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irga5000 [103]
3 years ago
7

A binary tree is full if all of its vertices have either zero or two children. Let Bn denote the number of full binary trees wit

h n vertices.
(a) By drawing out all full binary trees with 3, 5, or 7 vertices, determine the exact values of B3, B5, and B7. Why have we left out even numbers of vertices, like B4?


(b) For general n, derive a recurrence relation for Bn.

(c) Show by induction that Bn is (2n). 2.14. You are given an array of n elements, and

Computers and Technology
1 answer:
Arlecino [84]3 years ago
7 0

Answer:

(a) B_3 = 1\\B_5 = 2\\B_7 = 5

(b) See attached

(c) B_n = 2^{(n-3)/2}

Explanation:

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write a java program to accept three item names and prices, and output them. Also output the average price if one of the items i
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Answer:

// program in java.

// package

import java.util.*;

// class definition

class Main

{

// main method of the class

public static void main (String[] args) throws java.lang.Exception

{

   try{

    // scanner object to read input

Scanner scr=new Scanner(System.in);

 // string array

String name[] = new String[3];

 // price array

      double price[] = new double[3];

      // variable

      double sum = 0,avg;

      boolean flag = false;

      // read three name and their price

      for(int i=0;i<3;i++)

      {

          System.out.print("Enter item "+(i+1)+" name:");

          name[i]=scr.next();

          System.out.print("Enter item "+(i+1)+" price:");

          price[i]=scr.nextDouble();

          sum=sum+price[i];

          // if any name is "peas"

          if(name[i].equalsIgnoreCase("peas"))

          flag = true;

      }

System.out.println("Name and their price:");

      for(int i=0;i<3;i++)

      {

          System.out.println(name[i]+":"+price[i]);

         

      }

      // if flag is true

      if(flag)

      {

      // calculate average

          avg=sum/3;

          // print average

          System.out.println("Average price is:"+avg);

      }

      else

      System.out.println("no average output");

   

   }catch(Exception ex){

       return;}

}

}

Explanation:

Read three name and their price from user.If any name is equal to "peas" without case sensitive then find the average of three price and print the average.If their is no name equal to "peas" then print "no average output".

Output:

Enter item 1 name:apple                                                                                                    

Enter item 1 price:20                                                                                                      

Enter item 2 name:kiwi                                                                                                    

Enter item 2 price:15                                                                                                      

Enter item 3 name:banana                                                                                                  

Enter item 3 price:20    

Name and their price:

apple:20

kiwi:15

banana:20                                                                                            

no average output

8 0
3 years ago
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