{"id":98,"date":"2026-01-28T12:08:23","date_gmt":"2026-01-28T12:08:23","guid":{"rendered":"https:\/\/staymind.shop\/?p=98"},"modified":"2026-01-28T12:54:30","modified_gmt":"2026-01-28T12:54:30","slug":"paper-of-design-and-analysis-of-algorithm-department-of-computer-science-and-software-engineering","status":"publish","type":"post","link":"https:\/\/staymind.shop\/?p=98","title":{"rendered":"Paper Of Design and Analysis Of Algorithm Department Of Computer Science and Software Engineering"},"content":{"rendered":"\n<p>Let&#8217;s cut to the chase:&nbsp;<strong>Design and Analysis of Algorithms (DAA)<\/strong>&nbsp;is not a subject. It&#8217;s a&nbsp;<strong>superpower<\/strong>. This past paper is your trial by fire to prove you don&#8217;t just write code\u2014you engineer solutions that are elegant, efficient, and scalable. It&#8217;s the difference between brute-forcing your way through a maze and deriving a theorem for the shortest path.<\/p>\n\n\n\n<p>Forget memorizing syntax. This is about raw, analytical problem-solving. It asks the fundamental question:&nbsp;<em>&#8220;Given a problem and unlimited computational power in theory, but very real constraints in practice, what is the most intelligent way to make the machine work?&#8221;<\/em><\/p>\n\n\n\n<p><strong>What This Paper Actually Measures: Your Computational Intelligence<\/strong><\/p>\n\n\n\n<p><strong>1. The Two Pillars: Design &amp; Analysis<\/strong><br>The title says it all. You are tested on a&nbsp;<strong>dual mastery<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Design:<\/strong>\u00a0Can you craft a clever, step-by-step strategy (an algorithm) to solve a problem?<\/li>\n\n\n\n<li><strong>Analysis:<\/strong>\u00a0Can you\u00a0<em>prove<\/em>\u00a0why your strategy is good? This means rigorously analyzing its\u00a0<strong>Time Complexity<\/strong>\u00a0(how fast it runs) and\u00a0<strong>Space Complexity<\/strong>\u00a0(how much memory it uses) using\u00a0<strong>Big O, \u0398 (Theta), and \u03a9 (Omega)<\/strong>\u00a0notation.<\/li>\n<\/ul>\n\n\n\n<p><strong>2. The Algorithmic Toolbox: Recognizing Patterns in Chaos<\/strong><br>Great algorithm designers see problems not as unique monsters, but as members of familiar families. The paper tests your fluency with these core&nbsp;<strong>algorithmic paradigms<\/strong>:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Divide and Conquer:<\/strong>\u00a0The art of breaking a problem into independent subproblems, solving them, and combining results. You&#8217;ll dissect\u00a0<strong>Merge Sort<\/strong>\u00a0and\u00a0<strong>QuickSort<\/strong>, derive their recurrences, and solve them to prove\u00a0<em>O(n log n)<\/em>\u00a0complexity. You&#8217;ll apply this to problems like finding the closest pair of points.<\/li>\n\n\n\n<li><strong>Greedy Algorithms:<\/strong>\u00a0The strategy of making the locally optimal choice at each step, hoping it leads to a global optimum. You&#8217;ll prove when it works (Huffman coding, Activity Selection) and when it fails. A classic question:\u00a0*&#8221;Prove that the greedy choice for Fractional Knapsack is optimal, but for 0\/1 Knapsack it is not.&#8221;*<\/li>\n\n\n\n<li><strong>Dynamic Programming (DP):<\/strong>\u00a0The paradigm of solving overlapping subproblems and storing their solutions to avoid recomputation. This is where many students hit a wall. You&#8217;ll need to:\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Identify the optimal substructure<\/strong>\u00a0(how the optimal solution incorporates optimal solutions to subproblems).<\/li>\n\n\n\n<li><strong>Define the recurrence relation<\/strong>\u00a0(the mathematical heart of the DP).<\/li>\n\n\n\n<li><strong>Implement it<\/strong>\u00a0(either top-down with memoization or bottom-up with tabulation).<br>Problems:\u00a0<strong>Fibonacci, Longest Common Subsequence, Matrix Chain Multiplication, Floyd-Warshall<\/strong>. You must not just solve them, but explain\u00a0<em>why<\/em>\u00a0DP is applicable.<\/li>\n<\/ol>\n<\/li>\n\n\n\n<li><strong>Graph Algorithms:<\/strong>\u00a0Modeling relationships. You&#8217;ll implement and analyze:\n<ul class=\"wp-block-list\">\n<li><strong>Traversal:<\/strong>\u00a0BFS (shortest path on unweighted graphs) and DFS (cycle detection, topological sort).<\/li>\n\n\n\n<li><strong>Shortest Path:<\/strong>\u00a0Dijkstra&#8217;s (greedy, for non-negative weights) and Bellman-Ford (handles negative weights).<\/li>\n\n\n\n<li><strong>Minimum Spanning Tree:<\/strong>\u00a0Kruskal&#8217;s (uses a Union-Find data structure) and Prim&#8217;s algorithms.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Backtracking &amp; Branch-and-Bound:<\/strong>\u00a0Systematic search for solutions, like solving the\u00a0<strong>N-Queens<\/strong>\u00a0or\u00a0<strong>0\/1 Knapsack<\/strong>\u00a0problem by exploring a state-space tree and pruning futile branches.<\/li>\n<\/ul>\n\n\n\n<p><strong>3. The &#8220;Hard&#8221; Problems: P, NP, and Intractability<\/strong><br>The course often culminates in a philosophical and practical bombshell:&nbsp;<strong>NP-Completeness<\/strong>. You won&#8217;t solve NP-Complete problems (that&#8217;s the million-dollar question), but you must:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Understand the classes\u00a0<strong>P<\/strong>\u00a0(problems solvable in polynomial time) and\u00a0<strong>NP<\/strong>\u00a0(problems whose solutions can be\u00a0<em>verified<\/em>\u00a0in polynomial time).<\/li>\n\n\n\n<li><strong>Prove a problem is NP-Complete<\/strong>\u00a0by performing a\u00a0<strong>polynomial-time reduction<\/strong>\u00a0from a known NP-Complete problem (like\u00a0<strong>3-SAT<\/strong>\u00a0or\u00a0<strong>Vertex Cover<\/strong>) to your new problem.<\/li>\n\n\n\n<li>This section tests your ability to recognize when you&#8217;re facing an intrinsically hard problem, so you can seek approximations or heuristics instead of an exact solution.<\/li>\n<\/ul>\n\n\n\n<p><strong>The Paper&#8217;s Ultimate Challenge: Proof and Justification<\/strong><br>This is not a coding exam. You might write pseudocode, but the&nbsp;<strong>primary currency is your reasoning<\/strong>.<br>You will be asked:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><em>&#8220;Prove the correctness of this greedy algorithm.&#8221;<\/em><\/li>\n\n\n\n<li>*&#8221;Solve this recurrence relation: T(n) = 2T(n\/2) + O(n).&#8221;*<\/li>\n\n\n\n<li><em>&#8220;Show that the Hamiltonian Cycle problem is NP-Complete by reducing from the Traveling Salesman Problem.&#8221;<\/em><\/li>\n<\/ul>\n\n\n\n<p><strong>How to Conquer This Past Paper:<\/strong><\/p>\n\n\n\n<ol start=\"1\" class=\"wp-block-list\">\n<li><strong>Master the &#8220;Three-Step&#8221; Approach for Any Problem:<\/strong>\n<ul class=\"wp-block-list\">\n<li><strong>Step 1 (Understand):<\/strong>\u00a0Restate the problem in your own words. Identify input, output, and constraints.<\/li>\n\n\n\n<li><strong>Step 2 (Design):<\/strong>\u00a0Which paradigm fits? Sketch the high-level strategy.<\/li>\n\n\n\n<li><strong>Step 3 (Analyze):<\/strong>\u00a0Derive the time\/space complexity\u00a0<em>before<\/em>\u00a0you write pseudocode. If it&#8217;s not efficient enough, go back to Step 2.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Practice Deriving Recurrences and Solving Them.<\/strong>\u00a0This is a mathematical muscle you must build. Know the Master Theorem inside out.<\/li>\n\n\n\n<li><strong>Draw, Draw, Draw.<\/strong>\u00a0Draw graphs, draw recursion trees, draw DP tables. Visualizing the data structure or the process is 90% of the solution.<\/li>\n\n\n\n<li><strong>For NP-Completeness, Practice Reductions.<\/strong>\u00a0This is a unique skill. Work through standard reductions until you understand the template: transform an instance of known problem A into an instance of new problem B in polynomial time, preserving the &#8220;yes\/no&#8221; answer.<\/li>\n\n\n\n<li><strong>Write Clean, Commented Pseudocode.<\/strong>\u00a0Use clear variable names. Write one-line comments that state the\u00a0<em>intent<\/em>\u00a0of each block (e.g.,\u00a0<code>\/\/ Relax all edges<\/code>\u00a0in Bellman-Ford).<\/li>\n<\/ol>\n\n\n\n<p>This past paper is your&nbsp;<strong>intellectual forge<\/strong>. It transforms you from someone who can solve problems into someone who can&nbsp;<strong>invent and validate the methods of solution themselves<\/strong>. Passing it with understanding means you hold the master key to computational efficiency\u2014a skill that defines the very best engineers and scientists.<\/p>\n\n\n\n<p><strong>Design and analysis of algorithm Mid Term Examination in 2021<br><\/strong><strong>Q1:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Which parameters are considered essential to analysis a good algorithm?<\/li>\n\n\n\n<li>Explain Flow Chart with the help of diagram and example?<\/li>\n<\/ol>\n\n\n\n<p><strong>Q2:<\/strong><\/p>\n\n\n\n<p>Write down Bubble Sort Algorithm?<\/p>\n\n\n\n<p><strong>Q3:<\/strong><\/p>\n\n\n\n<p>Perform Insertion Sort on following Array will all steps.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><td>6<\/td><td>4<\/td><td>3<\/td><td>8<\/td><td>9<\/td><td>2<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p><strong>Q4:<\/strong><\/p>\n\n\n\n<p>Draw Flow Chart of following code.<\/p>\n\n\n\n<p>int num;<\/p>\n\n\n\n<p>cout&lt;&lt;\u201denter number\u201d;<\/p>\n\n\n\n<p>cin&gt;&gt;num;<\/p>\n\n\n\n<p>if(num%2==0)<\/p>\n\n\n\n<p>cout&lt;&lt;\u201deven number\u201d;<\/p>\n\n\n\n<p>else<\/p>\n\n\n\n<p>cout&lt;&lt;\u201dodd number\u201d;<\/p>\n\n\n\n<p>return 0;<\/p>\n\n\n\n<p>int marks;<\/p>\n\n\n\n<p>cout&lt;&lt;\u201dEnter Marks\u201d;<\/p>\n\n\n\n<p>cin&gt;&gt;marks;<\/p>\n\n\n\n<p>if(marks&lt;50)<\/p>\n\n\n\n<p>cout&lt;&lt;\u201dFail\u201d;<\/p>\n\n\n\n<p>else if(marks&gt;=50 &amp;&amp; marks&lt;60)<\/p>\n\n\n\n<p>cout&lt;&lt;\u201d3<sup>rd<\/sup>\u201d;<\/p>\n\n\n\n<p>else if(marks&gt;=60 &amp;&amp;marks&lt;75)<\/p>\n\n\n\n<p>cout&lt;&lt;\u201d2<sup>nd<\/sup>\u201d;<\/p>\n\n\n\n<p>else if(marks&gt;=75 &amp;&amp;marks&lt;100)<\/p>\n\n\n\n<p>cout&lt;&lt;\u201d1<sup>st<\/sup>\u201d;<\/p>\n\n\n\n<p>return 0;<\/p>\n\n\n\n<p><strong>Q5:<\/strong><\/p>\n\n\n\n<p>Calculate Time Complexity of the following code.<\/p>\n\n\n\n<p>Int n,i;<\/p>\n\n\n\n<p>cin&gt;&gt;n;<\/p>\n\n\n\n<p>int a=0;<\/p>\n\n\n\n<p>i=n;<\/p>\n\n\n\n<p>while(i&gt;=1)<\/p>\n\n\n\n<p>{<\/p>\n\n\n\n<p>a=a+1;<\/p>\n\n\n\n<p>i=i\/2;<\/p>\n\n\n\n<p>}<\/p>\n\n\n\n<p><strong>Design and analysis of algorithm paper II in 2020<br><\/strong><\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"556\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-38-1024x556.png\" alt=\"\" class=\"wp-image-101\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-38-1024x556.png 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-38-300x163.png 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-38-768x417.png 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-38.png 1259w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p><strong>Design and analysis of algorithm Sessional II in 2020<br><\/strong><\/p>\n\n\n\n<p>If total weight he can hold in his knapsack is 13 kg, which fruits and vegetables will be picked by the farmer? Also write down the algorithm for your approach with its analysis.<\/p>\n\n\n\n<p>(Hint: Either he will take, or he will leave any particular item).<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Which parameters are considered essential to analyze a good algorithm? [2]<\/li>\n\n\n\n<li>Does input size matter? Suppose a program has run time O(n!) and the run time for<\/li>\n<\/ol>\n\n\n\n<p>n = 10 is 1 second how much it will take for N=16&nbsp; [3]<\/p>\n\n\n\n<ol start=\"3\" class=\"wp-block-list\">\n<li>Write down Algorithm Development Process steps in diagram format.[5]<\/li>\n\n\n\n<li>Running Time of an Algorithm depends on which parameter?[5]<\/li>\n\n\n\n<li>Find time complexity of the following code. [5]<\/li>\n<\/ol>\n\n\n\n<p>int sum = 0, j;<\/p>\n\n\n\n<p>for (j=0; j &lt; N; j++)<\/p>\n\n\n\n<p>for (j=0; j &lt; 100; j++)<\/p>\n\n\n\n<p>sum = sum +j;<\/p>\n\n\n\n<ol start=\"6\" class=\"wp-block-list\">\n<li>Find time complexity for the following [5]<\/li>\n<\/ol>\n\n\n\n<p>int j,k;<\/p>\n\n\n\n<p>for (j=0; j&lt;N; j++)<\/p>\n\n\n\n<p>for (k=2; k&lt;8; k++)<\/p>\n\n\n\n<p>sum += k+j;<\/p>\n\n\n\n<p><strong>Design and analysis of algorithm Final Paper in 2022<br><\/strong><\/p>\n\n\n\n<p><strong>Q.NO.1<\/strong><\/p>\n\n\n\n<p>In Philippines, coins of 1, 5, 10, 25 centavos (officially called sentimo), IP, SP and 10P (officially called Peso) and currency notes of 20P, 50P, 100P, 500P, 1000P are used. How can we make the following denominations using Coin Change Problem with greedy approach? Also write an algorithm for coin change problem using dynamic programming with its complexity analysis. [10]<\/p>\n\n\n\n<p>7.34 P<\/p>\n\n\n\n<p>2891.45 P<\/p>\n\n\n\n<p>390.21 P<\/p>\n\n\n\n<p>74.58 P<\/p>\n\n\n\n<p>0.99 P<\/p>\n\n\n\n<p>-2: Apply Bellman-Ford Algorithm on the following graph. Show values after each iteration in a tabular form. S is the Starting node.