COMP171 Data Structures and Algorithms Fall 2006 Midterm Examination
|
|
- Gervais Dennis
- 5 years ago
- Views:
Transcription
1 COMP171 Data Structures and Algorithms Fall 2006 Midterm Examination L1: Dr Qiang Yang L2: Dr Lei Chen Date: 6 Nov 2006 Time: 6-8p.m. Venue: LTA November 7, 2006 Question Marks 1 /12 2 /8 3 /25 4 /7 5 /15 6 /15 7 /18 Total /100 1
2 1. (12 marks) Recursion Consider the following recursive program. //n is any positive integer //m is a positive integer between 2 and 9 void fun(int n, int m) { if (n<m) cout << n; else { fun(n/m, m); cout << n%m; (a) (3 marks) What is the output for fun(15, 2)? Answer: 1111 (b) (3 marks) Given the following recursive code. Point out the possible errors in the code. //num is a positive integer int fac(int num) { if (num 1) return 1; else { return num*fac(num+1); Answer: The recursive function will never converge to the base case (ie. num 1) as the value passed to the function is always increasing (ie. fac(num+1)). 2
3 (c) (6 marks) Given the following function which computes fibonacci numbers using recursive function, write a non-recursive version of function f ib. //num is a positive integer int fib(int num) { if (num==0) return 0; if (num==1) return 1; return (fib(num 1)+fib(num 2)); Answer: int fib(int n) { int f[n+1]; f[0] = 0; f[1] = 1; for (int i=2; i<= n; i++) f[i] = f[i-1] + f[i-2]; return f[n]; 3
4 2. (8 marks) Merge Sort and Insertion Sort (a) (4 marks) Draw a binary tree to show step by step how Merge Sort sorts {142, 543, 123, 65, 453, 879, 572, 434. {142, 543, 123, 65, 453, 879, 572, 434 {142, 543, 123, 65 {453,879, 572, 434 {142, 543 {123, 65 {453, 879 {572, 434 {142 {543 {123 {65 {453 {879 {572 {434 {142, 543 {65, 123 {453, 879 {434,572 {65, 123, 142, 543 {434, 453, 572, 879 {65, 123, 142, 434, 453, 543, 572, 879 (b) (4 marks) Show under what order of input, the insertion sort will have worst-case and best-case situations for sorting the set {142, 543, 123, 65, 453, 879, 572, 434. Worst Case:the element always gets inserted at the front, so all the sorted elements must be moved at each insertion. The ith insertion requires (i-1) comparisons and moves. sorting in ascending order: {879, 572, 543, 453, 434, 142, 123, 65 sorting in descending order: {65, 123, 142, 434, 453, 543, 572, 879 Best Case: the element always gets inserted at the end, so we don t have to move anything, and only compare against the last sorted element. We have (n-1) insertions, each with exactly one comparison and no data moves per insertion. sorting in ascending order: {65, 123, 142, 434, 453, 543, 572, 879 sorting in descending order: {879, 572, 543, 453, 434, 142, 123, 65 4
5 3. Big-Oh (a) What is the time complexity of the equation T(n) given below?please give the tightest possible bound in big-oh notation. Assume n is a power of 2 (that is n = 2 k for some k). { T (n) = 2T (n/2) + n log n T (1) = 1 Results without derivations do not receive any points. Anawer: T (n = 2 k ) = 2T (n/2) + 2 k k = 2(2T (n/4) + 2 k 1 (k 1)) + 2 k k = 2 2 T (n/4) + 2 k (k 1) + 2 k k = 2 3 T (n/8) + 2 k (k 2) + 2 k (k 1) + 2 k k =... = 2 k T (1) + 2 k ( k) = 2 k ((k + 1) k/2 + 1) = n(((log n + 1) log n)/2 + 1) = O(n log n log n) 5
6 (b) Give a tightest possible bound for the Big-Oh runtime complexity of the following function in terms of the value of the input parameter n. Results without derivations do not receive any points. (Hint: The complexity of easy(n) is T (n).) 1 int easy(int n){ 2 int a, b, c; 3 if (n <= 1) 4 return 0; 5 else { 6 a = easy(n-1); 7 b = easy(n % 2); 8 c = easy(n-2)/2; 9 return a + b + c; Answer: T(N)=T(N-1)+ T(N-2)+ T(1) T(N-1)=T(N-2)+ T(N-3)+ T(1) T(2)=T(1)+T(0)+T(1) F(0)*T(N)=F(0)*T(N-1)+ F(0)*T(N-2)+ F(0)*T(1) F(1)*T(N-1)=F(1)*T(N-2)+ F(1)*T(N-3)+ F(1)*T(1) F(2)*T(N-2)=F(2)*T(N-3)+ F(2)*T(N-4)+ F(2)*T(1) F(N-2)*T(2)=F(N-2)*T(1)+F(N-2)*T(0)+ F(N-2)*T(1) Sum up T(N)=F(N-3)*T(1)+ F(N-2)*T(1)+F(N-2)*T(0)+ N 2 i=0 F(i)*T(1) =F(N)*T(1)+(F(N)-F(1))*T(1) =2F(N)*T(1)-T(1) (5/3) N 1 = O(2 N ) 6
7 (c) Multiple Choice: Circle the best answer for each question. If you circle two answers, you will receive zero for that question. i. The recurrence solves to: A. O(n) B. O( n) C. O(log n) D. O(log log n) E. O(log log log n) F. O(1) { T (n) = T ( 3 n) + 1 n > 2 T (n) = 1 n 2 Answer: D.Suppose the recurrence for T(n) stops at some n = a < 2, and takes k steps, then a 3k = n,then k = log 3 (log a n),so the answer is D,O(log log n). ii. If f(n) = n+n log n,which of the following is/are true? 1) O(n) 2) O(n 2 ) 3) Ω(n 2 ) 4) Ω(n log n) 5) Θ(n log n) 6) Θ(n) A. 1) only. B. 1) & 6). C. 2) only. D. 2) & 3). E. 2) & 4) & 5). F. 4) & 5). G. 2) & 3) & 4) & 5). Answer: E. n log n < f(n) < 2n log n,so 5) is correct.then 4 must be correct. Also notice that, 2) is correct,because n log n < n 2. 7
