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Tamiku [17]
3 years ago
12

The number of operations executed by algorithms A and B is 40n2 and 2n3, respectively. Determine n0 such that A is better than B

for n ≥ n0.
Computers and Technology
1 answer:
Tom [10]3 years ago
8 0

Answer:

Given that:

A= 40n^2

B = 2n^3

By given scenario:

40n^2=2n^3

dividing both sides by 2

20n^2=n^3

dividing both sides by n^2 we get

20 = n

Now putting n=20 in algorithms A and B:

A=40n^2

= 40 (20)^2

= 40 * (400)

A= 16000

B= 2n^3

= 2 (20)^3

= 2(8000)

B= 16000

Now as A and B got same on n = 20, then as given:

n0 <20 for n =20

Let us take n0 = 19, it will prove A is better than B.

We can also match the respective graphs of algorithms of A and B to see which one leads and which one lags, before they cross at n= 20.

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Write a program that reads an unspecified number of integers, determines how many positive and negative values have been read, a
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The program to this question can be given as:

Program:

import java.util.*;

//import package for user input  

class Main     //define class

{

public static void main(String a[])  

//define main function

{

int positive_number=0,negative_number=0,count=0,num; //define variable

double total=0,avg=0;  

//creating Scanner class object.

Scanner ob = new Scanner(System.in);

System.out.println("Enter an integer, when done input 0: "); //message

num= ob.nextInt();

//taking input from user

if (num==0)  //check number equal to 0  

{  

System.out.println("No numbers are entered except 0"); //message

System.exit(1);

}

else

{

while (num!= 0)  

{    

   if (num> 0)

   {

positive_number++; // Increase positives

}

else

{

negative_number++; // Increase negatives

}

total=total+num; // Accumulate total

count++;    // Increase the count

num=ob.nextInt();

}

// Calculate the average

avg=total/count;

// Display values

System.out.println("The positive number is:"+positive_number);

System.out.println("The negatives number is:"+negative_number);

System.out.println("total is:"+total);

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

}

}

}

Output:

Enter an integer, when done input 0: 22

2

1

4

0

The positive number is:4

The negatives number is:0

total is:29.0

average is:7.25

Explanation:

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