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Consider the following C-program fragment in which i, j and n are integer variables.
for (i = n, j = 0; i >0; i /= 2, j += i);
Q. Let val(j) denote the value stored in the variable j after termination of the for loop. Which one of the following is true?
- a)val(j) =θ(logn)
- b)vaI(j) = θ(sqrt(n))
- c)val(j) = θ(n)
- d)val(j) = θ(nlogn)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Consider the following C-program fragment in which i, j and n are inte...
The variable j is initially 0 and value of j is sum of values of i. i is initialized as n and is reduced to half in each iteration. j = n/2 + n/4 + n/8 + .. + 1 = Θ(n) Note the semicolon after the for loop, so there is nothing in the body.
Most Upvoted Answer
Consider the following C-program fragment in which i, j and n are inte...
Explanation:
The given program fragment is a for loop that initializes two variables, i and j. It then executes the loop as long as i is greater than 0, and after each iteration, it divides i by 2 and assigns its value to j.
The loop starts with i = n and j = 0. In each iteration, i is divided by 2 and its value is assigned to j. So, j takes the values of n, n/2, n/4, n/8, and so on until i becomes 0.
Let's analyze the values of j at each iteration:
- At the first iteration, j = n.
- At the second iteration, j = n/2.
- At the third iteration, j = n/4.
- At the fourth iteration, j = n/8.
- And so on.
We can observe that in each iteration, j is divided by 2. So, after k iterations, j will be equal to n divided by 2^k. We need to find the number of iterations required for i to become 0.
The condition for the loop termination is i > 0. In each iteration, i is divided by 2. So, the number of iterations required for i to become 0 is equal to the number of times i can be divided by 2 until it becomes less than or equal to 0.
To find this number of iterations, we can calculate the logarithm of n to the base 2, which gives us the exponent to which 2 must be raised to obtain n. Let's denote this value as k.
So, after k iterations, j will be equal to n divided by 2^k, which is equal to n divided by n, which simplifies to 1.
Therefore, val(j) = 1.
Conclusion:
The value stored in the variable j after termination of the for loop is 1, which is independent of the value of n.
Hence, the correct answer is option C) val(j) = n.
The given program fragment is a for loop that initializes two variables, i and j. It then executes the loop as long as i is greater than 0, and after each iteration, it divides i by 2 and assigns its value to j.
The loop starts with i = n and j = 0. In each iteration, i is divided by 2 and its value is assigned to j. So, j takes the values of n, n/2, n/4, n/8, and so on until i becomes 0.
Let's analyze the values of j at each iteration:
- At the first iteration, j = n.
- At the second iteration, j = n/2.
- At the third iteration, j = n/4.
- At the fourth iteration, j = n/8.
- And so on.
We can observe that in each iteration, j is divided by 2. So, after k iterations, j will be equal to n divided by 2^k. We need to find the number of iterations required for i to become 0.
The condition for the loop termination is i > 0. In each iteration, i is divided by 2. So, the number of iterations required for i to become 0 is equal to the number of times i can be divided by 2 until it becomes less than or equal to 0.
To find this number of iterations, we can calculate the logarithm of n to the base 2, which gives us the exponent to which 2 must be raised to obtain n. Let's denote this value as k.
So, after k iterations, j will be equal to n divided by 2^k, which is equal to n divided by n, which simplifies to 1.
Therefore, val(j) = 1.
Conclusion:
The value stored in the variable j after termination of the for loop is 1, which is independent of the value of n.
Hence, the correct answer is option C) val(j) = n.
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Consider the following C-program fragment in which i, j and n are integer variables.for (i = n, j = 0; i >0; i /= 2, j += i);Q. Let val(j) denote the value stored in the variable j after termination of the for loop. Which one of the following is true?a)val(j) =θ(logn)b)vaI(j) =θ(sqrt(n))c)val(j) =θ(n)d)val(j) = θ(nlogn)Correct answer is option 'C'. Can you explain this answer?
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