Virtual Labs

Which of the following recursive formula can be used to find the factorial of a number?

a: fact(n)=n*fact(n) Explanation

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b: fact(n)=n*fact(n+1) Explanation

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c: fact(n)=n*fact(n-1) Explanation

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d: fact(n)=n*fact(1) Explanation

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The time complexity of recursive implementation to find the factorial of a number is ______

a: O(n) Explanation

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b: O(1) Explanation

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c: O(n²) Explanation

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d: O(n³) Explanation

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Which of the following properties of the recursive function is/are correct?

a: Recursion helps to create a short code Explanation

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b: Recursion is effective where terms are generated successively to compute a value Explanation

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c: Recursion is useful for branching process Explanation

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d: All the above Explanation

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Which of the following is the base case in recursive implementation to find the factorial of a number?

a: return 1 Explanation

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b: fact(n)=n*fact(n-1) Explanation

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c: if(n==0) return 0 Explanation

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d: if(n==1) return 1 Explanation

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The data structure used to implement recursive function calls _____

a: Array Explanation

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b: Linked List Explanation

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c: Queue Explanation

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d: Stack Explanation

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What is the space complexity of a recursive function that makes n nested recursive calls?

a: O(1) Explanation

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b: O(log n) Explanation

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c: O(n) Explanation

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d: O(n²) Explanation

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What is the primary difference between direct and indirect recursion?

a: Direct recursion is more efficient than indirect recursion Explanation

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b: Direct recursion calls itself while indirect recursion involves a cycle of two or more functions Explanation

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c: Indirect recursion always leads to infinite loops Explanation

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d: Direct recursion can only be used with primitive data types Explanation

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Which optimization technique can help reduce both time and space complexity in recursive fibonacci calculation?

a: Using global variables Explanation

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b: Converting to iteration Explanation

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c: Memoization Explanation

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d: Tail recursion Explanation

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In the context of recursive algorithms, what is the 'recursive leap of faith'?

a: Assuming the base case will eventually be reached Explanation

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b: Assuming the recursive calls work correctly for smaller inputs Explanation

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c: Believing that recursion is always better than iteration Explanation

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d: Trusting that the compiler will optimize recursive calls Explanation

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