ASSIGNMENT BOOKLET. M.Sc.(Mathematics with Applications in Computer Science) Programming and Data Structures (1 st January, 2018 December, 2018)

Transcription

1 ASSIGNMENT BOOKLET MMT-001 M.Sc.(Mathematics with Applications in Computer Science) Programming and Data Structures (1 st January, 2018 December, 2018) School of Sciences Indira Gandhi National Open University Maidan Garhi, New Delhi

2 Dear Student, Please read the section on assignments in the Programme Guide for elective Courses that we sent you after your enrolment. As you may know already from the programme guide, the continuous evaluation component has % weightage. This assignment is for the continuous evaluation component of the course. Instructions for Formatting Your Assignments Before attempting the assignment please read the following instructions carefully. 1) On top of the first page of your answer sheet, please write the details exactly in the following format: ROLL NO : NAME : ADDRESS : COURSE CODE : COURSE TITLE : STUDY CENTRE : DATE PLEASE FOLLOW THE ABOVE FORMAT STRICTLY TO FACILITATE EVALUATION AND TO AVOID DELAY. 2) Use only foolscap size writing paper (but not of very thin variety) for writing your answers. 3) Leave a 4 cm margin on the left, top and bottom of your answer sheet. 4) Your answers should be precise. 5) While solving problems, clearly indicate which part of which question is being solved. 6) This assignment is valid only up to December, If you fail in this assignment or fail to submit it by December, 2018, then you need to get the assignment for the next year and submit it as per the instructions given therein. 8) You will not be allowed to appear for the term end examination without submitting the assignment. We strongly suggest that you retain a copy of your answer sheets. Wish you good luck. 2

3 Assignment Course Code: MMT-001 Assignment Code: MMT-001/TMA/2018 Maximum Marks: 100 1) a) In the following C program, what are the functions used? (3) # i n c l u d e < stdio.h> # i n c l u d e < math.h> i n t main () { i n t i; f o r (i = 0; i < 5; i ++) printf ("%f\n",power (i,3)); r e t u r n 0; b) Which of the following are valid integer constants? Give reasons for your answer. i) L i) 12.5 (2) c) Which of the following are valid float constants? Give reasons for your answer. i) ii) e-10 (2) d) Which of the following are valid C identifiers? Give reasons for your answer. i) 2ABC ii) _ABC iii) no.ofdays (3) 2) a) What are the errors in the following C program? (3) 1 # i n c l u d e < stdio.h> 2 i n t main () 3 { 4 f l o a t distance /* Distance travelled.*/,speed ; 5 printf (" Enter Distance travelled in Km.\ n"/* get distance travelled */ ); 6 scanf ("%f",distance ); 7 printf (" Enter time taken in hours.\ n"); 8 scanf ("%f",& time ); 9 Speed = distance / time ; 10 printf (" The speed is %f Km/hr.",speed ); 11 r e t u r n 0; 12 b) Arrange the operators in ascending order of priority: i) +=,*,>> ii) %,->, (2) c) What is the type of the C expressions in the following fragment? (2) i n t a,b; char alpha, beta, gamma ; double x; a* alpha - beta ; x*a+b; d) Rewrite Program 6.9 in page 11 of Block 2 in the form of a function that takes an unsigned long int as the argument and returns 1 if it is a prime and 0 if it is not a prime. (3) 3) a) Write the C expressions for each of the following expressions: i) cos( x x 2 +y 2 ) 3

4 ii) iii) x 1 x 2 + x x 1 x 2 3x + 7 x a e ( b ) 2 You can make use of the functions from the maths library. (3) b) What do the following functions do? Justify your answer. (4) f l o a t func1 ( f l o a t x) { r e t u r n (x >= 0? x? -x) i n t func2 ( i n t n) { i n t S = 0, i, m =0; f o r (i = 0;i < n ;i ++) { m=m +2* i +1; S=S+m; r e t u r n (S); c) Rewrite the program in listing 14, page number 19, Block 2, using while() loop instead of for() loop. (3) 4) a) In the program fragment given below, what are the values of the expressions in line numbers 2, 4 and 5? (3) 1 i n t x = 2, y = 2; 2 x ++ > y? x + 1 : y x = 2, y = 2; 4 ++ x > x? x:y; 5 ++ x * y --; b) Write a for() loop that prints all natural numbers less than 1000 that are 3 (mod 7). You should write your for() loop in such a way that body of the loop contains only a print statement. (3) c) Write a function double trapezoid(double f(double x),int a, int b) which can be used to integrate using trapezoid rule any function that fits the prototype of the function. For example, you should be able to find π 2 5) a) A function is defined on [0, ) as follows: 1 if x = 0 f (x) = sinx x if 0 < x < π 2 2 π if x π 2 0 sinxdx by using a function call trapezoid(sin, 0, π/2). (4) Write a C function to calculate this function in the interval [0,M) where M is the maximum possible long double number. You can use an approximation for π in your function. (4) b) A life-insurance saleswoman earns commission for selling policies as follows: If the policy amount is Rs. 15,000, the commission is 0.4% of policy amount. 4