8 4. In the following code for a stack machine, PUSH X means push X onto the stack, POP X means pop the top of the stack into X, and an operator without an operand (ADD, MULT) means pop the top two items off the stack, perform the indicated operation on them, and push the result back onto the stack.(note: ADD=Addition, MULT=Mulitplication.) 1) PUSH A 2) PUSH B 3) ADD 4) POP T 1 5) PUSH B 6) PUSH C 7) PUSH T 1 8) PUSH T 1 9) MULT 10) MULT 11) ADD 12) POP Z Please write down in the table below the content of the stack after each stack operation (the first two operations have already been given). In addition, please specify values of T 1 and Z using symbols A, B and C. No. The Content of the Stack 0) empty 1) A 2) A, B 3) A + B 4) empty 5) B 6) B, C 7) B, C, T 1 (or A + B) 8) B, C, T 1, T 1 (or B, C, A + B, A + B) (or B, C, T 1, A + B) (or B, C, A + B, T 1 ) 9) B, C, T1 2 (or B, C, (A + B) 2 ) 10) B, C T1 2 (or B, C (A + B) 2 ) 11) B + C T1 2 (or B + C (A + B) 2 ) 12) empty T 1 = A + B, Z = B + C (A + B) 2. 8
9 5. Heap (a) (10 marks) Table 1 shows an array of numbers. In Table 2, build a min-heap by inserting these numbers one by one from left to right, where you can use X to mean unoccupied. Fill in the results after each of the remaining insertions and heap-restoring operations. Note that the heap is stored in the array starting from array index 1 (so that the index 0 of the array is left empty). Index Input array Table 1: Input Table 2: Fill in the slots Index Input array Insert X X X X X Insert X X X X Insert X X X Insert X X Insert X Insert
10 (b) (5 marks) Heap Sort: For the array in Table 3, perform a heap sort using the same array and no additional array. Fill in the result after each of the deletion and heap-restoration operations. Also show the array after the deleted element is inserted back in order to produce a sorted array in the end. Table 3: Fill in the slots for sorting in increasing order Index Max Heap Deletion number first second third fourth fifth sixth
11 6. Multiple Choice Questions (Stack and Linked List) (a) What is the minimum height of the decision trees whose nodes are the comparison operations and whose leave nodes are the linear ordering of N numbers? (A) O(N^2) (B) O(N) (C) O(2^N) (D) Omega(Nlog(log(N))) (E) Omega(log(N!)) (F) Omega(N^2) (G) none of the above. Answer: (G). It should be order log(n). (b) If the variables are suitably initialized and if i remains within appropriated bounds, then the following code implements stack operations Push and Pop when the stack is represented as a vector V [1,..N] and a pointer i. Push: begin V[i] = x ; i := i + 1 ; end Pop: begin i := i - 1; x := V[i] ; end (i) Which of the following gives the correct initialization for this stack implementation? (A) i := 0 (B) i := 1 (C) i := N - 1 (D) i := N (E) None of the above Answer: (B) (ii) If it is assumed that suitable changes in the initialization code were also made, which of the following changes to Push and Pop would yield a correct implementation of stacks? I. Replace the code for Push with that for Pop and vice versa. II. Make Push decrement i and Pop increment i. III. Reverse the order of the statements in both Push and Pop. 11
12 (A) I only (B) II only (C) III only (D) I and II (E) II and III Answer: (E) 7. Quick Sort Applying the Quick Sort with the median of three methods that you have learnt from the lecture to the given array A[]. Please complete the full sorting process with the help of the following table. You must fill in the table with the contents of A[] and the final positions of the pivot(s) by marking it with p in the space provided. Note: The content of A[] must be in ascending order. Below is the pseudocode of quicksort: (swapping is indicated in line 14) void quicksort(a[], p, r){ int pivot = median_of_three(a[],p,r); // begin partitioning int i = p; int j = r-2; for(;;){ while(a[i] < pivot){ i++; while(a[j] > pivot){ j--; if(i < j) swap(a[i], A[j]); else break; swap(a[i], A[r-1]); <------***** swapping **** // recursive sort each partition quicksort(a, p, i-1); // Sort left partition quicksort(a, i+1, r); // Sort right partition Answer: 12
13 Note: If the student finishes the trace using either the routine in given above, or the lecture notes, then the student is considered right. Solution 1 - median of three Index A[] A[] after 1st swap of pivot P A[] after 2nd swap of pivot P P A[] after 3rd swap of pivot P P A[] after 4th swap of pivot A[] after 5th swap of pivot A[] after 6th swap of pivot A[] after 7th swap of pivot 13
14 Solution 2 - original Index A[] A[] after 1st swap of pivot P A[] after 2nd swap of pivot P P A[] after 3rd swap of pivot P A[] after 4th swap of pivot A[] after 5th swap of pivot A[] after 6th swap of pivot A[] after 7th swap of pivot 14
CSE 373 Spring 2010: Midterm #1 (closed book, closed notes, NO calculators allowed)
Name: Email address: CSE 373 Spring 2010: Midterm #1 (closed book, closed notes, NO calculators allowed) Instructions: Read the directions for each question carefully before answering. We may give partial
More informationCSE 373 Winter 2009: Midterm #1 (closed book, closed notes, NO calculators allowed)
Name: Email address: CSE 373 Winter 2009: Midterm #1 (closed book, closed notes, NO calculators allowed) Instructions: Read the directions for each question carefully before answering. We may give partial
More informationCSE 373 Autumn 2010: Midterm #1 (closed book, closed notes, NO calculators allowed)
Name: Email address: CSE 373 Autumn 2010: Midterm #1 (closed book, closed notes, NO calculators allowed) Instructions: Read the directions for each question carefully before answering. We may give partial
More informationCSE 332 Spring 2013: Midterm Exam (closed book, closed notes, no calculators)
Name: Email address: Quiz Section: CSE 332 Spring 2013: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will
More informationCSE 332 Autumn 2013: Midterm Exam (closed book, closed notes, no calculators)
Name: Email address: Quiz Section: CSE 332 Autumn 2013: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will
More information4. Sorting and Order-Statistics
4. Sorting and Order-Statistics 4. Sorting and Order-Statistics The sorting problem consists in the following : Input : a sequence of n elements (a 1, a 2,..., a n ). Output : a permutation (a 1, a 2,...,
More informationCSE 332 Spring 2014: Midterm Exam (closed book, closed notes, no calculators)
Name: Email address: Quiz Section: CSE 332 Spring 2014: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will
More informationCSE 332 Winter 2015: Midterm Exam (closed book, closed notes, no calculators)
_ UWNetID: Lecture Section: A CSE 332 Winter 2015: Midterm Exam (closed book, closed notes, no calculators) Instructions: Read the directions for each question carefully before answering. We will give
More informationBin Sort. Sorting integers in Range [1,...,n] Add all elements to table and then
Sorting1 Bin Sort Sorting integers in Range [1,...,n] Add all elements to table and then Retrieve in order 1, 2, 3,...,n Stable Sorting Method (repeated elements will end up in their original order) Numbers
More informationCOMP Data Structures
COMP 2140 - Data Structures Shahin Kamali Topic 5 - Sorting University of Manitoba Based on notes by S. Durocher. COMP 2140 - Data Structures 1 / 55 Overview Review: Insertion Sort Merge Sort Quicksort
More informationSorting. Bubble Sort. Pseudo Code for Bubble Sorting: Sorting is ordering a list of elements.
Sorting Sorting is ordering a list of elements. Types of sorting: There are many types of algorithms exist based on the following criteria: Based on Complexity Based on Memory usage (Internal & External
More informationO(n): printing a list of n items to the screen, looking at each item once.
UNIT IV Sorting: O notation efficiency of sorting bubble sort quick sort selection sort heap sort insertion sort shell sort merge sort radix sort. O NOTATION BIG OH (O) NOTATION Big oh : the function f(n)=o(g(n))
More informationHow much space does this routine use in the worst case for a given n? public static void use_space(int n) { int b; int [] A;
How much space does this routine use in the worst case for a given n? public static void use_space(int n) { int b; int [] A; } if (n
More informationCS 61B Summer 2005 (Porter) Midterm 2 July 21, SOLUTIONS. Do not open until told to begin
CS 61B Summer 2005 (Porter) Midterm 2 July 21, 2005 - SOLUTIONS Do not open until told to begin This exam is CLOSED BOOK, but you may use 1 letter-sized page of notes that you have created. Problem 0:
More informationQuicksort. Repeat the process recursively for the left- and rightsub-blocks.
