Veritas Logic & Computation Assignment 2: Loops

Iteration (For, While) Lab Assignment In this lab, you will be writing your own code to perform tasks that will require the use of looping, either a for loop or a while loop, or both. The class at the very bottom provides a block of code that helps with the syntax of getting keyboard input from the user, but the remainder of the code will be your own. Perform all of the activities below using the thoughts provided and answer any questions. Activity 1: Finding the sum of the odd numbers 1 through 2n + 1 Write a Java program to find the sum of all the odd natural numbers from 1 to 2n+1, inclusive, where n is a user-entered integer greater than or equal to 1. Your program should force the user to enter a valid number by printing an error message when the user enters an invalid number and continuing to prompt until the input is valid. When complete, print a message similar to "The sum of the odd numbers from 1 through 7 is 16." Some thoughts: What does it mean for a number to be odd? When holding the sum in a variable, do you need to initialize the variable first? If so, to what value? Would you want to use a for loop or a while loop here? Why? Activity 2: Checking to see if a String is a palindrome Write a Java program that determines if a user-entered string is a palindrome. When complete, print a message that includes the original string and whether it is or is not a palindrome. Some thoughts: Your code may want to make use of the string methods .charAt(i) which returns the character at the ith index (remember, the first character in a string is index 0) and .length() which returns the number of characters in the string (remember that the index of the last character is .length() – 1 because the index starts with 0). You declare strings using the String type, for example String myString; You may assign a string literal when declaring, such as String myString = "palindrome"; or you may assign text to the String variable after declaring it, such as myString = "abcdef"; You can compare strings for character-by-character equality using the .equals() method. For example, string1.equals(string2) which will return 'true' if all characters in each string are identical in each place and 'false' if not. Uppercasing and lowercasing matters, so "text" and "text" are equal, but "Text" and "text" are not equal. Activity 3: Determining if a year is a leap year Write a Java program that determines if a given year is a leap year. By definition, any year that is evenly divisible by 4 is a leap year with an additional rule: Years divisible by 100 are NOT leap years, UNLESS they are evenly divisible by 400. For example, 1900 was NOT a leap year, but 2000 was. Get the year from the user and make sure it is valid; if not, force the user to continue entering a year until it is valid. Print a statement such as "The year 2020 is a leap year." or "The year 2021 is not a leap year." Activity 4: Checking to see that a number is prime Write a Java program that determines if a user-supplied integer, n, is prime. Print out a simple statement such as 'The number 25 is not prime.' or 'The number 29 is prime.' Some thoughts: By definition, 2 is the first prime number because it is divisible by 1 and itself. The number 1 is not considered prime. Get the program to work first by checking a bunch of small numbers you know are prime. Here are some others to try: 499, 1217, 2731, 7879, 19319, and 79393. The larger the number, the longer it takes to determine if it is prime. How does your algorithm scale with the size of the number? In other words, if n is the number, how many iterations does your program require? Think about ways to make your program run faster. Can you perform fewer checks for factors? Can you limit the size of the numbers you need to check as factors? Activity 5: Calculate the nth Fibonacci number Write a Java program that computes the nth Fibonacci number in the sequence 1, 1, 2, 3, 5, 8, 13, 21, ... and n is a user-supplied number which you will need to validate before moving forward. For reference, in the sequence given, 21 is the 8th Fibonacci number. Print out something like 'The 8th Fibonacci number is 21.' Some thoughts: The size of the numbers in the sequence can get quite large. What type might you declare your variables? Do you need to limit the size of n that the user can enter? In what ways? Activity 6: Finding the greatest common divisor Write a Java program that computes the greatest common divisor, GCD (a.k.a. greatest common factor, GCF) of two user-supplied