VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur

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1 1 VALLIAMMAI ENGINEERING COLLEGE SRM Nagar, Kattankulathur DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING QUESTION BANK I SEMESTER CP102 ADVANCED DATA STRUCTURES AND ALGORITHMS Regulation 2013 Academic Year Prepared by Ms.A.VIDHYA, Assistant Professor

2 2 VALLIAMMAI ENGINEERING COLLEGE (A member of SRM Group of Institutions) SRM Nagar, Kattankulathur DEPARTMENT OF COMPUTER SCIENCE AND ENGINEERING Year and Semester : I / I Section : ME CSE 1 Subject Code : CP102 Subject Name : ADVANCED DATA STRUCTURE AND ALGORITHM Degree and Branch : ME-CSE Staff Incharge : Ms.A.VIDHYA UNIT I ITERATIVE AND RECURSIVE ALGORITHMS Iterative Algorithms: Measures of Progress and Loop Invariants-Paradigm Shift: Sequence of Actions versus Sequence of Assertions- Steps to Develop an Iterative Algorithm-Different Types of Iterative Algorithms--Typical Errors-Recursion-Forward versus Backward- Towers Of Hanoi- Checklist for Recursive Algorithms-The Stack Frame-Proving Correctness with Strong Induction- Examples of Recursive Algorithms-Sorting and Selecting Algorithms Operations on Integers- Ackermann s Function- Recursion on Trees-Tree Traversals- Examples- Generalizing the Problem - Heap Sort and Priority Queues-Representing Expressions. PART - A S. No. 1 Define sequence of action and sequence of assertion. BTL 1 2 Show how to prove the correctness of each step and an algorithm. Apply BTL 3 3 Discover the recurrence relation for Ackermann s function. Apply BTL 3 4 What do you mean by Loop Invariant? BTL 1 5 Give the proof of correction with Strong induction. BTL 2 Define recursion and Iteration with an example. BTL 1 Explain Recursive algorithm to count the number of nodes in a Binary Tree. BTL 4 8 Define precondition and Postcondition. BTL 1 9 Classify the main requirements of an iterative algorithm. BTL 4 10 Summarize the technical error in iterative algorithm. Evaluate BTL 5 11 Develop an example with more of input and more of output. BTL

3 12 Describe exit condition. BTL Assess on recursive programme to find GCD of two numbers. Evaluate BTL5 14 Discuss stack frame. BTL 2 Examine tree of stack frame. Apply BTL 3 1 Define the algorithm for Tower of Hanoi problem and give its running time. BTL 1 1 Pointout algorithm for power of integer. BTL 4 18 Define forward and backward recursive. BTL 1 19 Generalize sub instance and sub solution. BTL 20 Summarize algorithm for three tree traversal method. BTL 2 PART-B 1 i) Describe briefly about steps to develop iterative algorithm. ii) Differentiate sequence of actions Vs. sequence of assertions. 2 i) Apply the Towers of Honai problem with three disk. State the time complexity of the algorithm. Apply BTL3 ii) Illustrate about the checklist of recursive algorithms. 3 i) Write down the recursive algorithm for heap sort problem. ii) Write and describe an algorithm to search a key k in a N * N matrixin which each row is sorted in ascending order. What is the time complexity of your algorithm. 4 i) Give a recursive algorithm to find the k th smallest element of a set S. Write the recurrence equation and perform asymptotic analysis for worst case. ii) Write an algorithm and examine how to find the next least node in a binary search tree given a node and assess the time complexity of the algorithm. 5 i) Given a set of integers with repeated occurrences of elements. Write an algorithm and identify how to print the power set of S ensuring that the repeated elements are printed only once.for example S= {1,2,2}. For the above set S the power set will be {NULL,{1},{2},{2},{1,2},{1,2},{2,2},{1,2,2}}. The final output should print {NULL, {1},{2},{1,2},{2,2},{1,2,2}}. ii) Write a recursive algorithm to find the K th smallest one from a set of elements. Also illustrate the above algorithm with suitable examples. i)explain Ackermann's function using suitable algorithm.how is it used in algorithm analysis? ii) Explain in detail about strassen's matrix multiplication algorithm.