Quicksort As the name implies, this is the fastest known sorting algorithm in practice. It is excellent for average input but bad for the worst-case input. (you will see later). Basic idea: (another divide-and-conquer
More informationComputer Science 302 Spring 2007 Practice Final Examination: Part I
Computer Science 302 Spring 2007 Practice Final Examination: Part I Name: This practice examination is much longer than the real final examination will be. If you can work all the problems here, you will
More informationCS2223: Algorithms Sorting Algorithms, Heap Sort, Linear-time sort, Median and Order Statistics
CS2223: Algorithms Sorting Algorithms, Heap Sort, Linear-time sort, Median and Order Statistics 1 Sorting 1.1 Problem Statement You are given a sequence of n numbers < a 1, a 2,..., a n >. You need to
More informationCSE373 Fall 2013, Midterm Examination October 18, 2013
CSE373 Fall 2013, Midterm Examination October 18, 2013 Please do not turn the page until the bell rings. Rules: The exam is closed-book, closed-note, closed calculator, closed electronics. Please stop
More informationECE250: Algorithms and Data Structures Midterm Review
ECE250: Algorithms and Data Structures Midterm Review Ladan Tahvildari, PEng, SMIEEE Associate Professor Software Technologies Applied Research (STAR) Group Dept. of Elect. & Comp. Eng. University of Waterloo
More informationCSE373: Data Structure & Algorithms Lecture 21: More Comparison Sorting. Aaron Bauer Winter 2014
CSE373: Data Structure & Algorithms Lecture 21: More Comparison Sorting Aaron Bauer Winter 2014 The main problem, stated carefully For now, assume we have n comparable elements in an array and we want
More informationScientific Computing. Algorithm Analysis
ECE257 Numerical Methods and Scientific Computing Algorithm Analysis Today s s class: Introduction to algorithm analysis Growth of functions Introduction What is an algorithm? A sequence of computation
More informationCSE 2320 Section 002, Fall 2015 Exam 2 Time: 80 mins
CSE 2320 Section 002, Fall 201 Exam 2 Time: 80 mins Name:. Student ID:. Total exam points: 100. Question Points Out of 1 24 2 10 3 10 4 18 6 1 16 Total 100 If you have the smallest doubt about what a question
More informationOverview of Sorting Algorithms
Unit 7 Sorting s Simple Sorting algorithms Quicksort Improving Quicksort Overview of Sorting s Given a collection of items we want to arrange them in an increasing or decreasing order. You probably have
More informationCSE 373 MAY 24 TH ANALYSIS AND NON- COMPARISON SORTING
CSE 373 MAY 24 TH ANALYSIS AND NON- COMPARISON SORTING ASSORTED MINUTIAE HW6 Out Due next Wednesday ASSORTED MINUTIAE HW6 Out Due next Wednesday Only two late days allowed ASSORTED MINUTIAE HW6 Out Due
More information08 A: Sorting III. CS1102S: Data Structures and Algorithms. Martin Henz. March 10, Generated on Tuesday 9 th March, 2010, 09:58
08 A: Sorting III CS1102S: Data Structures and Algorithms Martin Henz March 10, 2010 Generated on Tuesday 9 th March, 2010, 09:58 CS1102S: Data Structures and Algorithms 08 A: Sorting III 1 1 Recap: Sorting
More informationSorting Pearson Education, Inc. All rights reserved.
1 19 Sorting 2 19.1 Introduction (Cont.) Sorting data Place data in order Typically ascending or descending Based on one or more sort keys Algorithms Insertion sort Selection sort Merge sort More efficient,
More informationBasic Data Structures (Version 7) Name:
Prerequisite Concepts for Analysis of Algorithms Basic Data Structures (Version 7) Name: Email: Concept: mathematics notation 1. log 2 n is: Code: 21481 (A) o(log 10 n) (B) ω(log 10 n) (C) Θ(log 10 n)
More informationCSE 332, Spring 2010, Midterm Examination 30 April 2010
CSE 332, Spring 2010, Midterm Examination 30 April 2010 Please do not turn the page until the bell rings. Rules: The exam is closed-book, closed-note. You may use a calculator for basic arithmetic only.
More informationRecall from Last Time: Big-Oh Notation
CSE 326 Lecture 3: Analysis of Algorithms Today, we will review: Big-Oh, Little-Oh, Omega (Ω), and Theta (Θ): (Fraternities of functions ) Examples of time and space efficiency analysis Covered in Chapter
More informationFINALTERM EXAMINATION Fall 2009 CS301- Data Structures Question No: 1 ( Marks: 1 ) - Please choose one The data of the problem is of 2GB and the hard
FINALTERM EXAMINATION Fall 2009 CS301- Data Structures Question No: 1 The data of the problem is of 2GB and the hard disk is of 1GB capacity, to solve this problem we should Use better data structures
More informationCS Sorting Terms & Definitions. Comparing Sorting Algorithms. Bubble Sort. Bubble Sort: Graphical Trace
CS 704 Introduction to Data Structures and Software Engineering Sorting Terms & Definitions Internal sorts holds all data in RAM External sorts use Files Ascending : Low to High Descending : High to Low
More informationDepartment of Computer Science Admission Test for PhD Program. Part I Time : 30 min Max Marks: 15
Department of Computer Science Admission Test for PhD Program Part I Time : 0 min Max Marks: 5 Each Q carries marks. ¼ mark will be deducted for every wrong answer. Part II of only those candidates will
More informationProblem. Input: An array A = (A[1],..., A[n]) with length n. Output: a permutation A of A, that is sorted: A [i] A [j] for all. 1 i j n.
