NPTEL Week 3 on Functions and Program Running Time

Assessment 3 on Functions and Program Running Time

1. What does the code segment below print?

int fun(int x)
{
    ++x;
}
int main()
{
    int x=1;
    fun(x);
    printf(“%d”,x);
    return 0;
}

Ans: 1

1 point

2. What is the output of the following code snippet?

int fun(int x, int y, int z)
{
    y=y+4;
    z=x+y+z;
}
int main()
{
    int x=10;
    int y=3;
    fun(y,x,x);
    y=x+2;
    fun(x,y,y);
    x=y+2;
    printf(“%d,%d”,x,y);
    return 0;
}

Ans:14,12

1 point

3. What is the output of the following code snippet?

int fun(int *x, int *y, int *z)
{
    *y=*y+4;
    *z=*x+*y+*z;
}
int main()
{
    int x=10;
    int y=3;
    fun(&y,&x,&x);
    y=x+2;
    fun(&x,&y,&y);
    x=y+2;
    printf(“%d,%d”,x,y);
    return 0;
}

Ans:107,105

1 point

4. What does the below recursive function do ?

int * func(int *arr, int n){
    if(n==1 || n==0)
        return arr;
    else{
        int temp=arr[0];
        arr[0]=arr[n-1];
        arr[n-1]=temp;
        return func(++arr,n-2);
    }
}

 Sort the given array.

 Copy first half of the array into the other half.

 Reverse the given array.

 None of these.

Ans: Reverse the given array.

1 point

5. Let S(n) denote the sum of first n natural numbers. Specify which of the following statements are correct.

 S(n)=O(n^2)

 S(n)≠O(n^3)

 S(n)=O(n)

 S(n)=O(n^3)

Ans: Option A & D( S(n)=O(n^2) & S(n)=O(n^3) )

1 point

6. Let S(n) denote the sum of squares of first n natural numbers. Specify which of the following statements are correct.

 S(n)=O(n^3)

 S(n)≠O(n^3)

 S(n)=O(n)

 S(n)≠O(n^2)

Ans: Option A & D( S(n)=O(n^2) & S(n)=O(n^3) )

1 point

7. Consider the following segment of code:

for(i=0;i<n/2;i++)
{
            .
            .
            .           
}

Let the body of for loop take O(n^3) time. Let S(n) represent the total running time of the whole segment. Specify which of the following statements are correct.

 S(n)=O(n^3)

 S(n)≠O(n^3)

 S(n)=O(n^4)

 S(n)≠O(n^5)

Ans: option B & C ( S(n)≠O(n^3) &  S(n)=O(n^4) )

1 point

8. Consider the following code segment. Assume n to be a positive integer.

for(i=1; i<=n; i++)
{
    for(j=1; j<=n; j=j+i)
    {
        printf(“Hi”);
    }
}

Let T(n) represent the total running time of the above code segment. Specify which of the following statements are correct.

 T(n)=O(n^2)

 T(n)=O(n*log n)

 T(n)≠O(n^4)

 T(n)=O(log n)

Ans: Option A & B (T(n)=O(n^2) & T(n)=O(n*log n) )

1 point

9. Let the function f(n) = n + 2n + 3n+ …+ (n – 1 )*n. Assume n to be a positive integer. Specify whether the following statement is true or false. f(n) = O(n^2)

 True

 False

Ans : False

1 point

10. Specify whether the following statement is true or false. If a function T(n) = O(n^i), then T(n) = O(n^j) whenever i < j and i, j are positive integers.

 True

 False

Ans : True