Assignment 4-1.pdf x Converting Decimal to Bin x Java Basic Op rced/227433-22635

Question

Assignment 4-1.pdf x Converting Decimal to Bin x Java Basic Op rced/227433-22635.201620/Assignment9%204-1.pdf? &d2ISessionVal; MBO 2. Give the tracing of towers of Hanoi algorithm for 4 disks. 3. Proof by induction that the complexity of the following method is ologn). powerB(int x, int n) if (namo) return 1; return x; if (n is even) return powerB(x x, n/2); else return n/2) x; 4. write a recursive method that accepts a positive integer (in decima) au corresponding binary representation. For example, for input 10, it will display 101 5. (TextBook Q#3)Suppose that the ADT stack included the void method disp displays the entries in a stack. Implement this method for each of the follov implementations LinkedStack, as outlined in Listing 6-1. b) Array Stack, as outlined in Listing 6-2. c) VectorStack, as outlined in Listing 6-3. 6. Define a method getFrequency(anEntry) for the Linked List implementatio ADT. The method returns the number of occurrences of anEntry in the stac

Explanation / Answer

Answer:

T(n)= T(n/2)+c

This will be the recurrence relation

because function n/2 and rest are constants..

so primarily dependent on n/2

Proof:

T(n) = T(n/2) + c

=   1 , T(2) = 0

1. Base Case : n = 2

T(2) = log2 = 1

2. Now assume T(n) = logn

3. Induction Step:

T(n + 1) = log(n +1)

= logn x log1 = logn

Now, T(n +1 ) = T(n +1/ 2)

= > T( n + 1) = 1/2 x T(n + 1 )

                        = 1/2 logn = logn

proved.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---