Problem 5. Sorting Simple Sorting, Quicksort, Mergesort Input: An array A = (A[1],..., A[n]) with length n. Output: a permutation A of A, that is sorted: A [i] A [j] for all 1 i j n. 98 99 Selection Sort
More informationIntroduction. Sorting. Definitions and Terminology: Program efficiency. Sorting Algorithm Analysis. 13. Sorting. 13. Sorting.
Sorting Introduction Slides. Table of Contents. Introduction 3. Bubblesort 4. Bubblesort Complexity 5. Bubblesort Complexity (cont) 6. Selection Sort 7. Selection Sort Complexity 8. Duplex Selection Sort
More informationCS S-11 Sorting in Θ(nlgn) 1. Base Case: A list of length 1 or length 0 is already sorted. Recursive Case:
CS245-2015S-11 Sorting in Θ(nlgn) 1 11-0: Merge Sort Recursive Sorting Base Case: A list of length 1 or length 0 is already sorted Recursive Case: Split the list in half Recursively sort two halves Merge
More informationCSE 3101: Introduction to the Design and Analysis of Algorithms. Office hours: Wed 4-6 pm (CSEB 3043), or by appointment.
CSE 3101: Introduction to the Design and Analysis of Algorithms Instructor: Suprakash Datta (datta[at]cse.yorku.ca) ext 77875 Lectures: Tues, BC 215, 7 10 PM Office hours: Wed 4-6 pm (CSEB 3043), or by
More informationDeterministic and Randomized Quicksort. Andreas Klappenecker
Deterministic and Randomized Quicksort Andreas Klappenecker Overview Deterministic Quicksort Modify Quicksort to obtain better asymptotic bound Linear-time median algorithm Randomized Quicksort Deterministic
More informationTotal Points: 60. Duration: 1hr
CS800 : Algorithms Fall 201 Nov 22, 201 Quiz 2 Practice Total Points: 0. Duration: 1hr 1. (,10) points Binary Heap. (a) The following is a sequence of elements presented to you (in order from left to right):
More informationData Structures Question Bank Multiple Choice
Section 1. Fundamentals: Complexity, Algorthm Analysis 1. An algorithm solves A single problem or function Multiple problems or functions Has a single programming language implementation 2. A solution
More informationMidterm solutions. n f 3 (n) = 3
Introduction to Computer Science 1, SE361 DGIST April 20, 2016 Professors Min-Soo Kim and Taesup Moon Midterm solutions Midterm solutions The midterm is a 1.5 hour exam (4:30pm 6:00pm). This is a closed
More informationSAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 6. Sorting Algorithms
SAMPLE OF THE STUDY MATERIAL PART OF CHAPTER 6 6.0 Introduction Sorting algorithms used in computer science are often classified by: Computational complexity (worst, average and best behavior) of element
More informationComputer Science Foundation Exam. May 6, Computer Science. Section 1A. No Calculators! KEY. Score: 50
Computer Science Foundation Exam May 6, 2005 Computer Science Section 1A No Calculators! Name: KEY SSN: Score: 50 In this section of the exam, there are four (4) problems. You must do all of them. The
More informationINSTITUTE OF AERONAUTICAL ENGINEERING
INSTITUTE OF AERONAUTICAL ENGINEERING (Autonomous) Dundigal, Hyderabad - 500 043 COMPUTER SCIENCE AND ENGINEERING TUTORIAL QUESTION BANK Course Name Course Code Class Branch DATA STRUCTURES ACS002 B. Tech
More informationFaster Sorting Methods
Faster Sorting Methods Chapter 9 Contents Merge Sort Merging Arrays Recursive Merge Sort The Efficiency of Merge Sort Iterative Merge Sort Merge Sort in the Java Class Library Contents Quick Sort The Efficiency
More informationSorting. Sorting. Stable Sorting. In-place Sort. Bubble Sort. Bubble Sort. Selection (Tournament) Heapsort (Smoothsort) Mergesort Quicksort Bogosort
Principles of Imperative Computation V. Adamchik CS 15-1 Lecture Carnegie Mellon University Sorting Sorting Sorting is ordering a list of objects. comparison non-comparison Hoare Knuth Bubble (Shell, Gnome)
More informationRecitation 9. Prelim Review
Recitation 9 Prelim Review 1 Heaps 2 Review: Binary heap min heap 1 2 99 4 3 PriorityQueue Maintains max or min of collection (no duplicates) Follows heap order invariant at every level Always balanced!
