Loop

Consider the following C code. Assume that unsigned long int type length is 64 bits.

unsigned long int fun(unsigned long int n){
unsigned long int i, j = 0, sum = 0;
for (i = n; i > 1; i = i/2) j++;
for ( ; j > 1; j = j/2) sum++;
return(sum);
}  

The value returned when we call fun with the input 2^{40} is

Consider the C program fragment below which is meant to divide x by y using repeated subtractions. The variables x, y, q and r are all unsigned int.

while (r >= y) {
r = r - y;
q = q +1;
}

Which of the following conditions on the variables x, y, q and r before the execution of the fragment will ensure that the loop terminates in a state satisfying the condition x==(y*q+r)?

The following function computes X^{Y} for positive integers X and Y.

int exp(int X,int Y){
    int res=1, a=X, b=Y;
    while (b!=0){
    if(b%2==0){a=a*a;  b=b/2;}
    else {res=res*a;  b=b-1;}
   }
   return res;
}

Which one of the following conditions is TRUE before every iteration of the loop?

The following function computes the maximum value contained in an integer array p[] of size n (n>=1).

 
int max(int*p, int n){
   int a=0,b=n-1;
   while (__________){
   if (p[a]<=p[b]){a=a+1;} 
   else {b=b-1;}
   }
   return p[a];
}

The missing loop condition is

Consider the following pseudo code, where x and y are positive integers.

 begin
   q := 0
    r := x 
    while r \geq  y  do
         begin
               r := r - y
              q := q + 1
        end
end 

The post condition that needs to be satisfied after the program terminates is

Consider the following pseudo code. What is the total number of multiplications to be performed?

 D= 2
for i = 1 to n do
   for j = i to n do
      for k = j + 1 to n do
           D = D * 3 

Consider the following C function in which size is the number of elements in the array E:

 int MyX(int *E, unsigned int size)
{
  int Y = 0;
  int Z;
  int i, j, k; 
    for(i = 0; i < size; i++)
    Y = Y + E[i];
  for(i = 0; i < size; i++)
    for(j = i; j < size; j++)
    {
       Z = 0;
       for(k = i; k <= j; k++)
           Z= Z + E[k];
       if (Z > Y)
            Y = Z;
   }
return Y;
}

The value returned by the function MyX is the

Consider the following segment of C-code:

 int j, n;
   j = 1;
   while (j <=n)
   j=j*2; 

The number of comparisons made in the execution of the loop for any n \gt 0 is:

Consider the following C-function in which a[n] and b[m] are two sorted integer arrays and c[n+m] be another integer array.

void xyz (int a[],int b[],int c[]){
   int i, j, k;
   i=j=k=0;
   while((i < n))&&(j < m)
            if (a[i] < b[j]c[k++]=a[i++];
            else c[k++]=b[j++];
}

Which of the following condition(s) hold(s) after the termination of the while loop ?

I. j\ltm, k=n+j-1, and a [n-1]\ltb[j] if i=n
II. i\ltn, k=m+i-1, and b[m-1]\leqa[i] if j=m

Consider line number 3 of the following C-program.

int min ( ) { /* Line 1 */
int I, N; /* Line 2 */
fro (I =0, I < N, I++); /* Line 3 */
}

Identify the compiler's response about this line while creating the object-module: