Important RGPV Question
CS-402 (Analysis And Design Of Algorithms )
IV Sem, CS
UNIT 1- Algorithms, Designing algorithms, analyzing algorithms
Q.1)Â Explain Divide and Conquer techniques
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Q.2)Â Sort the following array using heap-sort techniques. 7 heap-sort
(5, 8, 3, 9, 2, 10, 1, 45, 32)
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Q.3) Define Big “Oh” with example.
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Q.4) What do you mean by performance analysis of an algorithm? Explain.
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Q.5)Write short note on Quick Sort.
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Q.6) Trace the quick sort algorithm to sort the list C, O, L, L, E, G, E in alphabetical order.
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Q.7) Â Discuss Strassen’s matrix multiplication and derive its time complexity.
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Q.8) Design merge sort algorithm and discuss its best-case, average-case and worst-case Efficiency.
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Q.9) Discuss briefly Heap sort.
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Q.10) Give an algorithm for quick sort and analyze the algorithm.
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Q.11) Explain Heap? Sort the following data using heap sort.
81, 39, 10, 36, 45, 15, 55, 23, 91, 88, 12
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Q.12) Solve the following recurrence relations using the substitution method.
RGPV June 2023
Q.13) What do you mean by Asymptotic Notations? Explain different asymptotic notations used in algorithms.
RGPV Dec 2020, June 2020
Q.14) What is the need of obtaining the time and space complexity measures of an algorithm? Justify your answer by some example.
RGPV Dec 2020, June 2020
Q.15) Sort the following array using Heap sort.
66, 33, 40, 20, 50, 88, 60, 11, 77, 30, 45, 65
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Q.16) Write short notes
a) Subset sort problem
b) Big ‘oh’ Notation
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Q.17) Show the various steps involved in the quick sorting of (23, 67, 12, 78, 33, 28, 97, 10, 6, 87, 39).
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Q.18) Explain merge sort algorithm and find the complexity of the algorithm.
RGPV June 2020
UNIT 2- Study of Greedy strategy, examples of greedy method like optimal merge patterns
 Q.1) Explain Prim’s algorithm with example.
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Q.2)Â Solve the following instances of the single source shortest path problem with vertex ‘a’ as the source.
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Q.3) “How to solve the Knapsack problem with greedy method? Explain.
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Q.4) Write an algorithm for single source shortest path and explain with an example.
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Q.5) Discuss briefly about the minimum spanning tree.
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Q.6) Find an optimal solution for following 0/1 Knapsack problem using dynamic programming:
Number of objects n = 4, Knapsack Capacity M = 5, Weights
and Profits
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Q.7) Â Show that if r is a spanning tree for the undirected graph
G, then the addition of an edge q, q∈E(t) and q∈ E(G), to creates a unique cycle.
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Q.8)
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Q.9) Give an example of a set of knapsack instances for which
The set should include one instance for each n.
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Q.10) Tabulate the differences between Kruskal’s and Prim’s algorithm.
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Q.11) What is Knapsack problem? How can we solve using Greedy approach?
RGPV Dec 2020
Q.12) Write algorithm for single source shortest path and find its complexity?
RGPV Dec 2020
Q.13) Â Apply Kruskal’s and Prim’s algorithm for the following graph? Write their time complexities. Find the minimum cost in each case.
RGPV Dec 2020
Q.14) Using Dijkstra’s algorithm find the shortest path from A to D for the following graph.
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Q.15) Write an algorithm to solve Knapsack problem using Greedy technique. Find the optimal solution to the Knapsack instance n = 7, m = 15 (P1, P2, P3… P7) (10, 515, 7, 6, 18, 3) = (W1, W2, W3… W7)= (2, 3, 5, 7, 1, 4, 1)
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UNIT 3- Concept of dynamic programming
Q.1)Â What do you mean by forward and backward approach of problem solving in Dynamic Programming?
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Q.2)Â How the reliability of a system is determined using dynamic programming? Discuss.
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Q.3) How reliability design can be obtained using dynamic programming?
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Q.4) What is multistage graph? Write down its properties?
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Q.5) Use the Floyd-Warshall algorithm and find shortest path between all pairs of vertices for the following graph.
RGPV Dec 2020
Q.6) Explain Floyd-Warshall algorithm with an example of your choice.
RGPV June 2020
UNIT 4- Backtracking concept and its examples like 8 queen’s problem
Q.1)Â Write short notes.
i) Parallel Algorithm
ii) Graph Coloring
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Q.2)Â Explain the 8 queen’s problem and apply the backtracking to solve the 8 queen’s problem.
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Q.3) Write the control abstraction for LC-Search. Explain how Traveling Salesperson problem is solved using LCBB.
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Q.4) Generalize Hamiltonian so that it processes a graph whose edges have costs associated with them and finds a Hamiltonian cycle with minimum cost. Assume that all edge costs are positive.
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Q.5)
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Q.6) What is the meaning of Lower bound theory and how can it be used in solving algebraic problems?
RGPV Dec 2020
Q.7) Â Write short notes.
a) Hamiltonian cycle
b) Â Graph coloring problem
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Q.8) Explain how to solve travelling salesman problem by the method of branch and bound and analyze complexity of the algorithm.
RGPV June 2020
Q.9) Construct state space tree for solving four queen’s problem using backtracking.
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Q.10) What is Backtracking? Discuss any one problem solved by backtracking. Also give its advantages and disadvantages.
RGPV June 2020
UNIT 5- Binary search trees, height balanced trees
  Q.1) Discuss in detail NP complete problems with example.
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Q.2)Â Construct B tree of order 5 for the list of elements.
2, 8, 5, 6, 13, 9, 14, 12, 19, 24, 18, 15, 5, 16, 20, 21
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Q.3) Compare Bfs and Dfs.
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Q.4)Show preorder, inorder and postorder for the following tree.
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Q.5) Discuss the differences between BFS and DFS.
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Q.6) What are 2-3 trees used for? Why are 2-3 trees better than BST trees? Write the limitations of 2-3 tree in CSE.
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Q.7) Â Write a function to construct the binary tree with a given inorder sequence I and given postorder sequence P. What is the complexity of the function?
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Q.8) Give an example of an n-vertex graph for which the depth of recursion of DFS starting from a particular vertex V is n-1 whereas the queue of BFS has at most one vertex at any given time, if BFS is started from the same vertex V.
RGPV Nov 2023
Q.9) In what way is an AVL tree is better than a binary tree insert these keys in to an AVL tree.
RGPV Dec 2020
Q.10) What are B-trees? Write down its properties? What is the need for B tree? What is the height of a B tree of order m?
RGPV Dec 2020
Q.11) Write short notes.
a) NP-Completeness
b) Tree Traversals
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Q.12) Differentiate between DFS and BFS algorithms by an example.
RGPV June 2020
Q.13) Â What are B-trees? How are they created? Give its advantages.
RGPV June 2020
EXTRA QUESTIONS
Q.1)Â How can comparison trees be used for deriving lower bounds on problem of sorting.
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Q.2)Â
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— Best of Luck for Exam —