More informationCLO Assessment CLO1 Q1(10) CLO2 Q2 (10) CLO3 Q4 (10) CLO4 Q3a (4)
CS210 Data Structures (171) Final Exam Name: ID Instructions: This exam contains four questions with multiple parts. Time allowed: 180 minutes Closed Book, Closed Notes. There are 10 pages in this exam
More informationMergesort again. 1. Split the list into two equal parts
Quicksort Mergesort again 1. Split the list into two equal parts 5 3 9 2 8 7 3 2 1 4 5 3 9 2 8 7 3 2 1 4 Mergesort again 2. Recursively mergesort the two parts 5 3 9 2 8 7 3 2 1 4 2 3 5 8 9 1 2 3 4 7 Mergesort
More informationCS 216 Exam 1 Fall SOLUTION
CS 216 Exam 1 Fall 2004 - SOLUTION Name: Lab Section: Email Address: Student ID # This exam is closed note, closed book. You will have an hour and fifty minutes total to complete the exam. You may NOT
More informationDivide and Conquer 4-0
Divide and Conquer 4-0 Divide-and-Conquer The most-well known algorithm design strategy: 1. Divide instance of problem into two or more smaller instances 2. Solve smaller instances recursively 3. Obtain
More informationEECS 2011M: Fundamentals of Data Structures
M: Fundamentals of Data Structures Instructor: Suprakash Datta Office : LAS 3043 Course page: http://www.eecs.yorku.ca/course/2011m Also on Moodle Note: Some slides in this lecture are adopted from James
More informationCSCE 2014 Final Exam Spring Version A
CSCE 2014 Final Exam Spring 2017 Version A Student Name: Student UAID: Instructions: This is a two-hour exam. Students are allowed one 8.5 by 11 page of study notes. Calculators, cell phones and computers
More informationLecture 5: Sorting Part A
Lecture 5: Sorting Part A Heapsort Running time O(n lg n), like merge sort Sorts in place (as insertion sort), only constant number of array elements are stored outside the input array at any time Combines
More informationAlgorithm Complexity Analysis: Big-O Notation (Chapter 10.4) Dr. Yingwu Zhu
Algorithm Complexity Analysis: Big-O Notation (Chapter 10.4) Dr. Yingwu Zhu Measure Algorithm Efficiency Space utilization: amount of memory required Time efficiency: amount of time required to accomplish
More informationAnalyze the obvious algorithm, 5 points Here is the most obvious algorithm for this problem: (LastLargerElement[A[1..n]:
CSE 101 Homework 1 Background (Order and Recurrence Relations), correctness proofs, time analysis, and speeding up algorithms with restructuring, preprocessing and data structures. Due Thursday, April
More informationData Structure and Algorithm, Spring 2013 Midterm Examination 120 points Time: 2:20pm-5:20pm (180 minutes), Tuesday, April 16, 2013
Data Structure and Algorithm, Spring 2013 Midterm Examination 120 points Time: 2:20pm-5:20pm (180 minutes), Tuesday, April 16, 2013 Problem 1. In each of the following question, please specify if the statement
More informationDivide & Conquer. 2. Conquer the sub-problems by solving them recursively. 1. Divide the problem into number of sub-problems
Divide & Conquer Divide & Conquer The Divide & Conquer approach breaks down the problem into multiple smaller sub-problems, solves the sub-problems recursively, then combines the solutions of the sub-problems
More informationIntroduction. Sorting. Table of Contents
Sorting Introduction Table of Contents Introduction Bubblesort Selection Sort Duplex Selection Sort Duplex Selection Sort (cont) Comparison Analysis Comparison Analysis (cont) Time Analysis Time Analysis
More informationHow many leaves on the decision tree? There are n! leaves, because every permutation appears at least once.
Chapter 8. Sorting in Linear Time Types of Sort Algorithms The only operation that may be used to gain order information about a sequence is comparison of pairs of elements. Quick Sort -- comparison-based
More informationCS 315 Data Structures Spring 2012 Final examination Total Points: 80
CS 315 Data Structures Spring 2012 Final examination Total Points: 80 Name This is an open-book/open-notes exam. Write the answers in the space provided. Answer for a total of 80 points, including at least
More informationCS 137 Part 8. Merge Sort, Quick Sort, Binary Search. November 20th, 2017
CS 137 Part 8 Merge Sort, Quick Sort, Binary Search November 20th, 2017 This Week We re going to see two more complicated sorting algorithms that will be our first introduction to O(n log n) sorting algorithms.
More informationCSC 273 Data Structures
CSC 273 Data Structures Lecture 6 - Faster Sorting Methods Merge Sort Divides an array into halves Sorts the two halves, Then merges them into one sorted array. The algorithm for merge sort is usually
More informationUniversity of Waterloo CS240, Winter 2010 Assignment 2
University of Waterloo CS240, Winter 2010 Assignment 2 Due Date: Wednesday, February 10, at 5:00pm Please read http://www.student.cs.uwaterloo.ca/~cs240/w10/guidelines.pdf for guidelines on submission.
More informationUniversity of the Western Cape Department of Computer Science
University of the Western Cape Department of Computer Science Algorithms and Complexity CSC212 Paper II Final Examination 13 November 2015 Time: 90 Minutes. Marks: 100. UWC number Surname, first name Mark
More informationCSci 231 Final Review
CSci 231 Final Review Here is a list of topics for the final. Generally you are responsible for anything discussed in class (except topics that appear italicized), and anything appearing on the homeworks.