4 i) Write and An al y ze recurrence routines to : a. Return the maximum of data fields of nodes in a binary tree. 13 b. Return the height of the binary tree. c. Return the number of leaves in binary tree. 8 i) Develop a Pre and Post conditions, checklist and 13 recursive algorithm for Towers of Hanoi problem. 9 i)examine the different types of iterative algorithm.explain each types with suitable examples.analyse the running time complexities of the chosen examples ii)identify and quote the contrast between backward working algorithms with forward working algorithm. i) Justify the Towers of Hanoi is recursive algorithm and explain the steps. Evaluate BTL5 ii)what is priority Queue? Write its advantages. Assess it with an example. 11 i) Classify the different types of iterative algorithms.expalin Apply BTL3 each types with suitable examples. the running time complexities of the chosen examples i) Describe any searching algorithm in recursive algorithm with basic steps. ii) Describe any sorting algorithm in recursive algorithm with basic steps. 13 (i)what are types of heap sort strategy? Show that the heap sort requires o(n log n) number of operations regardless of the order of input. (ii)explain how recursion can be implemented on trees with suitable example 14 i) How can you represent multivariate expressions with binary trees?discuss with examples. 13 PART-C Q.NO 1 Analyse the running time of quick sort for best, worst, average case Convert the given expression into expression tree. 2 Evaluate the expression tree using recursive algorithm. Take your own values of the operands in the expression. i. ((a+b)*(c/d)/e) Evaluate BTL 5 3 Develop an algorithm to search a key K in N*N matrix in which each row is stored in ascending order. Examine the time BTL complexity of your algorithm. 4 Specify and formulate some recursive algorithms which matches for some problems. BTL

5 5 UNIT II OPTIMISATION ALGORITHMS S. Optimization Problems-Graph Search Algorithms-Generic Search-Breadth-First Search Dijkstra s Shortest-Weighted-Path -Depth-First Search-Recursive Depth-First Search-Linear Ordering of a Partial Order- Network Flows and Linear Programming-Hill Climbing-Primal Dual Hill Climbing- Steepest Ascent Hill Climbing-Linear Programming-Recursive Backtracking-Developing Recursive Backtracking Algorithm- Pruning Branches-Satisfiability Question par PART - A PART Q.NO 1 List the ingredients and specification of optimization problem. BTL 1 2 Show the difference between Breadth-First search and Depth- First search. Apply BTL 3 3 Solve optimization specification for longest common subsequence problem. Apply BTL 3 4 write an algorithm to find strongly connected components of a graph. BTL 1 5 Give flow problems. BTL What is exit condition for dijkstras's algorithm? BTL 1 the ingredients of Optimization problem. BTL 4 Define local and global maximum. BTL 1 Explain optimization algorithm. BTL 4 Evaluate on How to prove path is shortest. Evaluate BTL 5 What is network flow problem? Generalize its specification. BTL Summarize pruning path and bipartite. BTL 2 Compare forward edges and cross edges. Evaluate BTL5 Distinguish primal dual hill climbing and steepest ascent hill climbing. BTL 2 Illustrate min cut specification. Apply BTL 3 Define map coloring problem is solved using Recursive Backtracking algorithm. BTL 1 on satisfiability. BTL 4 What is the running time complexity of 8 Queen s problem? BTL Compose pruning branch. BTL Give the steps to fixing the algorithm. BTL 2