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"912\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.29.28-PM-1-1024x912.jpeg\" alt=\"\" class=\"wp-image-103\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.29.28-PM-1-1024x912.jpeg 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.29.28-PM-1-300x267.jpeg 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.29.28-PM-1-768x684.jpeg 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.29.28-PM-1.jpeg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"502\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.31.27-PM-1024x502.jpeg\" alt=\"\" class=\"wp-image-104\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.31.27-PM-1024x502.jpeg 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.31.27-PM-300x147.jpeg 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.31.27-PM-768x376.jpeg 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.31.27-PM.jpeg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"450\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.33.12-PM-1024x450.jpeg\" alt=\"\" class=\"wp-image-106\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.33.12-PM-1024x450.jpeg 1024w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.33.12-PM-300x132.jpeg 300w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.33.12-PM-768x338.jpeg 768w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/WhatsApp-Image-2022-01-13-at-9.33.12-PM.jpeg 1280w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n<\/div>\n\n\n<p>Q-5\/Write down the algorithm for Huffman Encoding Technique with its complexity analysis. Consider your name and registration number as a string, apply Huffman Encoding Technique on this string (e.g. MUHAMMAD-ALI-MUSA-FA14-BCS-101).<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"634\" height=\"552\" src=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-40.png\" alt=\"\" class=\"wp-image-108\" srcset=\"https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-40.png 634w, https:\/\/staymind.shop\/wp-content\/uploads\/2026\/01\/image-40-300x261.png 300w\" sizes=\"auto, (max-width: 634px) 100vw, 634px\" \/><\/figure>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Let&#8217;s cut to the chase:&nbsp;Design and Analysis of Algorithms (DAA)&nbsp;is not a subject. It&#8217;s a&nbsp;superpower. This past paper is your trial by fire to prove you don&#8217;t just write code\u2014you engineer solutions that are elegant, efficient, and scalable. It&#8217;s the difference between brute-forcing your way through a maze and deriving a theorem for the shortest [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":143,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[28],"tags":[4,29,5,6,7,8,10],"class_list":["post-98","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-design-and-analysis-of-algorithm","tag-comsats","tag-design-and-analysis-of-algorithm","tag-new","tag-paper","tag-past","tag-past_paper","tag-start"],"_links":{"self":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts\/98","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=98"}],"version-history":[{"count":1,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts\/98\/revisions"}],"predecessor-version":[{"id":109,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/posts\/98\/revisions\/109"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=\/wp\/v2\/media\/143"}],"wp:attachment":[{"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=98"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=98"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/staymind.shop\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=98"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}