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"totitle": "Algorithms and Data Structures - Getting Started",
"*": "<tr><td colspan=\"2\" class=\"diff-lineno\" id=\"mw-diff-left-l1\">Line 1:</td>\n<td colspan=\"2\" class=\"diff-lineno\">Line 1:</td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\"><strong>MediaWiki has been installed.</strong></del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">''This page is part of [[Programming and CS - Getting Started]]''</ins></div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">Consult </del>the [https://www.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Help:Contents User's Guide</del>] <del class=\"diffchange diffchange-inline\">for information on using </del>the <del class=\"diffchange diffchange-inline\">wiki software</del>.</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Reading=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [https://www.tutorialspoint.com/data_structures_algorithms/index.htm TutorialsPoint] - start with this, it covers </ins>the <ins class=\"diffchange diffchange-inline\">basic data structures and algorithms (material typically covered in CS 201 Programming Structures, CS 202 Data Structures and Algorithms, CS 500 Programming Fundamentals at ISU).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* </ins>[https://www.<ins class=\"diffchange diffchange-inline\">amazon</ins>.<ins class=\"diffchange diffchange-inline\">com</ins>/<ins class=\"diffchange diffchange-inline\">Introduction-Algorithms-3rd-MIT-Press</ins>/<ins class=\"diffchange diffchange-inline\">dp/0262033844 Introduction to Algorithms] - or start with this.\u00a0 This includes both basic data structures and algorithms and further material that is typically covered in CS 458 Algorithms and CS 420 Theory of Computation at ISU.\u00a0 </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* [https</ins>:/<ins class=\"diffchange diffchange-inline\">/www.cs.princeton.edu/~wayne/kleinberg-tardos/ Algorithm Design</ins>] <ins class=\"diffchange diffchange-inline\">- these are slides to accompany </ins>the <ins class=\"diffchange diffchange-inline\">Algorithm Design textbook.\u00a0 This textbook leans more towards material that is typically covered in CS 458 Algorithms and CS 658 Algorithms II at ISU, and is a fairly modern treatment of algorithms</ins>.</div></td></tr>\n<tr><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-deleted\"><br></td><td class=\"diff-marker\"></td><td class=\"diff-context diff-side-added\"><br></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>=<del class=\"diffchange diffchange-inline\">= Getting started =</del>=</div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>=<ins class=\"diffchange diffchange-inline\">Data Structures Basics</ins>=</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div><del class=\"diffchange diffchange-inline\">* [https:</del>//<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki/Special:MyLanguage</del>/<del class=\"diffchange diffchange-inline\">Manual:Configuration_settings Configuration settings </del>list<del class=\"diffchange diffchange-inline\">]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">For each of the following basic data structures, you should have memorized the algorithms for insert, lookup, delete, the worst-case </ins>/ <ins class=\"diffchange diffchange-inline\">average-case </ins>/ <ins class=\"diffchange diffchange-inline\">best-case running times (including why the running time is what it is), uses of each data structure, and be able to use the data structure in your programs.\u00a0 </ins></div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* <del class=\"diffchange diffchange-inline\">[https:</del>//<del class=\"diffchange diffchange-inline\">www.mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special:MyLanguage/Manual:FAQ MediaWiki FAQ]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* <del class=\"diffchange diffchange-inline\">[https:/</del>/<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia</del>.<del class=\"diffchange diffchange-inline\">org/postorius/lists/mediawiki</del>-<del class=\"diffchange diffchange-inline\">announce</del>.<del class=\"diffchange diffchange-inline\">lists</del>.<del class=\"diffchange diffchange-inline\">wikimedia</del>.<del class=\"diffchange diffchange-inline\">org/ MediaWiki release mailing list]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Note - this material is typically covered in CS 201 Programming Structures, CS 202 Data Structures and Algorithms, and CS 500 Programming Fundamentals at ISU</ins>. \u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* <del class=\"diffchange diffchange-inline\">[https:</del>//<del class=\"diffchange diffchange-inline\">www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org</del>/<del class=\"diffchange diffchange-inline\">wiki</del>/<del class=\"diffchange diffchange-inline\">Special:MyLanguage/Localisation#Translation_resources Localise MediaWiki </del>for <del class=\"diffchange diffchange-inline\">your language]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td class=\"diff-marker\" data-marker=\"\u2212\"></td><td class=\"diff-deletedline diff-side-deleted\"><div>* <del class=\"diffchange diffchange-inline\">[https:</del>/<del class=\"diffchange diffchange-inline\">/www</del>.<del class=\"diffchange diffchange-inline\">mediawiki</del>.<del class=\"diffchange diffchange-inline\">org/wiki/Special</del>:<del class=\"diffchange diffchange-inline\">MyLanguage/Manual</del>:<del class=\"diffchange diffchange-inline\">Combating_spam Learn how to combat spam on your wiki]</del></div></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Array (unsorted)''' - O(1) insert, O(n) lookup using linear search, O(1) delete if you have an index to what is being deleted.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Array (sorted)''' - O(n) insert, O(log(n)) lookup using binary search, O(n) delete because need to shift to keep in sorted order</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Linked list''' - O(1) insert, O(n) lookup using linear search, O(1) delete.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Arrays </ins>/ <ins class=\"diffchange diffchange-inline\">linked lists''' - used when data is small enough that O(n) running time is acceptable.\u00a0 Code is very simple.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Stack''' - stored using a linked list or array, one use is in keeping track of local variables in a running program, another is arithmetic using RPN.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Queue''' - stored using a linked list, used when there is a \"line\" waiting for some resource where the first in the line gets the resource first.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Binary search tree (not necessarily balanced)''' - operations are O(height of tree), which can be n in the worst-case of a completely unbalanced tree but is typically O(log(n)) on random data.