integers. Recall that the GCD (GCF) is the largest number that will divide evenly into both numbers. For example, for the numbers 24 and 32, the GCD is 8. When complete output a message such as 'The GCD of 24 and 32 is 8.' Some thoughts: Does it matter for any reason whether or not the two user-supplied numbers are positive? Why or why not? Brute force is a valid way to solve this problem, though not very efficient for large numbers. In this case, think about the largest factor you would ever need to test. What is the GCD if the two numbers are equal? What if the two numbers are even? Both odd? One even and one odd? Activity 7 (BONUS): The GCD Revisited Research the algorithm Euclid used for finding the GCD and implement it. Activity 8: Finding the least common multiple Write a Java program that computes the least common multiple, LCM of two user-supplied integers. Recall, the LCM is the smallest number into which the two numbers will divide evenly. For example, if the two numbers are 24 and 32, the LCM is 96 because 96/24 = 4 and 96/32 = 3. When complete, output a message such as 'The LCM of 24 and 32 is 96.' Some thoughts: What if both numbers are zero? What if only one of the numbers is zero? The LCM and GCD are related. Can you determine how? Activity 9: The Collatz Conjecture The Collatz sequence, named after Lothar Collatz, is a list of numbers formed according to the following rules: Starting with any positive integer, n, the first term of the Collatz sequence is C1=n. Each successive term Ck+1 is formed from the previous term Ck according to the function: Ck+1={1/2Ck if n is even 3Ck+1 if n is odd For example, if n = 5, the sequence goes 5, 16, 8, 4, 2, 1. For n = 7, the sequence goes 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1. The Collatz conjecture is quite simple: This process will eventually reach the number 1, regardless of which positive integer is chosen initially, yet remains unproven to this day. Maybe you will be the one to someday provide a proof? Write a Java program that prints out the Collatz sequence for a user-supplied value of n as defined above. Count the number of steps taken until the sequence gets to 1 and also print out the count. If it does not eventually arrive at 1, either your program did something wrong or you have found a counterexample to the conjecture and therefore proven it false!!! import java.util.Scanner; public class Main { public static void main(String args[]) { // Out of bounds!!! Scanner myScanner = new Scanner(System.in); //Your scanner initialized, use as you see fit. //Activity 1 System.out.println("Please enter a positive integer."); int n = myScanner.nextInt(); while(n < 1) { System.out.println("Not a positive integer! Try again."); n = myScanner.nextInt(); } int sum = 0; int boundary = 2 * n + 1; for(int i = 1; i <= boundary; i+=2) { sum+=i; //sum = sum + i; System.out.print(i + " "); } System.out.println("The sum of my odd numbers is: " + sum); //Activity 2 //Activity 3 System.out.println("Enter a year"); int year = myScanner.nextInt(); if(year % 4 == 0 && !(year % 100 == 0) ) { System.out.println("The year " + year + " is a leap year"); } else if(year % 4 == 0 && (year % 100 == 0 && year % 400 == 0)) { System.out.println("The year " + year + " is a leap year"); } else { System.out.println("The year " + year + " is NOT a leap year"); } //Activity 4 //Activity 5 System.out.println("Please enter a positive integer."); n = myScanner.nextInt(); int term = 0; int n1 = 1; int n2 = 0; for(int i = 2; i <= n; i++) { term = n1 + n2; n2 = n1; n1 = term; } System.out.println("The " + n + "th Fibonacci term is " + term); //Activity 6 System.out.println("Gimme two positive numbers"); int num1 = myScanner.nextInt(); int num2 = myScanner.nextInt(); int smaller = 0; if(num1 > num2) { smaller = num2; } else { smaller = num1; } int gcf = 0; for(int i = 1; i <= smaller; i++) { if(num1 % i == 0 && num2 % i == 0) { gcf = i; if(i % 2 == 0) { System.out.println("Even!"); } } } System.out.println("The gcf is " + gcf); //Activity 7 //Activity 8 int num3 = myScanner.nextInt(); int num4 = myScanner.nextInt(); int lcm = 0; if(num3 < num4) { lcm = num4; } else { lcm = num3; } boolean run = true; while(run) { lcm++; if(lcm % num3 == 0 && lcm % num4 == 0) { System.out.println("Found the lcm!" + lcm); run = false; } } System.out.println("The lcm is: " + lcm); //Activity 9 System.out.println("Give me a number"); int ck = myScanner.nextInt(); while(ck != 1) { if(ck % 2 == 0) { ck = ck / 2; } else { ck = ck * 3 + 1; } System.out.print(ck + " "); } //Out of bounds!!! } }