Question

You will write a C program, q1 sequence.c, that computes the value of the nth term in any recursive sequence with the following structure:

an = c1 · an−1 + c2 · an−2

a0 > 0

a1 > 0

c1 6= 0

c2 6= 0

Your C program will take 5 integer arguments on the command line: n, a0, a1, c1 and c2. n must be an integer greater than or equal to 0. If more or fewer arguments are provided, your program should print out an error message andcorrect usage information, and then exit. Use atoi() to verify that none of the arguments violate the restrictions above (e.g. n cannot be negative, but may be zero, while c1 can not be zero); if any arguments violate the restrictions, print out an error message and correct usage information, and then exit.

Your program, after checking arguments, should call a recursive function, check sequence(), which takes the five arguments as described above. If n == 0 or n == 1, your function should return the value of the base cases a0 and a1. Otherwise, it should recursively calculate an using the equation above. Your program should also establish a global variable, number iterations, which increments every time check sequence() is called. Once the result of check sequence() is returned, your program should print that result, as well as the number of iterations that check sequence() ran.

You will use good C development practices for this question. You are expected to have a q1 sequence.h header file defining check sequence(), as well as any other functions you may have used in your program, and include this in your .c file. You are also expected to turn in a makefile which has at least four rules in it:

• A rule for compiling q1 sequence.c into a q1 sequence.o file. Use the -c option for gcc to compile this file.

• A rule for creating an executable from your q1 sequence.o file, q1 sequence.

• A clean rule for removing your executable and .o file, as well as any other temporary files or output files you may have generated.

• A test rule which runs your program with test cases and checks them against the test output.

Your makefile may contain any additional rules that you feel would be useful.

Exactly how you format the output of your program and your tests is up to you, but it should clearly indicate which value is the calculated sequence value and which is the number of iterations. Each test case must report its results by echoing to the command line, such as "Test case n: PASSED". Exactly how you check the program’s output is also up to you, but you may wish to create a shell script which can be run to test the output. You may also wish to use the diff command to compare your results with the test cases, and an if block in the shell, using the test command. The basic syntax for this is:

i f ( t e s t \$VARIABLE −eq 0 ) ; then

echo ” Test was t r u e ” ;

e l s e echo ” Test was f a l s e ” ;

f i

Use comments within your makefile or testing script to justify each of the test cases you run: what are you trying to test? Why these test cases? You must cover at least three failure cases of your choice, and at least five test cases with valid parameters, including these three:

1. 10 1 1 1 1: returns a value of 89 and 177 iterations

2. 5 1 3 3 -2: returns a value of 63 and 15 iterations

3. 8 2 5 -3 6: returns a value of -52407 and 67 iterations

When you have completed this question, you must remove all object files and executables, and then use the tar command to compress your code and test cases files into a single archive, a2q1.tar. a2q1.tar should contain:

• q1 sequence.h

q1 sequence.c

• Makefile

Answer 1

• I have pasted the code and screenshot of successful run below.
• In case of any doubts just comment down.

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-------------------------Code-----------------------

#include <stdio.h>
#include <stdlib.h>

int numIterations = 0;

int check_sequence(int n, int a0, int a1, int c1, int c2){
   numIterations++;
   if(n==0) return a0;
   if(n==1) return a1;
   return c1*check_sequence(n-1,a0,a1,c1,c2) + c2*check_sequence(n-2,a0,a1,c1,c2);
}

int main(int argc, char const *argv[]){
   if(argc<6) {printf("Fewer arguments provided\n"); return 0;}
   else if(argc>6) {printf("More arguments provided\n"); return 0;}
   int n = atoi(argv[1]);
   int a0 = atoi(argv[2]);
   int a1 = atoi(argv[3]);
   int c1 = atoi(argv[4]);
   int c2 = atoi(argv[5]);
   if(n<0){
       printf("n cannot be negative\n");
       return 0;
   }
   if(c1==0 || c2==0){
       printf("ci cannot be zero\n");
       return 0;
   }
   if(a0<=0 || a1<=0){
       printf("ai must be positive\n");
       return 0;
   }

   int result = check_sequence(n,a0,a1,c1,c2);
   printf("returns a value of %d and %d iterations\n", result, numIterations);

   return 0;
}