\u00a0 Code for operations is very simple.\u00a0 BSTs used when data is large enough that array </ins>/ <ins class=\"diffchange diffchange-inline\">linked </ins>list <ins class=\"diffchange diffchange-inline\">too slow, preferred over hash table if you might need to consider a range of values (e.g., all people with last name starting with Joh).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>* <ins class=\"diffchange diffchange-inline\">'''Binary search tree (balanced)''' - operations are O(height of tree), tree height is kept O(log(n)) by rebalancing</ins>/<ins class=\"diffchange diffchange-inline\">shifting the tree if it becomes too unbalanced.\u00a0 </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Hash table (deal with collisions using chaining</ins>/<ins class=\"diffchange diffchange-inline\">buckets)''' - operations are O(size of linked list buckets), size of buckets is O(1) if size of hash table chosen appropriately and data is random, operations are n in worst case (all items collide and stay in one bucket)</ins>. <ins class=\"diffchange diffchange-inline\"> Hash table used when lookup</ins>/<ins class=\"diffchange diffchange-inline\">insert</ins>/<ins class=\"diffchange diffchange-inline\">delete need to be fast and having data stored in sorted order does not matter.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>* <ins class=\"diffchange diffchange-inline\">'''Hash table (deal with collisions using probing)''' - performance similar to hash table with chaining</ins>/<ins class=\"diffchange diffchange-inline\">buckets but could be worse as the hash table fills up</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Heap''' - operations are O(log(n)), used when need to have access to the largest or smallest item</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Asymptotic Analysis (Big O)=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Note </ins>- <ins class=\"diffchange diffchange-inline\">this material is typically covered in CS 201 Programming Structures, CS 202 Data Structures and Algorithms, and CS 500 Programming Fundamentals at ISU</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">You should have memorized the two main definitions of big O, and the definitions of little o, big Omega, small omega, and big Theta</ins>. <ins class=\"diffchange diffchange-inline\"> You should have memorized, can use, and can prove the following rules of thumb</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>* <ins class=\"diffchange diffchange-inline\">'''constant factors''' - in any formula, constant multiples can be removed (e.g., 3*n<sup>2<</ins>/<ins class=\"diffchange diffchange-inline\">sup> is Theta(n<sup>2<</ins>/<ins class=\"diffchange diffchange-inline\">sup>)).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''polynomials''' - for any formula that has only polynomial terms, the formula is O(term with the largest exponent).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''logarithms < polynomials < exponentials''' - any formula involving fixed powers of polynomials is O(any fixed positive polynomial powers), e</ins>.<ins class=\"diffchange diffchange-inline\">g</ins>.<ins class=\"diffchange diffchange-inline\">, (log(n))<sup>10<</ins>/<ins class=\"diffchange diffchange-inline\">sup> is O(n<sup>0.01<</ins>/<ins class=\"diffchange diffchange-inline\">sup>).\u00a0 Note that in practice you might likely prefer the latter, but in terms of big O the former is smaller ''eventually, </ins>for <ins class=\"diffchange diffchange-inline\">large enough n''.\u00a0 Similarly, any fixed power of a polynomial is O(any fixed positive power of an exponential).</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">You should be able to take a list of formulas and put them into \"big O order\" using the above rules of thumb.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Algorithms Basics=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Note - this material is typically covered in CS 201 Programming Structures, CS 202 Data Structures and Algorithms, and CS 500 Programming Fundamentals at ISU. </ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==Searching==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Linear Search''' -\u00a0 Worst Case O(n). Used to search an unsorted array and linked list.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Binary Search''' -\u00a0 Worst Case O(log n). Used to search a sorted array.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">==Sorting==</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">Sorting algorithms can be stable or unstable. A stable sorting algorithm will keep the original order of elements that are similar. An unstable algorithm does not guarantee that similar elements will keep their original order.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>* <ins class=\"diffchange diffchange-inline\">'''Bubble Sort''' - Worst Case O(n^2). Simple sorting algorithm which 'bubbles' the larger</ins>/<ins class=\"diffchange diffchange-inline\">smaller numbers to the end of the array. Bubble sort is a stable sorting algorithm.</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* '''Merge Sort''' -\u00a0 Worst Case O(n*log(n). Sorting algorithm which recursively splits the array in half, then reorders each section of the array as it puts the pieces back together</ins>. <ins class=\"diffchange diffchange-inline\">Merge sort is a stable sorting algorithm</ins>.</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Graph Algorithms=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Breath First Search (BFS): (placeholder)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Depth First Search\u00a0 (DFS): (placeholder)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Prim's Minimum Spanning Tree Algorithm: (placeholder)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Kruskal's Minimum Spanning Forest Algorithm</ins>: <ins class=\"diffchange diffchange-inline\">(placeholder)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">* Dijkstra's Shortest Path Algorithm</ins>: <ins class=\"diffchange diffchange-inline\">(placeholder)</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=NP Completeness=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Algorithm technique - dynamic programming=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Algorithm technique - greedy=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Algorithm technique - divide and conquer=</ins></div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div>\u00a0</div></td></tr>\n<tr><td colspan=\"2\" class=\"diff-side-deleted\"></td><td class=\"diff-marker\" data-marker=\"+\"></td><td class=\"diff-addedline diff-side-added\"><div><ins class=\"diffchange diffchange-inline\">=Algorithm technique - linear programming=</ins></div></td></tr>\n"
}
}