5 If policy amount is Rs. 15,000 but less than or equal to Rs. 30,000, the commission is Rs % of the amount in excess of Rs. 15,000. If the policy amount is more than Rs. 30,000, the commission is Rs % of the amount in excess of Rs. 30,000. Write a C program that reads the amount of insurance sold and outputs the commission of the saleswoman. (6) 6) a) What does the following program do? Explain, line by line, starting from line 5, how it works. (5) 1 # i n c l u d e < stdio.h> 2 i n t main () 3 { 4 i n t i, k; 5 char * string = "To be or not to be."; 6 f o r (i = 1;*++ string ;) 7 i ++; 8 f o r (k = 1;k <= i; k ++) 9 printf ("%c",string [-k ]); 10 r e t u r n 0; 11 b) Write a program that does the following: (5) i) Declares a struct that stores the name and marks of a student in the programming course. ii) iii) iv) Uses typedef to name the struct as data. Declares a variable of type data, read the details of a student from the terminal using scanf() and stores it in the variable declared. Prints whether the marks of the student is above 40% or below 40% using a function that takes data as input and prints appropriate output. 7) a) The following program reads an unsigned long integer and prints its binary expansion. Explain, line by line, starting from line 5, how it works.(note: This program is written for a machine in which unsigned long is 4 bytes long. Also, you may have to append L to the number you are entering.) (7) 1 # i n c l u d e < stdio.h> 2 i n t main () 3 { 4 unsigned long i n t i,j =1; 5 i n t k,a [33]; 6 printf (" Enter a natural number :\n"); 7 scanf ("%lu\n",&i); 8 f o r (k = 0; k <= 32; j*= 2,k ++) 9 a[k]=i&j?1:0; 10 w h i l e (a[--k ]==0); 11 f o r (;k >=0;k - -) 12 printf ("%d",a[k ]); 13 r e t u r n 0; 14 b) What does the following function do? Explain, line by line, how it works. (5) 5

6 1 i n t function ( unsigned long i) 2 { 3 i n t k =1; 4 w h i l e (i > >=1){ 5 k ++; 6 7 r e t u r n k; 8 8) Refer to Program-12.1 in page 26 of Block 3 which implements a list using array. We have used 20 characters to store colours although all of them have less than 20 characters. Modify the program as follows so that no space is wasted. Declare the array colours as an array of pointers to char instead of char as follows: char * colours [ MAX_L ] Modify the initialisation part where each element of the list is set to -. Modify the function ins_element(). It should have an array of chars of length 20 called tempstring. It should use tempstring to read the string that has to be entered into the list and count the number of characters in the string. It should have a pointer to char called temp_ptr. The function should then allocate enough memory dynamically to hold the input string and make temp_ptr point to this memory. The input string is then copied to this memory area. The string should be copied into the list using appropriate pointer assignment statement. The function del_element should free the memory holding the string and write the string "-" in its place after allocating enough memory. (10) 9) a) How will you represent the following array as a sparse array using vector representation? (3) b) Based on Example 5 in Unit 12, write functions to add and multiply polynomials. (7) 10) Write a C program that creates a binary search tree ands add the numbers 10, 5,0,9,7,6,5 and 8 to the tree in the given order. You can assume the binary node declaration given in page 73 of block 3. Your program should have a function to add nodes to a binary search tree. Note that there are mistakes in pseudocode given in page 80 of Block 3. The eigth line should read elsif ( value < value stored in current node ) The 21st line should read elseif ( value > value stored in current node ) Write a function to find a key in a binary search tree. (8) 6