6 1 i) Using Breadth First Search and optimization techniques describe and solve the shortest path problem. ii)discuss and write the depth first search iterative algorithm to traverse graph and optimize the same in terms of space and time. 2 i) Explain the reachability problem of Graphs with appropriate algorithm and running time analysis. ii) which graph search algorithm is more appropriate to test if a graph is bipartite? explain. 3 Tell the computational complexity of single source shortest path algorithm for the following graph representations. a. Adjacency matrix representation. b. Adjacency list representation. i)write an algorithm and explain the sum of any path from 4 root to leaf such that the sum of all nodes along the path is maximum compared to all other path. the algorithm. ii)explain briefly about network flows with an example. What is acyclic path? Write an algorithm to print all acyclic paths in a given graph from a node a. 5 i) Illustrate DFS with the help of a graph with seven nodes. ii) Demonstrate the iterative andrecursive algorithm for DFS on the same graph,and compare theirrunning time. i) Judge wh ether the problem BFS is belong to graph search algorithm. ii) Linear order consistent can be foundwith given partial order using problem DFS.Justify with example. 8 i) Demonstrate the concept of Dijkstras shortest weighted path. ii) Examine briefly about generic search algorithm. 9 i)describe Travelling Salesman Problem with Hill Climbing Algorithm. Discuss the solution. ii) Write notes on linear programming. 10 i) How the primal dual hill climbing achieving global maximum and explain it. ii)write and Explain down the steps involved in developing a recursive backtracking algorithm for queens problem. 11 Describe the Steepest hill climbing achieving global maximum and explain it Solve and discuss the shortest path problem using Optimization techniques & Dijkstra s shortest weighted 13 path algorithm? Apply Evaluate BTL3 BTL5 BTL3

7 13 Develop the Dijkstra s shortest weighted path algorithm with suitable code, example and l oop invariants Explain the concept of pruning branches and satisfiability problem 13 S. No. PART C Consider a computation of Dijkstra s algorithm on the following graph. The algorithm should use Graph search algorithm. 1 path weight Trace BFS and DFS on the following two graphs. For each do the following: Evaluate BTL 5 2 BTL 3 i. Start at the node s, and when there is a choice, follow edges from left to right. Number the node 1, 2, 3 in the order that they are found, starting with node s=1. ii. What is the data structure used by each search to store nodes that are found but not yet handled? iii. Circle the nodes that are in this data structure when node 8 is first found Source node Starting with the flow given below; complete the network flow algorithm.(for any graph) Apply BTL 3

8 8 4 How using Optimization techniques & Dijkstra s shortest weighted path algorithm are supported for solving the shortest path problem? UNIT-3 DYNAMIC PROGRAMMING ALGORITHMS Developing a Dynamic Programming Algorithm-Subtle Points - Question for the Little Bird Sub-instances and Sub-solutions - Set of Substances-Decreasing Time and Space-Number of Solutions-Code. Reductions and NP-Completeness Satisfiability - Proving NP Completeness - 3-Coloring - Bipartite Matching. Randomized Algorithms - Randomness to Hide Worst Cases Optimization Problems with a Random Structure. Q.NO 1 Pointout the purpose of two nested loops in dynamic BTL 4 2 programming. Explain about little bird. Evaluate BTL 5 3 the chromatic number of a graph.give example. BTL 4 Differentiate Monte Carlo and Las Vegas algorithms. BTL 2 5 Summarize the classifications made based on reductions. Evaluate BTL5 Describe the format definition of three models of randomized algorithms. BTL 2 Illustrate on how can you write a faster dynamic programming Apply BTL 3 algorithm. 8 Tell how sub instances are created in dynamic programming. BTL 1 9 Halting problem. BTL 4 10 Give an example of print neatly problem. BTL 1 11 Compose reduction problem? List the classification made based on reductions? BTL 12 Discuss circuit satisfiability problem. BTL 2 13 What is memorization? BTL 1 14 Solve NP complete problem. List the three example for NP Complete problem. Apply BTL 3