More informationSorting. Two types of sort internal - all done in memory external - secondary storage may be used
Sorting Sunday, October 21, 2007 11:47 PM Two types of sort internal - all done in memory external - secondary storage may be used 13.1 Quadratic sorting methods data to be sorted has relational operators
More informationCOMP 250 Fall Homework #4
COMP 250 Fall 2006 - Homework #4 1) (35 points) Manipulation of symbolic expressions See http://www.mcb.mcgill.ca/~blanchem/250/hw4/treenodesolution.java 2) (10 points) Binary search trees Consider a binary
More informationMeasuring algorithm efficiency
CMPT 225 Measuring algorithm efficiency Timing Counting Cost functions Cases Best case Average case Worst case Searching Sorting O Notation O notation's mathematical basis O notation classes and notations
More informationSorting. Sorting in Arrays. SelectionSort. SelectionSort. Binary search works great, but how do we create a sorted array in the first place?
Sorting Binary search works great, but how do we create a sorted array in the first place? Sorting in Arrays Sorting algorithms: Selection sort: O(n 2 ) time Merge sort: O(nlog 2 (n)) time Quicksort: O(n
More informationCilk, Matrix Multiplication, and Sorting
6.895 Theory of Parallel Systems Lecture 2 Lecturer: Charles Leiserson Cilk, Matrix Multiplication, and Sorting Lecture Summary 1. Parallel Processing With Cilk This section provides a brief introduction
More informationSorting. There exist sorting algorithms which have shown to be more efficient in practice.
Sorting Next to storing and retrieving data, sorting of data is one of the more common algorithmic tasks, with many different ways to perform it. Whenever we perform a web search and/or view statistics
More informationDraw a diagram of an empty circular queue and describe it to the reader.
1020_1030_testquestions.text Wed Sep 10 10:40:46 2014 1 1983/84 COSC1020/30 Tests >>> The following was given to students. >>> Students can have a good idea of test questions by examining and trying the
More informationQ1 Q2 Q3 Q4 Q5 Q6 Total
Name: SSN: Computer Science Foundation Exam May 5, 006 Computer Science Section 1A Q1 Q Q3 Q4 Q5 Q6 Total KNW KNW KNW ANL,DSN KNW DSN You have to do all the 6 problems in this section of the exam. Partial
More informationComputer Science Foundation Exam
Computer Science Foundation Exam January 13, 2018 Section I A DATA STRUCTURES SOLUTIONS NO books, notes, or calculators may be used, and you must work entirely on your own. Question # Max Pts Category
More informationCSE373: Data Structure & Algorithms Lecture 18: Comparison Sorting. Dan Grossman Fall 2013
CSE373: Data Structure & Algorithms Lecture 18: Comparison Sorting Dan Grossman Fall 2013 Introduction to Sorting Stacks, queues, priority queues, and dictionaries all focused on providing one element
More informationThe divide and conquer strategy has three basic parts. For a given problem of size n,
1 Divide & Conquer One strategy for designing efficient algorithms is the divide and conquer approach, which is also called, more simply, a recursive approach. The analysis of recursive algorithms often
More informationSorting Shabsi Walfish NYU - Fundamental Algorithms Summer 2006
Sorting The Sorting Problem Input is a sequence of n items (a 1, a 2,, a n ) The mapping we want is determined by a comparison operation, denoted by Output is a sequence (b 1, b 2,, b n ) such that: {
More informationUNIVERSITY REGULATIONS
CPSC 221: Algorithms and Data Structures Midterm Exam, 2013 February 15 Name: Student ID: Signature: Section (circle one): MWF(201) TTh(202) You have 60 minutes to solve the 5 problems on this exam. A
More informationCSE 373 Autumn 2010: Midterm #2 (closed book, closed notes, NO calculators allowed)
Name: Email address: CSE 373 Autumn 2010: Midterm #2 (closed book, closed notes, NO calculators allowed) Instructions: Read the directions for each question carefully before answering. We may give partial
More informationCSCI 104 Log Structured Merge Trees. Mark Redekopp
1 CSCI 10 Log Structured Merge Trees Mark Redekopp Series Summation Review Let n = 1 + + + + k = σk i=0 n = k+1-1 i. What is n? What is log (1) + log () + log () + log (8)++ log ( k ) = 0 + 1 + + 3+ +
More informationDivide and Conquer Sorting Algorithms and Noncomparison-based
Divide and Conquer Sorting Algorithms and Noncomparison-based Sorting Algorithms COMP1927 16x1 Sedgewick Chapters 7 and 8 Sedgewick Chapter 6.10, Chapter 10 DIVIDE AND CONQUER SORTING ALGORITHMS Step 1
More informationCPSC 311 Lecture Notes. Sorting and Order Statistics (Chapters 6-9)
CPSC 311 Lecture Notes Sorting and Order Statistics (Chapters 6-9) Acknowledgement: These notes are compiled by Nancy Amato at Texas A&M University. Parts of these course notes are based on notes from
More informationComputer Science 210 Data Structures Siena College Fall Topic Notes: Priority Queues and Heaps
