1G. This program, unlike the previous 6 programs, will have several functions in
ID: 3791727 • Letter: 1
Question
1G.
This program, unlike the previous 6 programs, will have several functions in it: besides main, it willhave the following 7 functions:public static int triangle( int n )public static int multiply( int a, int b )public static void square( int size )public static void hollowSquare( int size )public static int factorial( int n )public static long fibonacci( int n )public static boolean prime( long n )These 7 functions should work as described below.Your main program should call each of these 7 functions. You decide the details of your main function.I don't much care what you decide to put in your main program, so it would be a good idea to use it toconvince yourself that your 7 functions are working properly.
MAKE SURE THAT INT N CAN BE INPUT BY USER AND INT A,B, AND INT SIZE TO BE INPUTED BY USER
1. public static int triangle( int n )return the triangle function of n. The triangle function of a number is the sum of all integers up to thatnumber. For instance, the triangle function of 5 is 1+2+3+4+5 == 15. No I/O in the function.
2. public static int multiply( int a, int b )
return the product of a and b. Don’t use the multiply operation (*), instead do repeated addition. Yourprogram should do the right thing for negative args.
3. public static void square( int size )
Output a square of *’s with the given size. For instance, square( 7 ) should output
*******
*******
*******
*******
*******
*******
*******
4. public static void hollowSquare( int size )
Output a hollow square of *’s with the given size. For instance, hollowSquare( 7 ) should output
******** (should be a hollow square)
* *
* *
* *
* *
* *
********
5. public static int factorial( int n )
Return n factorial. n factorial is the product of all positive integers up to n. For instance, factorial(5)should return 1*2*3*4*5 == 120. (Factorials of negative integers are not meaningful, you don’t needto worry about them.)
6. public static long fibonacci( int n )
Return the Fibonacci function of n. The Fibonacci function starts with Fibonacci(0) = 0, Fibonacci(1) = 1,and thereafter the Fibonacci function of a number is the sum of the Fibonacci function of the preceding2 numbers. So, Fibonacci(0) = 0 Fibonacci(1) = 1
Fibonacci(2) = 1
Fibonacci(3) = 2
Fibonacci(4) = 3
Fibonacci(5) = 5
Fibonacci(6) = 8, and so on
7. public static boolean prime( long n )
Return whether n is a prime number. A prime number, as you probably know, is a number >= 2 thathas no positive factors except one and itself. The 4 smallest prime numbers are 2, 3, 5, and 7. A decentalgorithm for determining whether n is prime is if n is less than 4, then it’s prime iff it’s greater than 1 otherwise, if n is even then it's not prime otherwise, for f taking on the values of 3, 5, 7, 9, 11, ... { if f is greater than n/f, then we're done: n is prime if n is divisible by f, then we're done: n is not prime }
Explanation / Answer
PROGRAM CODE:
package util;
import java.util.Scanner;
public class MathFunctions {
//The triangle function of a number is the sum of all integers up to that number
public static int triangle( int n )
{
int result = 0;
for(int i=1; i<=n; i++)
result += i;
return result;
}
//returns the product of a and b
public static int multiply( int a, int b )
{
if(a == 0 || b == 0)
return 0;
int result = Math.abs(b);
for(int i=1; i<Math.abs(a); i++)
{
result += b;
}
if(a < 0 || b< 0)
result *= -1;
return result;
}
//Output a square of *’s with the given size
public static void square( int size )
{
String line = "";
for(int i=0; i<size; i++)
line += "*";
for(int i=0; i<size; i++)
System.out.println(line);
}
//Output a hollow square of *’s with the given size
public static void hollowSquare( int size )
{
String line = "";
String hollowLine = "*";
for(int i=0; i<=size; i++)
line += "*";
for(int i=0; i<size-2; i++)
hollowLine += " ";
hollowLine += "*";
System.out.println(line);
for(int i=0; i<size-2; i++)
System.out.println(hollowLine);
System.out.println(line);
}
//Returns n factorial
public static int factorial( int n )
{
int result = 1;
for(int i=1; i<=n; i++)
{
result *= i;
}
return result;
}
//Return the Fibonacci function of n
public static long fibonacci( int n )
{
int n1=0,n2=1,result = 0;
for(int i=2;i<n;++i)//loop starts from 2 because 0 and 1 are already printed
{
result=n1+n2;
n1=n2;
n2=result;
}
return result;
}
//returns true if n is prime , false otherwise
public static boolean prime( long n )
{
if(n%2 == 0)
return false;
else
{
int mid = (int)n/2;
for(int i=3; i<=mid; i++)
{
if(n%i==0)
{
return false;
}
}
}
return true;
}
public static void main(String[] args) {
Scanner keyboard = new Scanner(System.in);
int N, a, b, size;
System.out.print("Enter the N value: ");
N = keyboard.nextInt();
System.out.print("Enter the value for a: ");
a = keyboard.nextInt();
System.out.print("Enter the value for b: ");
b= keyboard.nextInt();
System.out.print("Enter the size: ");
size = keyboard.nextInt();
System.out.println(" Triangle(n): " + triangle(N));
System.out.println("Multiply(a,b): " + multiply(a, b));
System.out.println("Square(size): " );
square(size);
System.out.println("Hollow Sqaure(size): ");
hollowSquare(size);
System.out.println("Factorial(n) : " + factorial(N));
System.out.println("Fibonacci(n): " + fibonacci(N));
System.out.println("Prime(n): " + prime(N));
}
}
OUTPUT:
Enter the N value: 10
Enter the value for a: 12
Enter the value for b: 13
Enter the size: 6
Triangle(n): 55
Multiply(a,b): 156
Square(size):
******
******
******
******
******
******
Hollow Sqaure(size):
*******
* *
* *
* *
* *
*******
Factorial(n) : 3628800
Fibonacci(n): 34
Prime(n): false
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