.pop();​     var median = this.values.pop();​
-    rightSplit.children2 ​= this.children2.splice(splitIndex);​+    rightSplit.children ​= this.children.splice(splitIndex);​
  
-    return ​[median, rightSplit];+    return ​{leftSplit:​this,​ median:median, rightSplit:​rightSplit};
 }; };
  
Line 76: Line 79:
         if (i === c || value < this.values[i]) {         if (i === c || value < this.values[i]) {
             // Recurse and search the ordered child for `value`.             // Recurse and search the ordered child for `value`.
-            var foundNode = this.children2[i].find(value,​ asStack);+            var foundNode = this.children[i].find(value,​ asStack);
             if (asStack && foundNode) foundNode.push([this,​ i]);             if (asStack && foundNode) foundNode.push([this,​ i]);
             return foundNode;             return foundNode;
Line 86: Line 89:
     }     }
     return null;     return null;
 +};
 +
 +BTree.prototype.findMin = function () {
 +    if (this.children.length > 0) {
 +        var foundNode = this.children[0].findMin();​
 +        foundNode.push([this,​ 0]);
 +        return foundNode;
 +    }
 +    else {
 +        return [[this, 0]];
 +    }
 }; };
  
Line 94: Line 108:
     var nodeToRemove = nodeStack[0][0],​ indexToRemove = nodeStack[0][1];​     var nodeToRemove = nodeStack[0][0],​ indexToRemove = nodeStack[0][1];​
     ​     ​
-    if (nodeToRemove.children2.length === 0) {+    if (nodeToRemove.children.length === 0) {
         nodeToRemove.values.splice(indexToRemove,​ 1);         nodeToRemove.values.splice(indexToRemove,​ 1);
-        nodeToRemove.rebalance(nodeStack[1][0], nodeStack[1][1]);+        ​nodeStack.shift();​ 
 +        ​nodeToRemove.rebalance(nodeStack);​
     }     }
     else {     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);​
     }     }
 }; };
  
-BTree.prototype.rebalance = function (parent, parentIndex) {+BTree.prototype.rebalance = function (nodeStack) { 
 +    var parent, parentIndex
 +    if (nodeStack.length > 0) { 
 +        parent = nodeStack[0][0],​ parentIndex = nodeStack[0][1];​ 
 +    }
     var minValues = Math.floor(this.order/​2);​     var minValues = Math.floor(this.order/​2);​
-    if (this.values < minValues && parent) {+    if (this.values.length ​< minValues && parent) {
         // Rotate right?         // Rotate right?
         var didRotate = false;         var didRotate = false;
         if (parentIndex > 0) {         if (parentIndex > 0) {
-            var leftSibling = parent.children2[parentIndex-1];​+            var leftSibling = parent.children[parentIndex-1];​
             if (leftSibling.values.length > minValues) {             if (leftSibling.values.length > minValues) {
-                this.values.splice(0, 0, parent.values[parentIndex-1]);​+                this.values.unshift(parent.values[parentIndex-1]);​
                 parent.values[parentIndex-1] = leftSibling.values.pop();​                 parent.values[parentIndex-1] = leftSibling.values.pop();​
-                ​// handle rotating ​children+                ​if (leftSibling.children.length > 0) { 
 +                    this.children.unshift(leftSibling.children.pop());​ 
 +                } 
 +                ​
                 didRotate = true;                 didRotate = true;
             }             }
         }         }
         // Rotate left?         // Rotate left?
-        if (!didRotate && parentIndex < parent.children2.length-1) { +        if (!didRotate && parentIndex < parent.children.length-1) { 
-            var rightSibling = parent.children2[parentIndex+1];​+            var rightSibling = parent.children[parentIndex+1];​
             if (rightSibling.values.length > minValues) {             if (rightSibling.values.length > minValues) {
                 this.values.push(parent.values[parentIndex]);​                 this.values.push(parent.values[parentIndex]);​
-                parent.values[parentIndex] = rightSibling.values.splice(0, 1); +                parent.values[parentIndex] = rightSibling.values.shift(); 
-                ​// handle rotating ​children+                ​if (rightSibling.children.length > 0) { 
 +                    this.children.push(rightSibling.children.shift());​ 
 +                }
                 didRotate = true;                 didRotate = true;
             }             }
Line 139: Line 172:
             }             }
             leftSibling.values.push(parent.values[mergeIndex]);​             leftSibling.values.push(parent.values[mergeIndex]);​
-            ​Array.prototype.push.apply(leftSibling.values,​ rightSibling.values);​+            ​extendArray(leftSibling.values,​ rightSibling.values); 
 +            extendArray(leftSibling.children,​ rightSibling.children);
             parent.values.splice(mergeIndex,​ 1);             parent.values.splice(mergeIndex,​ 1);
-            parent.children2.splice(mergeIndex+1,​ 1); +            parent.children.splice(mergeIndex+1,​ 1); 
-            ​//parent.rebalance(?, ?);+            ​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.forEach = function (callback) { BTree.prototype.forEach = function (callback) {
-    var numChildren = this.children2.length;+    var numChildren = this.children.length;
     if (numChildren > 0) {     if (numChildren > 0) {
         for (var i=0; i<​numChildren;​ i++) {         for (var i=0; i<​numChildren;​ i++) {
-            this.children2[i].forEach(callback);​+            this.children[i].forEach(callback);​
             if (i<​numChildren-1) {             if (i<​numChildren-1) {
                 callback(this.values[i]);​                 callback(this.values[i]);​
Line 167: Line 207:
 var btree = new BTree(3); var btree = new BTree(3);
  