9 Demonstrate randomized algorithm. Apply BTL 3 What is expander graph? BTL 1 Express graph colouring. BTL 2 How to prove the solution is optimization? BTL 1 Compare and contrast cook vs Karp defined reductions. BTL 4 Describe instance map and solution map. BTL 1 9 PART-B Q.N O Question 1 i) Discuss the steps involved in developing dynamic programming algorithm with an example. ii) Write an algorithm for solving 3 and reduce time and space complexity of the coloring problem algorithm. 2 i) Develop an efficient algorithm to calculate the length of the longest common substring in the given two strings. ii) Consider a bipartite graph G = (V,E) with bipartition (A,B) : V = A U B. Assume that, for some vertex sets A1 A and B1 B, there exists a matching MA covering all vertices in A1 and a matching MB covering all vertices in B1. Prove that there always exists a matching covering all vertices in A1 U B1. 3 What is the three-color problem? Check whether the given graph is 3-colorable. Competen ce BTL

10 4 What is the smallest cut in the graph? Write an algorithm to compute the minimal cut in the graph shown below and show the output i) Explain on how to decrease time and space in dynamic programming problems. ii) Pointout the steps needed to prove NP completeness and apply it to the 3 Coloring problems. i) What do you mean by Question of the Little Bird? What are the local and global considerations in it? Also assess about repeated Questions and reversing the order. Evaluate BTL5 ii) A dynamic programming algorithm is fast only if the given instance does not have many sub instances. Justify and prove this statement. i) Demonatrate NP complete problem.explain the steps for proving that a computational problem is NP complete with an Apply BTL3 example. ii) Justify the problem network flows can use in linear programming and explain it. 8 Demonstrate Randomized Algorithms? Examine Randomness to Hide Worst Cases. how 13 Apply BTL3 9 Discuss in details about the models for randomness to hide worst cases in an optimization problem. Highlight 13 any of the models using quick sort and randomized counting problem. 10 i) Describe and Reduce the NP Completeness problem and prove it 3-Col < = Poly Course Scheduling ii) Examine and Reduce the NP Completeness problem and prove it Bipartite < = Poly Network flow. 11 i) Define NP Completeness problem and prove it CIR-SAT < = Poly 3-COL. ii) Examine how to decrease time and space in dynamic programming problems. 12 How randomized primality testing could be performed? 13 Explain with example. 13 Discuss how Bipartie matching could be performed? 13 Explain with an example. 14 (i)explain the concept of about little bird, sub instances and sub-solution. (ii) write and analyze an algorithm to shuffle an array of length N using randomized approach.

11 Q.NO 1 Question Part C Consider printing neatly the text this week has seven dates in it ok in a column with width M=11 and analyse. This is represented as the printing neatly instance {M; l1,.,ln} = {11;4,4,3,5,5,2,2,2}. a. Fill in the birdadvice[0.. n] and cost[0..n] tables for this example the origina l instance, its solution, and its cost are in the bottom row. b. When filling in this last row, give solutions and costs associated with each of the possible bird answers. 11 Competence B BTL T ANALYSIS BTL 4 For each of the following problems, Evaluate I, S, Valid(I,S), and Cost(S). i. Graph coloring: given a graph, color its nodes so that two nodes do not have the same color if they have an edge between them. Use as few colors as possible. 2 ii. iii. Independent set: given a graph, find a largest subset of the nodes for which there are no edges between any pair in the set. Airplane: given the requirements of an airplane, design it, optimizing its performance. Apply BTL 5 iv. Business: given a description of a business, make a business plan to maximize its profits. v. Factoring: given an integer, factor it, e.g., =2x3. vi. Cryptography: given an encrypted message3, decode it. 3 Develop Optimization Problems with a Random Structure. 4 Design network flows and give the use in linear programming and explain it. UNIT-IV SHARED OBJECTS AND CONCURRENT OBJECTS Shared Objects and Synchronization -Properties of Mutual Exclusion-The Mora l- The Producer Consumer Problem -The Readers Writers Problem-Realities of Parallelization Parallel Programming- Principles- Mutual Exclusion-Time- Critical Sections Thread Solutions-The Filter Lock-Fairness-Lamport s Bakery Algorithm-Bounded Timestamps-Lower Bounds on the Number of Locations-Concurrent Objects- Concurrency and Correctness Sequential Objects- Quiescent Consistency- Sequential Consistency-Linearizability- Formal Definitions- Progress Conditions- The Java Memory Model PART -A Q.NO

