• Exercise 1.1. Complete the class below to design a function which uses input/ouput to return the diameter of a circle, given its radius

public class Circle{
  public static void main(String [] args){

 // 1. start by declaring your variables

// 2. Display the sentence "Value of radius: " on the screen

// 3. Read the input value and store it in the radius variable

// 4. Compute the perimeter using the appropriate formula

/* 5. display the result using the sentence "The circle with radius " 
+ your value of the radius + 
"has as perimeter: "+ the perimeter you just computed */
}

}

• Exercise 1.2. Given the function below, (1) Write down the main function that displays the result of the function f(x) for x=0, (2) Modify the main function so that it computes the result f(x) for every integer x between -5 and 5, (3) To determine the maximum value of f(x) on [-5,5], compute the value of f(x) for each of those values and store the max in a variable max

public static int f(int x){
  int resultat;
  resultat = -x*x + 3*x - 2;
  return resultat;
}

• Exercise 1.3. The p-norm of a vector v = (v1,v2,…, vn) is defined as the pth root of the the sum of the components vi raised to the power p. For the special case of p=2, the gives the traditional Euclidean norm which represents the length of the vector. Give an implementation of a method named ‘norm’ such that norm(v, p) returns the p-norm of the vector v where v is represented as an array of coordinates
• Exercise 1.4. Write an application that reads the length of the sides of a triangle from the user. Compute the area of the triangle using Heron’s formula . Print the area to 3 decimal places.
• Exercise 1.5. Write an application that prompts for and reads the user first and last name (separately). Then print a string composed of the first letter of the user’s first name followed by the first 5 characters of the user’s last name, followed by a random number in the range 10 to 99. (Similar algorithms are sometimes used to generate usernames for new computer accounts)
• Exercise 1.6. Write a short Java program that outputs all possible strings formed by using the characters ‘c’, ‘a’, ‘t’, ‘d’, ‘o’ and ‘g’ exactly once.
• Exercise 1.7. Write a short Java program that takes as input three integers a,b and c and from the Java console, and determines if they can be used in a correct arithmetic formula (in the given order) like “a+b=c”, “a=b-c” or “a*b=c”
• Exercise 1.8. Write a short Java program that can take a positive integer greater than 2 and write out the number of times one must repeatedly divide this number by 2 before getting a value less than 2.
• Exercise 1.9. Write a short Java program that takes two arrays a and b of length n storing the int values, and returns the dot product of a and b. That is returns an array c of length n such that c[i] = a[i]*b[i], for i=1,…, n.

import java.util.Scanner;
public class PalindromeTester{
  // -----------------------------------------------
  // Test strings to see if they are palindromes 
  // -----------------------------------------------
  public static void main(String [] args){
   String str, another = "y";
   int left; right;
   Scanner scan = new Scanner(System.in);
   while(another.equalsIgnoreCase("y")) // allows y or Y{
    System.out.println("Enter a potential palindrome: ");
    str = scan.nextLine();

    left = 0;
    right = str.length()-1;

    while(str.charAt(left) == str.charAt(right) && left < right){
    left++;
    right--; }
    System.out.println();
    if(left < right) 
        System.out.println("That string is NOT a palindrome");
    else
       System.out.println("That string IS a palindrome");
   System.out.println();
   System.out.print("Test another palindrome (y/n)? ");
   another = scan.nextLine();
}}}