Computer Science 0 Data Structures Siena College Fall 08 Topic Notes: Priority Queues and Heaps Heaps and Priority Queues From here, we will look at some ways that trees are used in other structures. First,
More informationCS 506, Sect 002 Homework 5 Dr. David Nassimi Foundations of CS Due: Week 11, Mon. Apr. 7 Spring 2014
CS 506, Sect 002 Homework 5 Dr. David Nassimi Foundations of CS Due: Week 11, Mon. Apr. 7 Spring 2014 Study: Chapter 4 Analysis of Algorithms, Recursive Algorithms, and Recurrence Equations 1. Prove the
More informationCpt S 122 Data Structures. Sorting
Cpt S 122 Data Structures Sorting Nirmalya Roy School of Electrical Engineering and Computer Science Washington State University Sorting Process of re-arranging data in ascending or descending order Given
More information21# 33# 90# 91# 34# # 39# # # 31# 98# 0# 1# 2# 3# 4# 5# 6# 7# 8# 9# 10# #
1. Prove that n log n n is Ω(n). York University EECS 11Z Winter 1 Problem Set 3 Instructor: James Elder Solutions log n n. Thus n log n n n n n log n n Ω(n).. Show that n is Ω (n log n). We seek a c >,
More informationUniversity of Waterloo Department of Electrical and Computer Engineering ECE250 Algorithms and Data Structures Fall 2014
University of Waterloo Department of Electrical and Computer Engineering ECE250 Algorithms and Data Structures Fall 2014 Midterm Examination Instructor: Ladan Tahvildari, PhD, PEng, SMIEEE Date: Tuesday,
More informationMatriculation number:
Department of Informatics Prof. Dr. Michael Böhlen Binzmühlestrasse 14 8050 Zurich Phone: +41 44 635 4333 Email: boehlen@ifi.uzh.ch AlgoDat Repetition Exam Spring 2018 18.05.2018 Name: Matriculation number:
More informationProgramming in Haskell Aug-Nov 2015
Programming in Haskell Aug-Nov 2015 LECTURE 11 SEPTEMBER 10, 2015 S P SURESH CHENNAI MATHEMATICAL INSTITUTE Measuring efficiency Measuring efficiency Computation is reduction Application of definitions
More informationMUHAMMAD FAISAL MIT 4 th Semester Al-Barq Campus (VGJW01) Gujranwala
MUHAMMAD FAISAL MIT 4 th Semester Al-Barq Campus (VGJW01) Gujranwala faisalgrw123@gmail.com Reference MCQ s For MIDTERM EXAMS CS502- Design and Analysis of Algorithms 1. For the sieve technique we solve
More informationAssignment 2. CS 234 Fall 2018 Sandy Graham. Create()
Assignment 2 CS 234 Fall 2018 Sandy Graham Coverage: Modules 3 and 4. This assignment consists of a written component and a programming component. Please read the course website carefully to ensure that
More informationComputer Science Spring 2005 Final Examination, May 12, 2005
Computer Science 302 00 Spring 2005 Final Examination, May 2, 2005 Name: No books, notes, or scratch paper. Use pen or pencil, any color. Use the backs of the pages for scratch paper. If you need more
More informationStacks, Queues (cont d)
Stacks, Queues (cont d) CSE 2011 Winter 2007 February 1, 2007 1 The Adapter Pattern Using methods of one class to implement methods of another class Example: using List to implement Stack and Queue 2 1
More informationQuestion 7.11 Show how heapsort processes the input:
Question 7.11 Show how heapsort processes the input: 142, 543, 123, 65, 453, 879, 572, 434, 111, 242, 811, 102. Solution. Step 1 Build the heap. 1.1 Place all the data into a complete binary tree in the
More informationCS 310 Advanced Data Structures and Algorithms
CS 310 Advanced Data Structures and Algorithms Sorting June 13, 2017 Tong Wang UMass Boston CS 310 June 13, 2017 1 / 42 Sorting One of the most fundamental problems in CS Input: a series of elements with
More informationCSCI 102L - Data Structures Midterm Exam #2 Spring 2011
CSCI 102L - Data Structures Midterm Exam #2 Spring 2011 (12:30pm - 1:50pm, Thursday, March 24) Instructor: Bill Cheng ( This exam is closed book, closed notes, closed everything. No cheat sheet allowed.
More informationCOMP 250 Fall Solution - Homework #4
COMP 250 Fall 2013 - Solution - Homework #4 1) // Evaluates a single operation static public double apply(string op, double x1, double x2) { if (op.equals("add")) return x1+x2; if (op.equals("mult")) return
More informationLecture Notes 14 More sorting CSS Data Structures and Object-Oriented Programming Professor Clark F. Olson
Lecture Notes 14 More sorting CSS 501 - Data Structures and Object-Oriented Programming Professor Clark F. Olson Reading for this lecture: Carrano, Chapter 11 Merge sort Next, we will examine two recursive
More informationCMSC351 - Fall 2014, Homework #2
CMSC351 - Fall 2014, Homework #2 Due: October 8th at the start of class Name: Section: Grades depend on neatness and clarity. Write your answers with enough detail about your approach and concepts used,
More informationProblem Set 6 Due: 11:59 Sunday, April 29
CS230 Data Structures Handout # 36 Prof. Lyn Turbak Monday, April 23 Wellesley College Problem Set 6 Due: 11:59 Sunday, April 29 Reading: You are expected to read and understand all of the following handouts,
More information