Question

- Find the exact number of times (in terms of n) the innermost statement (X = X + 1) is executed in the following code. That is, find the final value of X. Then express the total running time in terms of O( ), Ω( ), or Θ( ) as appropriate.

X = 0; for k = 1 to n for j = 1 to n – k X = X + 1; |

- The following program computes and returns
*(*log*2**n**),*assuming the input n is an integer power of 2. That is,*n=**2**j*for some integer j ≥ 0.

int LOG (int n){ int m, k; m = n; k = 0; while (m > 1) { m = m/2; k = k + 1; } ruturn (k) } |

- First, trace the execution of this program for a specific input value, n = 16. Tabulate the values of m and k at the beginning, just before the first execution of the while loop, and after each execution of the while loop.

- Prove by induction that at the end of each execution of the while loop, the following relation holds between variables m and k. (This relation between the variables is called the loop invariant.)

*m=n/**2**k*

- Then conclude that at the end, after the last iteration of the
while loop, the program returns
*k=*log*2**n*

Answer #1

**SOLUTION -**

**IF YOU HAVE ANY DOUBT PLEASE COMMENT DOWN BELOW I WILL
SOLVE IT FOR YOU:)
----------------PLEASE RATE THE ANSWER-----------THANK
YOU!!!!!!!!----------**

For each pseudo-code function below (after the next ==== line), write a useful loop invariant capturing correctness for the
main loop in each of the following programs and briefly argue initialization, preservation, and termination.
EXAMPLE PROBLEM:
//Function to return the max of an array A
Maximum(array of integers A)
Local integer
integer m
m=0
for i = 1 to n
if A[i] > m
then m = A[i]
end function Maximum
EXAMPLE SOLUTION:
The loop invariant is m = max(0,...

*********I need question 6 answered which is from question 5
which is *********
Question 5 : Program Correctness I (1 point)
Use the loop invariant (I) to show that the code below correctly
computes
n P−1 k=0 2k
(this sum represents the sum of the first n even integers where
n ≥ 1).
Algorithm 1 evenSum(int n)
1: p = 2(n − 1)
2: i = n − 1
3: while i > 0 do
4: //(I) p = nP−1...

1) Create a flowchart for the program below and Trace the
program below with input of 3 and then again with input of 5.
#include <iostream>
using namespace std;
int Fall(int x, int m)
{ int Xm = 1, i=x;
while(i>=x-m+1)
{ Xm = Xm*i;
i=i-1;
}
return Xm;
}
int Delta(int x, int m)
{ int ans = 0;
ans = Fall(x+1,m);
ans = ans - Fall(x,m);
return ans;
}
void main()
{ int x = 0, m =...

int main() {
while (1) {
float d;
scanf("%f", &d);
float x;
for (x = d; x <= d + 1000.0; x = x + 1000.0) {
}
printf("loop exited with x = %.14g\n", x);
}
return 0;
}
If you run the program, you will see. What number should
I use as an input to make this an infinite loop?

JAVA / I KNOW THERE IS MORE THAN ONE QUESTION BUT THEY ARE SO
EASY FO YOU I NEED YOUR HELP PLEASE HELP ME. I WILL GIVE UPVOTE AND
GOOD COMMENT THANK YOU SO MUCH !!!
QUESTION 1
What is the output after the code executes? Assume there are no
syntax errors and the code will compile.
int x = 10;
do
{
System.out.println ( x );
x -= 3;
}
while (x > 0);
A.
10
7
4
1...

can someone edit my c++ code where it will output to a file. I
am currently using xcode.
#include <iostream>
#include <cctype>
#include <cstring>
#include <fstream>
using namespace std;
bool inputNum(int [],int&,istream&);
void multiply(int[],int,int[],int,int[],int&);
void print(int[],int,int,int);
int main()
{ifstream input;
int num1[35],num2[35],len1,len2,num3[60],len3=10,i;
input.open("multiplyV2.txt"); //open file
if(input.fail()) //is it ok?
{ cout<<"file did not open please check it\n";
system("pause");
return 1;
}
while(inputNum(num1,len1,input))
{inputNum(num2,len2,input);
multiply(num1,len1,num2,len2,num3,len3);
print(num1,len1,len3,1);
print(num2,len2,len3,2);
for(i=0;i<len3;i++)
cout<<"-";
cout<<endl;
print(num3,len3,len3,1);
//cout<<len1<<" "<<len2<<"
"<<len3<<endl;
cout<<endl;
}
system("pause");
}
void...

/*
This program should check if the given integer number is
prime.
Reminder, an integer number greater than 1 is prime if
it divisible only by itself and by 1.
In other words a prime number divided by any other natural
number
(besides 1 and itself) will have a non-zero remainder.
Your task:
Write a method called checkPrime(n) that will
take
an integer greater than 1 as an input, and return true
if that integer is prime; otherwise, it should...

Write a function
called TaylorSin.m that takes as input an array x, and positive
integer N, and returns the Nth Taylor polynomial approximation of
sin(x), centered at a = 0. The first line of your code should
read
function s =
TaylorSin(x,N)
HINT: in computing k!,
use kfact = k*(k-1)*kfact since you are counting by 2

Do a theta analysis and count the
number of computations it performed in each
function/method of the following code:
import java.io.*;
import java.util.Scanner;
class sort
{
int a[];
int n;
long endTime ;
long totalTime;
long startTime;
static BufferedReader br = new BufferedReader(new
InputStreamReader(System.in));
public sort(int nn) // Constructor
{
a = new int[nn];
n = nn;
endTime= 0;
totalTime =0;
startTime =0;
}
public static void main(String args[]) throws IOException
{
System.out.print("\nEnter number of students: ");
int nn =...

1) Consider the following Java program. Which statement updates
the appearance of a button?
import java.awt.event.*;
import javax.swing.*;
public class Clicker extends JFrame implements ActionListener
{
int count;
JButton button;
Clicker() {
super("Click Me");
button = new
JButton(String.valueOf(count));
add(button);
button.addActionListener(this);
setSize(200,100);
setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
setVisible(true);
}
public void actionPerformed(ActionEvent e)
{
count++;
button.setText(String.valueOf(count));
}
public static void main(String[] args) { new
Clicker(); }
}
a. add(button);...

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