Tutorial Exercises: Set 6

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Exercise 1

Declare a structure to represent complex numbers. Dynamically allocate a memory of 100 complex structures. Store in the k-th index of the dynamic array the complex number k² + i sqrt(k).

Solution 1

   typedef struct {
      double re;
      double im;
   } complex;

   ...

   complex *p;
   int k;

   p = (complex *)malloc(100 * sizeof(complex));
   for (k=0; k<100; ++k) {
      p[k].re = k * k;
      p[k].im = sqrt(k);
   }

Exercise 2

Define the following structure to represent a 2-d integer matrix.

   typedef struct {
      int r;
      int c;
      int elt[MAXDIM][MAXDIM];
   } matrix;

Write a function that accepts as input a dimension d (not bigger than MAXDIM) and returns the d x d identity matrix.

Solution 2

   matrix setid ( int d )
   {
      matrix M;
      int i, j;

      M.r = M.c = d;
      for (i=0; i<d; ++i) for (j=0; j<d; ++j)
         M.elt[i][j] = (i == j) ? 1 : 0;
      return M;
   }

Exercise 3

Define a 2-d matrix with dynamic memory as follows:

   typedef struct {
      int r;
      int c;
      int **elt;
   } matrix;

Write a function that accepts as input a dimension d and returns the d x d identity matrix.

Solution 3

   matrix setid ( int d )
   {
      matrix M;
      int i, j;

      M.r = M.c = d;
      M.elt = (int **)malloc(d * sizeof(int *));
      for (i=0; i<d; ++i) {
         M.elt[i] = (int *)malloc(d * sizeof(int));
         for (j=0; j<0; ++j) M.elt[i][j] = (i == j) ? 1 : 0;
      }
      return M;
   }

Exercise 4

Write a function that accepts two matrices and returns their product, provided that the input matrices are of compatible dimensions. Use the data type with static memory (as in Exercise 2).

Solution 4

   matrix matmul ( matrix M, matrix N )
   {
      int i, j, k;
      matrix P;

      if (M.c != N.r) {
         printf("Input matrices are of incompatible dimensions.\n");
         P.r = P.c = 0;
         return P;
      }

      P.r = M.r; P.c = N.c;
      for (i=0; i<M.r; ++i) for (j=0; j<N.c; ++j) {
         P.elt[i][j] = 0;
         for (k=0; k<M.c; ++k) P.elt[i][j] += M.elt[i][k] * N.elt[k][j];
      }
      return P;
   }

Exercise 5

Write a main() function that supports the following command-line arguments: a positive integer n, and optionally another positive integer r. If r is not supplied, then the program takes the default value r=2. The program then prints the r-th root of n.

Solution 5

   int main ( int argc, char *argv[] )
   {
      int n, r;

      if (argc < 2) {
         fprintf(stderr,"Error: too few arguments\n");
         exit(1);
      }

      n = atoi(argv[1]);
      if (argc > 2) r = atoi(argv[2]); else r = 2;
      printf("%d-th root of %d is %lf\n", r, n, pow((double)n,1.0/(double)r));
      exit(0);
   }

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