Software Development Exam > Software Development Questions > What is the space complexity of the following...
Start Learning for Free
What is the space complexity of the following code snippet?
int fib(int n) {
if (n <= 1) {
return n;
}
return fib(n - 1) + fib(n - 2);
}
int result = fib(5);
int fib(int n) {
if (n <= 1) {
return n;
}
return fib(n - 1) + fib(n - 2);
}
int result = fib(5);
- a)O(n)
- b)O(log n)
- c)O(sqrt(n))
- d)O(2^n)
Correct answer is option 'D'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Most Upvoted Answer
What is the space complexity of the following code snippet?int fib(int...
Understanding Space Complexity
The space complexity of an algorithm refers to the amount of memory space required by the algorithm as a function of the input size. In the case of the recursive Fibonacci function, the space complexity can be analyzed based on the function calls and the call stack.
Recursive Calls and Call Stack
- Each time the `fib` function is called, a new frame is added to the call stack.
- For `fib(n)`, two recursive calls are made: `fib(n-1)` and `fib(n-2)`.
- This results in a binary tree of calls, where each node represents a function call, and the height of this tree corresponds to the depth of the recursion.
Height of the Call Stack
- The maximum depth of recursion for `fib(n)` is `O(n)`, as the function will keep calling itself until it reaches the base case (when `n` is 0 or 1).
- However, the space complexity is not just about the height of the stack; it also considers the number of calls that are simultaneously active.
Total Space Complexity
- The number of recursive calls grows exponentially, leading to many overlapping calls in the recursion tree.
- Although the maximum depth is `O(n)`, the total number of calls made is `O(2^n)` due to the exponential growth of the call tree.
Conclusion
- Therefore, the overall space complexity of the recursive Fibonacci function is **O(2^n)**.
- This makes option 'D' the correct answer, as it captures the exponential growth of the space required for the recursive calls.
The space complexity of an algorithm refers to the amount of memory space required by the algorithm as a function of the input size. In the case of the recursive Fibonacci function, the space complexity can be analyzed based on the function calls and the call stack.
Recursive Calls and Call Stack
- Each time the `fib` function is called, a new frame is added to the call stack.
- For `fib(n)`, two recursive calls are made: `fib(n-1)` and `fib(n-2)`.
- This results in a binary tree of calls, where each node represents a function call, and the height of this tree corresponds to the depth of the recursion.
Height of the Call Stack
- The maximum depth of recursion for `fib(n)` is `O(n)`, as the function will keep calling itself until it reaches the base case (when `n` is 0 or 1).
- However, the space complexity is not just about the height of the stack; it also considers the number of calls that are simultaneously active.
Total Space Complexity
- The number of recursive calls grows exponentially, leading to many overlapping calls in the recursion tree.
- Although the maximum depth is `O(n)`, the total number of calls made is `O(2^n)` due to the exponential growth of the call tree.
Conclusion
- Therefore, the overall space complexity of the recursive Fibonacci function is **O(2^n)**.
- This makes option 'D' the correct answer, as it captures the exponential growth of the space required for the recursive calls.
Free Test
FREE
| Start Free Test |
Community Answer
What is the space complexity of the following code snippet?int fib(int...
The given code implements the Fibonacci sequence using recursion. It recursively calls the function twice for each value until n <= 1. The number of function calls grows exponentially with n. Hence, the space complexity is O(2^n).
Attention Software Development Students!
To make sure you are not studying endlessly, EduRev has designed Software Development study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Software Development.
|
Explore Courses for Software Development exam
|
|
Top Courses for Software DevelopmentView all
What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer?
Question Description
What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? for Software Development 2024 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer?.
What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? for Software Development 2024 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Software Development 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer?.
Solutions for What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Software Development.
Download more important topics, notes, lectures and mock test series for Software Development Exam by signing up for free.
Here you can find the meaning of What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer?, a detailed solution for What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice What is the space complexity of the following code snippet?int fib(int n) { if (n <= 1) { return n; } return fib(n - 1) + fib(n - 2);}int result = fib(5);a)O(n)b)O(log n)c)O(sqrt(n))d)O(2^n)Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice Software Development tests.
|
|
Explore Courses for Software Development exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup