ds-algo-study

<!DOCTYPE html> <html lang="en"> <head> <meta charset="UTF-8" /> <meta name="viewport" content="width=device-width, initial-scale=1.0" /> <meta name="description" content="A description of the page and its contents" /> <link rel="stylesheet" href="styles.css" /> <title>Page Title</title> <link rel="stylesheet" href="./../../assets/style.css"/> <link rel="stylesheet" href="./../../assets/prism.css"/> <script async src="./../../assets/prism.js"></script> </head> <body> <h1 id="example-binary-tree">Example Binary Tree</h1> <h3 id="visual-aid">Visual Aid</h3> <hr /> <h2 id="picture-alt"><img src="https://assets.aaonline.io/data_structures_algorithms/trees/images/graph_a.png" alt="picture alt" /></h2> <hr /> <h3 id="example-code">Example Code</h3> <hr /> <div id=">pre data-role=" codeBlock" data-info="js" class="language-javascript"><code><a title="1">class TreeNode {</a> <a title="2"> constructor(val) {</a> <a title="3"> this.val = val;</a> <a title="4"> this.left = null;</a> <a title="5"> this.right = null;</a> <a id=-6" title="6"> }</a> <a title="7">}</a> <a title="8"></a> <a title="9">let a = new TreeNode("a");</a> <a id=-10" title="10">let b = new TreeNode("b");</a> <a title="11">let c = new TreeNode("c");</a> <a id=-12" title="12">let d = new TreeNode("d");</a> <a id=-13" title="13">let e = new TreeNode("e");</a> <a id=-14" title="14">let f = new TreeNode("f");</a> <a id=-15" title="15"></a> <a id=-16" title="16">a.left = b;</a> <a id=-17" title="17">a.right = c;</a> <a id=-18" title="18">b.left = d;</a> <a id=-19" title="19">b.right = e;</a> <a id=-20" title="20">c.right = f;</a></code></pre></div> <hr /> <hr /> <h1 id="terms">Terms</h1> <ul> <li>tree - graph with no cycles</li> <li>binary tree - tree where nodes have at most 2 nodes</li> <li>root - the ultimate parent, the single node of a tree that can access every other node through edges; by definition the root will not have a parent</li> <li>internal node - a node that has children</li> <li>leaf - a node that does not have any children</li> <li>path - a series of nodes that can be traveled through edges - for example A, B, E is a path through the above tree</li> </ul> <hr /> <h1 id="search-patterns">Search Patterns</h1> <ul> <li>Breadth First Search - Check all nodes at a level before moving down a level <ul> <li>Think of this of searching horizontally in rows</li> </ul></li> <li>Depth First Search - Check the depth as far as it goes for one child, before moving on to the next child. <ul> <li>Think of this as searching vertically in diagonals</li> <li>Pre-Order Traversal - Access the data of the current node, recursively visit the left sub tree, recursively visit the right sub tree <ul> <li>All the way to the left, top down, going right after other options have already been logged.</li> </ul></li> <li>In-Order Traversal - Recursively visit the left sub tree, access the data of the current node, recursively visit the right sub tree <ul> <li>In the order they were the "current root", the actual return order of the recursive calls.</li> </ul></li> <li>Post-Order Traversal - Recursively visit the left sub tree, recursively visit the right sub tree, access the data of the current node. <ul> <li>Starting with the bottom most nodes working up through the tree</li> </ul></li> </ul></li> </ul> <hr /> <h1 id="constraints">Constraints</h1> <ul> <li>Binary trees have at most two children per node</li> <li>Given any node of the tree, the values on the left must be strictly less than that node</li> <li>Given any node of the tree, the values on the right must be strictly greater than or equal to that node</li> <li>Given these constraints a binary tree is necessarily a sorted data structure</li> <li>The worst binary trees devolve into a linked list, the best are height balanced (think branching).