Page 32, Exercise 4

a. Counts

void transpose(int a[][MAX_SIZE])

{
   int i, j;
   int temp;
   int count = 0;
   for (i = 0; i & lt; MAX_SIZE-1; i++) {
     	count ++; /*for i loop */
     for (j = i+1; j < MAX_SIZE; j++) {
	     	count ++; /*for j loop */
	        SWAP(a[i][j],a[j][i],temp); count+=3; /*for swap */
	  }
	  count++; /* last timne of j */
   }
   count++; /* last time of i */
   printf("Transpose Count: %d\n", count);
}

b. Simplified Counts

void transpose(int a[][MAX_SIZE])
{
   int i, j;
   int temp;
   int count = 0;
   for (i = 0; i < MAX_SIZE-1; i++) {
     for (j = i+1; j < MAX_SIZE; j++) {
	     	count ++; /*for j loop */
	        SWAP(a[i][j],a[j][i],temp); count+=3; /*for swap */
	  }
	  count+=2; 
   }
   count++; /* last time of i */
   printf("Transpose Count: %d\n", count);
}

c. Final Count for 5x5 matrix : 49

d. Step Count Table

void transpose(int a[][MAX_SIZE])
{
   int i, j;
   int temp;
   for (i = 0; i =< MAX_SIZE-1; i++)
     for (j = i+1; j < MAX_SIZE; j++)
	SWAP(a[i][j],a[j][i],temp);
}

0
0
0
0
1
1
3

0

1
1
1
1
MAX_S
MAX_S(MAX_S-1)+MAX_S
MAX_S(MAX_S-1)
1

0
0
0
0
MAX_S
MAX_S•MAX_S-1 + MAX_S
3(MAX_S(MAX_S-1))
0