The order of growth for the depth of recursion associated with the recursive factorial (returns N!) method

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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Given that (n!=1 if n=0, n!=n x (n-1) x (n-2) x ... x 1) The order of growth for the depth of recursion associated with the recursive factorial (returns N!) method is: A. O(N) B. O(N^2) C. O(log2N). D. O(1).

Given the following code, what are the constraints on the input argument?

int mystery(int num){

  if (num == 0) return 0;

  else

  if (num > 100) return -1;

  else

    return num + mystery(num – 1);

}

A. It must be between 0 and 100 inclusive.  B. It must be greater than 0.
C. It must be less than 0 or greater than 100.
D. It must be greater than or equal to 0.
 

The number of recursive calls that a method goes through before returning is called:  A. order of growth efficiency.  B. the depth of recursion.

C. combinatorial recursive count.

D. activation stack frame.
 

The following code is supposed to return the sum of the numbers between 1 and n inclusive, for positive n. An analysis of the code using the "Three Question" approach reveals that:

int sum(int n){

  if (n == 1)

    return 1;

  else

    return (n + sum(n));

}

A. it fails the base-case question.  B. it fails the smaller-caller question.
C. it fails the general-case question.
D. it passes on all three questions and is a valid algorithm.
 
 
 
 
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