</li> </ul> <hr /> <h1 id="pseudocode-for-insertion">PseudoCode For Insertion</h1> <ul> <li>Create a new node</li> <li>Start at the root <ul> <li>Check if there is a root <ul> <li>If not the root becomes the new node</li> </ul></li> <li>If there is a root check if the value of the new node is equal to, greater then, or less then the value of the root <ul> <li>If it is greater or equal to <ul> <li>Check to see if there is a node to the right <ul> <li>If there is, move to the new node and continue with the node to the right as the subtree root</li> <li>If there is not, add the new node as the right property of the current node</li> </ul></li> </ul></li> <li>If it is smaller <ul> <li>Check to see if there is a node to the left <ul> <li>If there is, move to the new node and continue with the node to the left as the subtree root</li> <li>If there is not, add the new node as the left property of the current node</li> </ul></li> </ul></li> </ul></li> </ul></li> </ul> <hr /> <h1 id="pseudocode-for-search-of-a-single-item">PseudoCode For Search Of A single Item</h1> <ul> <li>Start at the root <ul> <li>Check if there is a root <ul> <li>If not, there is nothing in the tree, so the search is over</li> </ul></li> <li>If there is a root, check if the value of the root is equal to, greater then, or less then the value were looking for; <ul> <li>If it is equal to the value <ul> <li>We found what we are searching for</li> </ul></li> <li>If it is less than the value <ul> <li>Check to see if there is a node to the left <ul> <li>If there isn't <ul> <li>the value isn't in our tree</li> </ul></li> <li>If there is <ul> <li>repeat these steps with the node to the left as the new subtree root</li> </ul></li> </ul></li> </ul></li> <li>If it is greater than the value <ul> <li>Check to see if there is a node to the right <ul> <li>If there isn't <ul> <li>the value isn't in our tree</li> </ul></li> <li>If there is <ul> <li>repeat these steps with the node to the right as the new subtree root</li> </ul></li> </ul></li> </ul></li> </ul></li> </ul></li> </ul> <hr /> <h1 id="pseudocode-for-breadth-first-search-traversal">PseudoCode For Breadth First Search Traversal</h1> <ul> <li>Create a queue class or use an array</li> <li>Create a variable to store the values of the nodes visited</li> <li>Place the root in the queue</li> <li>Loop as many times as there are items in the queue <ul> <li>Dequeue a node</li> <li>If there is a left value to the node dequeued, add it to the queue</li> <li>If there is a right value to the node dequeued, add it to the queue</li> <li>Push the nodes value into the variable that stores nodes visited</li> </ul></li> </ul> <hr /> <h1 id="pseudocode-for-depth-first-search-traversal">PseudoCode For Depth First Search Traversal</h1> <h2 id="pre-order">Pre-Order</h2> <h4 id="iterative">Iterative</h4> <ul> <li>Create a stack class or use an array</li> <li>Push the root into the stack</li> <li>Create a variable to store the values of the nodes visited</li> <li>Do this as long as there is something on the stack <ul> <li>Pop a node from the stack</li> <li>Push that nodes value into the variable that stores nodes visited.</li> <li>If there is a node to the right push it into the stack</li> <li>If there is a node to the left push it into the stack</li> </ul></li> <li>Return the variable storing the values</li> </ul> <h4 id="recursive">Recursive</h4> <ul> <li>Create a variable to store the current root</li> <li>Push the value of current root to the variable storing the values</li> <li>If the current root has a left propety call the function on that the left property</li> <li>If the current root has a right propety call the function on that the right property</li> <li>Spread the current root, the left values, and the right values</li> </ul> <h2 id="in-order">In-Order</h2> <h4 id="iterative-1">Iterative</h4> <ul> <li>Create a stack class or use an array</li> <li>Create a variable to store the current root</li> <li>Create a variable to store the values of the nodes visited</li> <li>Create a loop <ul> <li>While the current root exists <ul> <li>push the current root to the call stack</li> <li>current root is equal to the left of current root</li> </ul></li> <li>if the stack is empty break out of the loop</li> <li>set a variable to equal the popped value of the stack</li> <li>push that variable into the variable that stores values</li> <li>set the current root to the right of the current loop</li> </ul></li> <li>Return the variable storing the values</li> </ul> <h4 id="recursive-1">Recursive</h4> <ul> <li>Create a variable to store the current root</li> <li>Push the value of current root to the variable storing the values</li> <li>If the current root has a left propety call the function on that the left property</li> <li>If the current root has a right propety call the function on that the right property</li> <li>Spread the the left values, current root ,and the right values</li> </ul> <h2 id="post-order">Post-Order</h2> <h4 id="iterative-2">Iterative</h4> <ul> <li>Haven't figured this one out yet.</li> </ul> <h4 id="recursive-2">Recursive</h4> <ul> <li>Create a variable to store the current root</li> <li>Push the value of current root to the variable storing the values</li> <li>If the current root has a left propety call the function on that the left property</li> <li>If the current root has a right propety call the function on that the right property</li> <li>Spread the the left values, the right values, and current root</li> </ul> <hr /> <h1 id="example-binary-search-tree">Example Binary Search Tree</h1> <div id=">pre data-role=" codeBlock" data-info="js" class="language-javascript"><code><a title="1">class TreeNode {</a> <a id=-2" title="2"> constructor(val) {</a> <a id=-3" title="3"> this.val = val;</a> <a id=-4" title="4"> this.left = null;</a> <a id=-5" title="5"> this.right = null;</a> <a id=-6" title="6"> }</a> <a id=-7" title="7">}</a> <a id=-8" title="8"></a> <a id=-9" title="9">class BST {</a> <a id=-10" title="10"> constructor() {</a> <a id=-11" title="11"> this.root = null;</a> <a id=-12" title="12"> }</a> <a id=-13" title="13"></a> <a id=-14" title="14"> //Insert a new node</a> <a id=-15" title="15"></a> <a id=-16" title="16"> recursiveInsert(val, currentNode = this.root) {</a> <a id=-17" title="17"> if (!this.root) {</a> <a id=-18" title="18"> this.root = new TreeNode(val);</a> <a id=-19" title="19"> return this;</a> <a id=-20" title="20"> }</a> <a id=-21" title="21"> if (val < currentNode.val) {</a> <a id=-22" title="22"> if (!currentNode.left) {</a> <a id=-23" title="23"> currentNode.left = new TreeNode(val);</a> <a id=-24" title="24"> } else {</a> <a id=-25" title="25"> this.insert(val, currentNode.left);</a> <a id=-26" title="26"> }</a> <a id=-27" title="27"> } else {</a> <a id=-28" title="28"> if (!currentNode.right) {</a> <a id=-29" title="29"> currentNode.right = new TreeNode(val);</a> <a id=-30" title="30"> } else {</a> <a id=-31" title="31"> this.insert(val, currentNode.right);</a> <a id=-32" title="32"> }</a> <a id=-33" title="33"> }</a> <a id=-34" title="34"> }</a> <a id=-35" title="35"></a> <a id=-36" title="36"> iterativeInsert(val, currentNode = this.root) {</a> <a id=-37" title="37"> if (!this.root) {</a> <a id=-38" title="38"> this.root = new TreeNode(val);</a> <a id=-39" title="39"> return this;</a> <a id=-40" title="40"> }</a> <a id=-41" title="41"> if (val < currentNode.val) {</a> <a id=-42" title="42"> if (!currentNode.left) {</a> <a id=-43" title="43"> currentNode.left = new TreeNode();</a> <a id=-44" title="44"> } else {</a> <a id=-45" title="45"> while (true) {</a> <a id=-46" title="46"> if (val < currentNode.val) {</a> <a id=-47" title="47"> if (!currenNodet.left) {</a> <a id=-48" title="48"> currentNode.left = new TreeNode();</a> <a id=-49" title="49"> return this;</a> <a id=-50" title="50"> } else {</a> <a id=-51" title="51"> currentNode = currentNode.left;</a> <a id=-52" title="52"> }</a> <a id=-53" title="53"> } else {</a> <a id=-54" title="54"> if (!currentNode.right) {</a> <a id=-55" title="55"> currentNode.right = new TreeNode();</a> <a id=-56" title="56"> return this;</a> <a id=-57" title="57"> } else {</a> <a id=-58" title="58"> currentNode = currentNode.right;</a> <a id=-59" title="59"> }</a> <a id=-60" title="60"> }</a> <a id=-61" title="61"> }</a> <a id=-62" title="62"> }</a> <a id=-63" title="63"> }</a> <a id=-64" title="64"> }</a> <a id=-65" title="65"></a> <a id=-66" title="66"> //Search the tree</a> <a id=-67" title="67"></a> <a id=-68" title="68"> searchRecur(val, currentNode = this.root) {</a> <a id=-69" title="69"> if (!currentNode) return false;</a> <a id=-70" title="70"> if (val < currentNode.val) {</a> <a id=-71" title="71"> return this.searchRecur(val, currentNode.left);</a> <a id=-72" title="72"> } else if (val > currentNode.val) {</a> <a id=-73" title="73"> return this.searchRecur(val, currentNode.right);</a> <a id=-74" title="74"> } else {</a> <a id=-75" title="75"> return true;</a> <a id=-76" title="76"> }</a> <a id=-77" title="77"> }</a> <a id=-78" title="78"></a> <a id=-79" title="79"> searchIter(val) {</a> <a id=-80" title="80"> let currentNode = this.root;</a> <a id=-81" title="81"> while (currentNode) {</a> <a id=-82" title="82"> if (val < currentNode.val) {</a> <a id=-83" title="83"> currentNode = currentNode.left;</a> <a id=-84" title="84"> } else if (val > currentNode.val) {</a> <a id=-85" title="85"> currentNode = currentNode.right;</a> <a id=-86" title="86"> } else {</a> <a id=-87" title="87"> return true;</a> <a id=-88" title="88"> }</a> <a id=-89" title="89"> }</a> <a id=-90" title="90"> return false;</a> <a id=-91" title="91"> }</a> <a id=-92" title="92"></a> <a id=-93" title="93"> // Maybe works, who knows, pulled it off the internet....</a> <a id=-94" title="94"></a> <a id=-95" title="95"> deleteNodeHelper(root, key) {</a> <a id=-96" title="96"> if (root === null) {</a> <a id=-97" title="97"> return false;</a> <a id=-98" title="98"> }</a> <a id=-99" title="99"> if (key < root.val) {</a> <a id=-100" title="100"> root.left = deleteNodeHelper(root.left, key);</a> <a id=-101" title="101"> return root;</a> <a id=-102" title="102"> } else if (key > root.val) {</a> <a id=-103" title="103"> root.right = deleteNodeHelper(root.right, key);</a> <a id=-104" title="104"> return root;</a> <a id=-105" title="105"> } else {</a> <a id=-106" title="106"> if (root.left === null && root.right === null) {</a> <a id=-107" title="107"> root = null;</a> <a id=-108" title="108"> return root;</a> <a id=-109" title="109"> }</a> <a id=-110" title="110"> if (root.left === null) return root.right;</a> <a id=-111" title="111"> if (root.right === null) return root.left;</a> <a id=-112" title="112"></a> <a id=-113" title="113"> let currNode = root.right;</a> <a id=-114" title="114"> while (currNode.left !== null) {</a> <a id=-115" title="115"> currNode = currNode.left;</a> <a id=-116" title="116"> }</a> <a id=-117" title="117"> root.val = currNode.val;</a> <a id=-118" title="118"> root.right = deleteNodeHelper(root.right, currNode.val);</a> <a id=-119" title="119"> return root;</a> <a id=-120" title="120"> }</a> <a id=-121" title="121"> }</a> <a id=-122" title="122"></a> <a id=-123" title="123"> //Recursive Depth First Search</a> <a id=-124" title="124"></a> <a id=-125" title="125"> preOrderTraversal(root) {</a> <a id=-126" title="126"> if (!root) return [];</a> <a id=-127" title="127"> let left = this.preOrderTraversal(root.left);</a> <a id=-128" title="128"> let right = this.preOrderTraversal(root.right);</a> <a id=-129" title="129"> return [root.val, ...left, ...right];</a> <a id=-130" title="130"> }</a> <a id=-131" title="131"></a> <a id=-132" title="132"> preOrderTraversalV2(root) {</a> <a id=-133" title="133"> if (!root) return [];</a> <a id=-134" title="134"> let newArray = new Array();</a> <a id=-135" title="135"> newArray.push(root.val);</a> <a id=-136" title="136"> newArray.push(...this.preOrderTraversalV2(root.left));</a> <a id=-137" title="137"> newArray.push(...this.preOrderTraversalV2(root.right));</a> <a id=-138" title="138"> return newArray;</a> <a id=-139" title="139"> }</a> <a id=-140" title="140"></a> <a id=-141" title="141"> inOrderTraversal(root) {</a> <a id=-142" title="142"> if (!root) return [];</a> <a id=-143" title="143"> let left = this.inOrderTraversal(root.left);</a> <a id=-144" title="144"> let right = this.inOrderTraversal(root.right);</a> <a id=-145" title="145"> return [...left, root.val, ...right];</a> <a id=-146" title="146"> }</a> <a id=-147" title="147"></a> <a id=-148" title="148"> inOrderTraversalV2(root) {</a> <a id=-149" title="149"> if (!root) return [];</a> <a id=-150" title="150"> let newArray = new Array();</a> <a id=-151" title="151"> newArray.push(...this.inOrderTraversalV2(root.left));</a> <a id=-152" title="152"> newArray.push(root.val);</a> <a