Data Structure Questions and Answers – Sum of n Natural Numbers using Recursion

This set of Data Structure Questions and Answers for Aptitude test focuses on “Sum of n Natural Numbers using Recursion”.

1. Which of the following option is wrong about natural numbers?
a) Sum of first n natural numbers can be calculated by using Iteration method
b) Sum of first n natural numbers can be calculated by using Recursion method
c) Sum of first n natural numbers can be calculated by using Binomial coefficient method
d) No method is prescribed to calculate sum of first n natural number
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2. Which of the following gives the sum of the first n natural numbers?
a) nC2
b) (n-1)C2
c) (n+1)C2
d) (n+2)C2
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3. Consider the following iterative solution to find the sum of first n natural numbers:

#include<stdio.h>
int get_sum(int n)
{
      int sm = 0, i;
      for(i = 1; i <= n; i++)
        ________;
      return sm;
}
int main()
{
    int n = 10;
    int ans = get_sum(n);
    printf("%d",ans);
    return 0;
}

Which of the following lines completes the above code?
a) sm = i
b) sm += i
c) i = sm
d) i += sm
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4. What is the output of the following code?

#include<stdio.h>
int get_sum(int n)
{
      int sm, i;
      for(i = 1; i <= n; i++)
        sm += i;
      return sm;
}
int main()
{
    int n = 10;
    int ans = get_sum(n);
    printf("%d",ans);
    return 0;
}

a) 55
b) 45
c) 35
d) Depends on compiler
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5. What is the time complexity of the following iterative method used to find the sum of the first n natural numbers?

#include<stdio.h>
int get_sum(int n)
{
      int sm, i;
      for(i = 1; i <= n; i++)
        sm += i;
      return sm;
}
int main()
{
    int n = 10;
    int ans = get_sum(n);
    printf("%d",ans);
    return 0;
}

a) O(1)
b) O(n)
c) O(n²)
d) O(n³)
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6. Consider the following code:

#include<stdio.h>
int recursive_sum(int n)
{
      if(n == 0)
        return 0;
      return ________;
}
int main()
{
    int n = 5;
    int ans = recursive_sum(n);
    printf("%d",ans);
    return 0;
}

Which of the following lines is the recurrence relation for the above code?
a) (n – 1) +recursive_sum(n)
b) n + recursive_sum(n)
c) n + recursive_sum(n – 1)
d) (n – 1) + recursive_sum(n – 1)
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7. Consider the following code:

#include<stdio.h>
int recursive_sum(int n)
{
      if(n == 0)
        return 0;
      return n + recursive_sum(n - 1);
}
int main()
{
     int n = 5;
     int ans = recursive_sum(n);
     printf("%d",ans);
     return 0;
}

Which of the following is the base case for the above recursive code?
a) if(n == 0)
b) return 0
c) return n + recursive_sum(n – 1)
d) if(n == 1)
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8. What is the time complexity of the following recursive implementation used to find the sum of the first n natural numbers?

#include<stdio.h>
int recursive_sum(int n)
{
      if(n == 0)
        return 0;
      return n + recursive_sum(n - 1);
}
int main()
{
     int n = 5;
     int ans = recursive_sum(n);
     printf("%d",ans);
     return 0;
}

a) O(1)
b) O(n)
c) O(n²)
d) O(n³)
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9. Which of the following methods used to find the sum of first n natural numbers has the least time complexity?
a) Recursion
b) Iteration
c) Binomial coefficient
d) All have equal time complexity
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10. What is the output of the following code?

#include<stdio.h>
int recursive_sum(int n)
{
      if(n == 0)
        return 0;
      return n + recursive_sum(n - 1);
}
int main()
{
      int n = 5;
      int ans = recursive_sum(n);
      printf("%d",ans);
      return 0;
}

a) 10
b) 15
c) 21
d) 14
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11. How many times is the function recursive_sum() called when the following code is executed?

#include<stdio.h>
int recursive_sum(int n)
{
      if(n == 0)
        return 0;
      return n + recursive_sum(n - 1);
}
int main()
{
     int n = 5;
     int ans = recursive_sum(n);
     printf("%d",ans);
     return 0;
}

a) 4
b) 5
c) 6
d) 7
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12. What is the output of the following code?

#include<stdio.h>
int recursive_sum(int n)
{
      if(n == 0)
        return 0;
      return n + recursive_sum(n - 1);
}
int main()
{
     int n = 0;
     int ans = recursive_sum(n);
     printf("%d",ans);
     return 0;
}

a) -1
b) 0
c) 1
d) runtime error
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13. What is the output of the following code?

#include<stdio.h>
int recursive_sum(int n)
{
      if(n == 0)
        return 0;
      return n + recursive_sum(n - 1);
}
int main()
{
     int n = -4;
     int ans = recursive_sum(n);
     printf("%d",ans);
     return 0;
}

a) 0
b) -10
c) 1
d) runtime error
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