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###### Engineering · Computer Science
Question details

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 ) {

}

}