id=-153" title="153"> newArray.push(...this.inOrderTraversalV2(root.right));</a> <a id=-154" title="154"> return newArray;</a> <a id=-155" title="155"> }</a> <a id=-156" title="156"></a> <a id=-157" title="157"> postOrderTraversal(root) {</a> <a id=-158" title="158"> if (!root) return [];</a> <a id=-159" title="159"> let left = this.postOrderTraversal(root.left);</a> <a id=-160" title="160"> let right = this.postOrderTraversal(root.right);</a> <a id=-161" title="161"> return [...left, ...right, root.val];</a> <a id=-162" title="162"> }</a> <a id=-163" title="163"></a> <a id=-164" title="164"> postOrderTraversalV2(root) {</a> <a id=-165" title="165"> if (!root) return [];</a> <a id=-166" title="166"> let newArray = new Array();</a> <a id=-167" title="167"> newArray.push(...this.postOrderTraversalV2(root.left));</a> <a id=-168" title="168"> newArray.push(...this.postOrderTraversalV2(root.right));</a> <a id=-169" title="169"> newArray.push(root.val);</a> <a id=-170" title="170"> return newArray;</a> <a id=-171" title="171"> }</a> <a id=-172" title="172"></a> <a id=-173" title="173"> // Iterative Depth First Search</a> <a id=-174" title="174"></a> <a id=-175" title="175"> iterativePreOrder(root) {</a> <a id=-176" title="176"> let stack = [root];</a> <a id=-177" title="177"> let results = [];</a> <a id=-178" title="178"> while (stack.length) {</a> <a id=-179" title="179"> let current = stack.pop();</a> <a id=-180" title="180"> results.push(current);</a> <a id=-181" title="181"> if (current.left) stack.push(current.left);</a> <a id=-182" title="182"> if (current.right) stack.push(current.right);</a> <a id=-183" title="183"> }</a> <a id=-184" title="184"> return results;</a> <a id=-185" title="185"> }</a> <a id=-186" title="186"></a> <a id=-187" title="187"> iterativeInOrder(root) {</a> <a id=-188" title="188"> let stack = [];</a> <a id=-189" title="189"> let current = root;</a> <a id=-190" title="190"> let results = [];</a> <a id=-191" title="191"> while (true) {</a> <a id=-192" title="192"> while (current) {</a> <a id=-193" title="193"> stack.push(current);</a> <a id=-194" title="194"> current = current.left;</a> <a id=-195" title="195"> }</a> <a id=-196" title="196"></a> <a id=-197" title="197"> if (!stack.length) break;</a> <a id=-198" title="198"> let removed = stack.pop();</a> <a id=-199" title="199"> results.push(removed);</a> <a id=-200" title="200"> current = current.right;</a> <a id=-201" title="201"> }</a> <a id=-202" title="202"> return results;</a> <a id=-203" title="203"> }</a> <a id=-204" title="204"></a> <a id=-205" title="205"> //To-Do iterativePostOrder</a> <a id=-206" title="206"></a> <a id=-207" title="207"> //Breadth First Search</a> <a id=-208" title="208"></a> <a id=-209" title="209"> breadthFirstSearch(root) {</a> <a id=-210" title="210"> let queue = [root];</a> <a id=-211" title="211"> let result = [];</a> <a id=-212" title="212"> while (queue.length) {</a> <a id=-213" title="213"> let current = queue.shift();</a> <a id=-214" title="214"> if (current.left) queue.push(current.left);</a> <a id=-215" title="215"> if (current.right) queue.push(current.left);</a> <a id=-216" title="216"> current.push(result);</a> <a id=-217" title="217"> }</a> <a id=-218" title="218"> return result;</a> <a id=-219" title="219"> }</a> <a id=-220" title="220"></a> <a id=-221" title="221"> // Converting a Sorted Array to a Binary Search Tree</a> <a id=-222" title="222"></a> <a id=-223" title="223"> sortedArrayToBST(nums) {</a> <a id=-224" title="224"> if (nums.length === 0) return null;</a> <a id=-225" title="225"></a> <a id=-226" title="226"> let mid = Math.floor(nums.length / 2);</a> <a id=-227" title="227"> let root = new TreeNode(nums[mid]);</a> <a id=-228" title="228"></a> <a id=-229" title="229"> let left = nums.slice(0, mid);</a> <a id=-230" title="230"> root.left = sortedArrayToBST(left);</a> <a id=-231" title="231"></a> <a id=-232" title="232"> let right = nums.slice(mid + 1);</a> <a id=-233" title="233"> root.right = sortedArrayToBST(right);</a> <a id=-234" title="234"></a> <a id=-235" title="235"> return root;</a> <a id=-236" title="236"> }</a> <a id=-237" title="237">}</a></code></pre></div>