-for (var i=0;​i<​10;​i++) { +function setup() { 
-    btree.insert(Math.floor(Math.random()*100));​+    // 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) { function fixBTree(fixbtree) {
Line 175: Line 219:
         var mybtree = new BTree(fixbtree.order);​         var mybtree = new BTree(fixbtree.order);​
         mybtree.values = fixbtree.values;​         mybtree.values = fixbtree.values;​
-        fixbtree.children2.forEach(function (x) { +        fixbtree.children.forEach(function (x) { 
-            mybtree.children2.push(fixBTree(x));​+            mybtree.children.push(fixBTree(x));​
         });         });
         return mybtree;         return mybtree;
Line 185: Line 229:
 function preRun() { function preRun() {
     btree = fixBTree(btree);​     btree = fixBTree(btree);​
 +}
 +
 +function extendArray(a,​ b) {
 +    Array.prototype.push.apply(a,​ b);
 }</​syntax>​ }</​syntax>​
  
 ======= Tests ======= ======= Tests =======
 <syntax js> <syntax js>
-function ​testBasicOrdering() { +function ​insertTest(order, count) { 
-    var btree = new BTree(3);+    var btree = new BTree(order);
  var inserted = [];  var inserted = [];
  var result = [];  var result = [];
         
-    for (var i=0;i<10;i++) {+    for (var i=0;i<count;i++) {
         var x = Math.floor(Math.random()*100);​         var x = Math.floor(Math.random()*100);​
         inserted.push(x);​         inserted.push(x);​
Line 202: Line 250:
     btree.forEach(function(x){result.push(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;});     inserted.sort(function(a,​b){return a-b;});
     ​     ​
Line 243: 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 256: Line 344:
             stroke: black;             stroke: black;
   marker-end:​ url(#​arrow);​   marker-end:​ url(#​arrow);​
 +        }
 +        tspan.index {
 +            fill: red;
         }         }
         input {         input {
Line 299: 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 307: Line 442:
         .nodeSize([60,​ 40])         .nodeSize([60,​ 40])
         .children(function(d) {         .children(function(d) {
-            ​return ​d.children2;+            ​var d3Children = d.node.children.map(d3Node);​ 
 +            var currentChildIndex = d3Children.indexOf(splitSibling);​ 
 +            if (currentChildIndex !== -1 && rightSplit && d3Children.indexOf(rightSplit) === -1) { 
 +                d3Children.splice(currentChildIndex+1,​ 0, rightSplit);​ 
 +            } 
 +            return d3Children;
         })         })
     .separation(function(a,​ b) {     .separation(function(a,​ b) {
-          ​return (a.parent == b.parent ? 1.1 : 1.3);+            ​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);​
  
Line 326: 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 352: Line 493:
     nodes.classed("​current",​ function(d) {return d===current;​});​     nodes.classed("​current",​ function(d) {return d===current;​});​
     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;​});​     /​*nodes.classed("​min",​ function(d) {return d===minNode;​});​
     ​     ​
Line 384: 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("​ + (348/2-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 455: Line 613:
     if (x) {     if (x) {
         var btree = x.lookupInScope("​btree"​);​         var btree = x.lookupInScope("​btree"​);​
-        ​var insertNode = thisInTopFunction(x, btree.split|| thisInTopFunction(x,​ btree.insertInternal) || thisInTopFunction(x,​ btree.insert) || thisInTopFunction(x,​ btree.find);​ +        ​if (btree) ​{ 
-        var foundNode = varInTopFunction(x, "​foundNode"​) || (x.returnedFrom === btree.find? x.returnedValue[0] : null) +            ​buildTree(x, btree, ​duration); 
-        var minNode;// = x.lookupInScope("​min"​) || varInTopFunction(x"​rightMin"​) || (x.returnedFrom === bst.findMin?​ x.returnedValue : null); +        ​}
-        ​if(btree)buildTree(insertNode,​ minNode, foundNode, btree, duration);+
     }     }
     ​     ​
algorithm/b-tree.1438676107.txt.gz · Last modified: 2015/08/04 01:15 (external edit)