12 1 What is mutual exclusion? Show the properties of mutual Apply BTL 3 2 exclusion. List the drawbacks in Bakery lock algorithm. BTL 1 3 Differentiate Transient and Persistent Communication. BTL 2 4. Tell the principal drawbacks of Sequential Consistency. BTL 1 5. the need to synchronize producer and consumer in the shared object concepts. BTL 4. Examine the use of quiescent consistency. BTL 1. Describe Lamport's Bakery algorithm. BTL 2 8. Show the structure of petri net. Apply BTL 3 9. Define shared object and linearizability. BTL Explain starvation freedom. BTL List the communication occur in concurrent system. BTL Develop reader and writer problem. BTL 13. Express Amdal law. BTL 2 14 What is monitors and semaphores? BTL 1 Classify danger zone and end of danger zone. Apply BTL 3 1 Classify the requirements of solution to critical section problem. BTL 4 1 Compare filter lock with Peterson lock. Evaluate BTL 5 18 Compose fairness. BTL 19. Distinguish Lock object state and covering state. BTL Summarize bounded timestamps. Evaluate BTL5 12 Part B Q.N O 1 2 i) Write an algorithm for Filter Lock mutual exclusion protocol and show how it achieves mutual exclusion property. ii) What is Linearizablity? Explain with example. i) Write short notes on Parallel Programming. ii) Explain in detail about the java memory model.how concurrency is handled is handled in this model? 3 Analyse 2-Thread solutions with respect to LockOne, 13 LockTwo i) Evaluate and the Peterson Java Memory Lock algorithm. model with Locks, 4 Volatile and Final fields. Evaluate BTL5 ii) Explain Lamport s bakery algorithm in detail with respect to deadlocks. i) Prove and describe upper bound on the time required for a 5. particular process to reach its critical region from the time when it enters in the Lamport s bakery algorithm.

13 ii) What is the role of semaphores in solving producer consumer problem? Explain. Classify the steps in solving mutual exclusion problem. among n processes namely p1,p2, pn. Write an algorithm Apply BTL3 for process pi. 13. Explain the strategies for developing Parallel Applications P A R T - C 8. i)explain lamport s Bakery algorithm for synchronization problem and compare it with bounded timestamp algorithm. ii) How to correct concurrent FIFO queue, Analyse with the help of algorithm? 9. (i)illustrate why quiescent consistent is compositional with an example. (ii)showthe contrast between quiescent consistent and sequential consistent. Highlight with an example the execution that is quiescent consistent but not sequential consistent and another that is sequential consistent but not quiescent consistent. Apply BTL3 10. i) Define and Explain the concept of mutual exclusion with example. ii) Narrate briefly about critical section problem in parallel programming. Quote your solution with lock algorithm. 11 i) Describe concurrent objects. ii) Discuss about on concurrency and correctness. 12. Express an algorithm for filter lock mutual exclusion protocol. and show how it achieves mutual exclusion property Describe the use of semapores in solving readers-writers problem by tracing the reader-writer solution Develop an algorithm to solve two thread problem. 13

