Implementing Methods - NEEDED URGENTLY

import java.util.List;

/** * * * A random assortment of methods reviewing topics that should * have been covered in your previous programming courses. * */

public class Lab0 { private Lab0() { // empty to prevent object creation } /** * Returns the value 1. * * @return the value 1 */ public static int one() { return 1; } /** *

Divisibility : When dividing an integer by a second nonzero integer, * the quotient may or may not be an integer.

*

For example, 12/3 = 4 while 9/4 = 2:25.

*

Definition : If {@code a} and {@code b} are integers with {@code a} * is not equal to zero , we say that {@code a} divides {@code b} * if there exists an integer {@code c} such that {@code b = ac}. * When {@code a} divides {@code b} we say that {@code a} is a factor of {@code b} * and that {@code b} is a multiple of {@code a} .

*

This method take two integers {@code a} and {@code b}, then it return true if * {@code a} divides {@code b }

* *

 * Example: * * isDivisible ( 3, 5) returns false * isDivisible ( 5, 21) returns false * isDivisible ( 75, 512) returns false * isDivisible ( 5, 10) returns true * isDivisible ( 22, 198) returns true * isDivisible ( 64, 512) returns true * 

* * @param a integer not equal to zero * @param b integer not equal to zero * @return true true if {@code a} divides {@code b } or {@code b} divides {@code a} * @pre. * {@code a != 0} , and {@code b != 0} */ public static boolean isDivisible ( int a , int b ) { } /** *

Modular Arithmetic

*

Definition: * If {@code a} and {@code b} are integers and {@code m} is a positive integer, * then {@code a} is congruent to {@code b} modulo {@code m} if {@code m} divides {@code a-b} . *

In the other words, two integers are congruent mod {@code m} if and only if * they have the same remainder when divided by {@code m} .

*

This method take three integers {@code a} and {@code b} and {@code m}, then it return true if * {@code a} is congruent to {@code b} modulo {@code m}

* *

 * Example: * * isCongruent ( 81,199,5) returns false * isCongruent ( -8,8, 5) returns false * isCongruent ( 24, 14, 6) returns false * isCongruent ( 10, 26, 8) returns true * isCongruent ( 17, 5, 6) returns true * isCongruent ( -1,1, 2) returns true * isCongruent ( -8,2, 5) returns true * isCongruent ( 38,23, 15) returns true * 

* * * @param a integer not equal to zero * @param b integer not equal to zero * @param m integer not equal to zero * @return true if {@code a} is congruent to {@code b} modulo {@code m} * @pre. * {@code m > 0} , {@code a != 0} , {@code b != 0} */ public static boolean isCongruent (int a , int b , int m ) { } /** * Returns the mathematical average of 3 values. * * @param a a value * @param b a value * @param c a value * @return the average of a, b, and c */ public static double avg(int a, int b, int c) { } /** *

Primes

*

A positive integer {@code n > 1} is called prime * if the only positive factors of {@code n} are {@code 1} and {@code n} . * A positive integer that is greater than one and is not prime is called composite.

*

An integer {@code n} is composite * if and only if there exists an integer {@code a} such that * {@code a} divides {@code n} and {@code 1 < a < n}.

* *

Hint: 1 is neither prime nor composite. It forms its own special category as a "unit".

* *

This method checks the positive integer if it is prime or not.

*

 * Example: * * isPrime ( -5) returns false * isPrime ( 6) returns false * isPrime ( 25) returns false * isPrime ( 2) returns true * isPrime ( 3) returns true * isPrime ( 13) returns true * isPrime ( 17) returns true * isPrime ( 29) returns true * 

* * @param n positive integer * @return true if number {@code n} is prime, else false * @pre. * {@code n > 0} */ public static boolean isPrime(int n) {

} /** * This method checks the element of the list of integers and * return the number (count) of of prime integers. * * *

 * Example: if the input list is * * [1,2,4,5,6,7] returns 3 ( hint: we have three prime integers : 2, 5, and 7) * [-1, -5, 6, 8, 16 , 18] returns 0 ( hint: none of these integers are prime ) * [ 9, 13, 17, 19, 37] returns 4 ( hint: we have four prime numbers: 13, 17, 19 and 37) * * 

* *

Note: This method does not modify the input list of integer {@code listofintegers}.

* * @param listofintegers a list of Integers * @return the number of prime integers in the given list of integers */ public static int countPrimeElements(List listofintegers) { } /** * This method check the input array of integers and return number of elements * that are congruent to {@code b} modulo {@code m}. * *

 * Example: * arrayofint= [1,6,8,5],b=14 m=3 returns 2 * arrayofint= [2,3,17,19,29], b=7, m=7 returns 0 * arrayofint= [81,45,65,99] b= 18 , m=3 returns 4 * * 

* *

Note: This method does not modify the input list of integer {@code arrayofint}.

* @param arrayofint input array of int , elements are not equal to zero * @param b integer not equal to zero * @param m positive integer * @return the number of elements that are congruent to {@code b} modulo {@code m}. * * @pre. * {@code m > 0} , {@code b != 0} , {@code arrayofint[i] != 0} * */ public static int countCongruentElement(int [] arrayofint, int b, int m ) { }

}