Week 5 Recursion
What does the following function print for n = 25? void fun( int n) { if (n == 0) return ; printf ( "%d" , n%2); fun(n/2); } 11001 10011 11111 00000
10011
Consider the following recursive function fun(x, y). What is the value of fun(4, 3) int fun( int x, int y) { if (x == 0) return y; return fun(x - 1, x + y); } 12 9 13 5
13
Given the following method declaration, what will redo(82, 3) return? public static int redo(int i, int j) { if (i==0) return 0; else return redo(i/j, j)+1; } 5 4 6 7
5
Which of the following is NOT TRUE? Choose all that apply. Stack overflow error happens only if the recursive solution does not have base case Recursion is always an efficient solution Infinite recursion result in the use of CPU infinitely Recursion uses divide-and-conquer to solve problems
Stack overflow error happens only if the recursive solution does not have base case Recursion is always an efficient solution Infinite recursion result in the use of CPU infinitely
Given the following method declaration, this method will return true if and only if: public boolean check(String s) { return s.length() >= 2 && (s.charAt(0) == s.charAt(1) || check(s.substring(1))); } The string s contains two or more of the same characters. The string s starts with two or more of the same characters. The string s contains two or more of the same character that are next to each other. The string s ends with two or more of the same characters
The string s contains two or more of the same character that are next to each other.
A recursive solution without a base case results in infinite loop infinite recursion stack overflow b and c
b and c
Prove that the Big-O of the towers of hanoi recursive algorithm is O(2^n), where n is the number of discs.
n/a Moves required for n disks in the algorithm is : Equation 1: Equation 2: Using the above two, we can use prove by induction to prove that the towers of Hanoi algorithm is O(2^n) Conjecture -> the towers of Hanoi algorithm is O(2^n) Base case: - for 1 disk, we need only one move Induction Hypothesis - for n disks, f(n) = 2^n -1 Based on the base case and the induction hypotheis , we have to show f(n+1) = (2^(n+1)) - 1 proof: f(n+1) = 2* f(n) + 1 ..... using Equation 1 = (2 * ( 2^n -1) ) + 1 ..... using the Induction Hypothesis = 2 *2^n - 2 + 1 = 2^n+1 - 1 using a^b.a^c = a^ (b+c) end of proof therefor , the algorithm is O(2^n)