14 Part -C 1 r-bounded waiting for a given mutual exclusion algorithm to mean that if D J a->d K B then then CS J A->CS K+r B there a way to define a doorway for the Peterson algorithm such that it provides r-bounded waiting for some value of r? 14 2 Programmers at the Flaky Computer Corporation designed the protocol shown below to achieve n-thread mutual exclusion, for each question, either sketch a proof, or display and explain an execution where it fails. i. Does this protocol satisfy mutual exclusion? ii. Is this protocol starvation-free? iii. Is this protocol deadlock-free? Class Flaky implements Lock{ Private int turn; Private Boolean busy=false; Public void lock(){ Int me=threadid.get(); Do{ Do{3 Public void unlock(){ Busy=false; } } Evaluate BTL5 3 Design and discuss about Thread with respect tothe Filter Lock. 4 Develop Lamport s Bakery Algorithm for mutual exclusion. Unit 5 CONCURRENT DATA STRUCTURES Practice-Linked Lists-The Role of Locking-List-Based Sets-Concurrent Reasoning- Coarse Grained Synchronization-Fine-Grained Synchronization-Optimistic Synchronization- Lazy Synchronization-Non-Blocking Synchronization-Concurrent Queues and the ABA Problem - Queues A Bounded Partial Queue-An Unbounded Total Queue-An Unbounded Lock-Free Queue-Memory Reclamation and the ABA Problem- Dual Data Structures- Concurrent Stacks and Elimination- An Unbounded Lock-Free Stack- Elimination-The Elimination Backoff Stack Q.NO Part A Generalize the concurrent data structures available. BTL Give the role of locking in sychronization. BTL 2 What is lazy synchronization?list its drawback. BTL 1 Show the role of locking in synchronization. Apply BTL 3

15 5 Explain how do you implement a List based Set? Give examples. BTL 4 Summarize the three different pool methods. Evaluate BTL 5 Compose Synchronization. BTL 8 Give the different varieties of pool? BTL 2 9 Compare coarse-gained synchronization with fine-grained. Evaluate BTL5 10 Show the fine grained synchronization. Apply BTL 3 11 How optimization synchronization is works? BTL 1 12 Describe about ABA problem. BTL 2 13 Tell about the role of locking in concurrent data BTL 1 14 structure.unlocking. Explain bounded partial queue. BTL 4 What is unbounded total queue? BTL 1 1 Discuss unbounded lock free queue. BTL 2 1 Examine naive synchronization queue. Apply BTL 3 18 What is elimination back of stack? BTL 1 19 Illustrate elimination array. BTL 4 20 Tell how dual data structures reduce the synchronization overhead. BTL 1 Part B Q.N O 1 i) Would the lazy algorithm still work if we marked a node as removed simply by setting its next field to null? Why or Why not? What about the lock-free algorithm? ii) The add() method of the lock-free algorithm never finds a marked node with the same key. Tell how the algorithm be modified so that it will simply insert its new added object into the existing marked node with same key if such a node exists in the list, thus saving the need to insert a new node? 2 3 What is ABA problem? How it related with memory reclamation Show the steps in the process of memory 13 reclamation using diagram and algorithm? i) Discuss and explain the illustration of an Unbounded Lock Free Queue with an example. ii) Compare Coarse grained synchronization with fine grained synchronization with appropriate routines and examples.

16 4 5 i) Construct elimination back off stack using a lockfree linearizable stack implementation. ii) How a bounded partial queue, differs from an unbounded one? Explain. Describe and discuss the data structures and code used for concurrent queues. 13 State ABA problem. Explain and apply the solution with an example i) Explain why the fine-grained locking algorithm is not subject to deadlock. ii) Explain why the optimistic and lazy locking algorithms are not subject to deadlock. Apply Apply BTL3 BTL3 1 8 Summarize and discuss about unbounded lock free stack Evaluate BTL5 and queue with an example State the synchronization and List its types i)describe about Concurrent stack with an example. Write in brief about the dual data structures. Mention ii) example. Describe about Concurrent queue. With an some of the examples for each of such data structures 13 and Describe their applications. 12 Perform push and pop operation in an unbounded lock free stack with the help of code and describe Design an bounded lock free stack and specify how elimination problem is implemented with an example.also comment on elimination back off stack Analyse in detail about memory Reclamation and the ABA problem 13 Part C 1 Analyse how to modify each of the linked list algorithms if object hash codes are not guaranteed to be 2 unique. Design an algorithm for concurrent linked list with suitable example. 3 Discriminate about concurrent stack and evaluate how to eliminate it. 4 Give a Generalize note about the lazy synchronization, Optimistic synchronization. Evaluate BTL5