Sunday, May 15, 2011

Stopwatch class for Java



In order to continue with my next "Factorial and Fibonacci" posts in some Java/JVM languages; I was looking for an official Java version of the .NET Timer class "Stopwatch" (System.Diagnostics.Stopwatch), so I can measure and display the elapsed time results in the same way I had been doing it in my previous posts.

Let's show some C# code of what I meant before continuing.

using System;
using System.Numerics;
using System.Diagnostics;

namespace CSStopwatchApp
{
    class StopwatchApp
    {
        static void Main(string[] args)
        {
            Stopwatch timer = new Stopwatch();
            timer.Start();
            Fibonacci(50);
            timer.Stop();

            Console.WriteLine("Elapsed time in ticks: {0}", 
                timer.Elapsed.Ticks);
            Console.WriteLine("Elapsed time in milliseconds: {0}", 
                timer.Elapsed.Milliseconds);
            Console.WriteLine("Elapsed time in seconds: {0}", 
                timer.Elapsed.Seconds);
            Console.WriteLine("Elapsed time in minutes: {0}", 
                timer.Elapsed.Minutes);
            Console.WriteLine("Elapsed time in hours: {0}", 
                timer.Elapsed.Hours);
            Console.WriteLine("Elapsed time with format: {0}", 
                timer.Elapsed);
        }
                
        private static BigInteger Fibonacci(int n)
        {
            if (n < 2)
                return 1;
            else
                return Fibonacci(n - 1) + Fibonacci(n - 2);
        }
    }
}

And the result:









However, looks like there isn't one, instead, there are 2 methods used to measure time in Java: System.nanoTime() and System.currentTimeMillis() being the first one more precise when timing code execution.


currentTimeMillis
public static long currentTimeMillis()
Returns the current time in milliseconds. Note that while the unit of time of the return value is a millisecond, the granularity of the value depends on the underlying operating system and may be larger. For example, many operating systems measure time in units of tens of milliseconds.

For example, to measure how long some code takes to execute:
long startTime = System.currentTimeMillis();
   // ... the code being measured ...
   long estimatedTime = System.currentTimeMillis() - startTime;

Returns:
the difference, measured in milliseconds, between the current time and midnight, January 1, 1970 UTC.

nanoTime
public static long nanoTime()
Returns the current value of the most precise available system timer, in nanoseconds.

This method can only be used to measure elapsed time and is not related to any other notion of system or wall-clock time. The value returned represents nanoseconds since some fixed but arbitrary time (perhaps in the future, so values may be negative). This method provides nanosecond precision, but not necessarily nanosecond accuracy. No guarantees are made about how frequently values change. Differences in successive calls that span greater than approximately 292 years (263 nanoseconds) will not accurately compute elapsed time due to numerical overflow.

For example, to measure how long some code takes to execute:
long startTime = System.nanoTime();
   // ... the code being measured ...
   long estimatedTime = System.nanoTime() - startTime;
 

Returns:
The current value of the system timer, in nanoseconds.


So, I decided to do my own version of the Stopwatch class, not before doing some google to see if someone did it already ;) you know, code reuse FTW!

Quickly I found a basic version using System.currentTimeMillis() written by Corey Goldberg and provided with a GPL license here: http://www.goldb.org/stopwatchjava.html (thanks man!), so I took it and extended it to use System.nanoTime() instead, and implemented some other missing methods and the most important (for me) the Elapsed time formatted as "hh:mm:ss.sss" using the SimpleDateFormat class, which looks like only considers 3 milliseconds... so I added the rest (the nanoseconds part) to have: 00:00:00.0000000 (hh:mm:ss.sssssss), just like the .NET version output it. Here it is:

Stopwatch class in Java

/*
 *  Copyright (c) 2011, Carlos Quintanilla
 *  Special thanks to Corey Goldberg (for his StopWatch.java | Java Timer Class)
 *  here http://www.goldb.org/stopwatchjava.html
 * 
 *  Stopwatch.java is free software; you can redistribute it and/or modify
 *  it under the terms of the GNU General Public License as published by
 *  the Free Software Foundation; either version 2 of the License, or
 *  (at your option) any later version.
 */

package stopwatchapp;

import java.text.SimpleDateFormat;
import java.util.Calendar;  

/**
 * @author Carlos Quintanilla
 */

public class Stopwatch {
    // constants
    private final long nsPerTick = 100;
    private final long nsPerMs = 1000000;
    private final long nsPerSs = 1000000000;
    private final long nsPerMm = 60000000000L;
    private final long nsPerHh = 3600000000000L;

    private long startTime = 0;
    private long stopTime = 0;
    private boolean running = false;
    
    /**
     * Starts measuring elapsed time
     * for an interval.
     */
    public void start() {
        this.startTime = System.nanoTime();       
        this.running = true;
    }
    
    /**
     * Stops measuring elapsed time
     * for an interval.
     */
    public void stop() {
        this.stopTime = System.nanoTime();
        this.running = false;
    }
    
    /**
     * Stops time interval measurement 
     * and resets the elapsed time to zero.
     */ 
    public void reset() {
        this.startTime = 0;
        this.stopTime = 0;
        this.running = false;
    }
    
    /**
     * Gets the total elapsed time measured 
     * by the current instance, in nanoseconds.
     * 1 Tick = 100 nanoseconds 
     */
    public long getElapsedTicks() {
        long elapsed;
        if (running) {
             elapsed = (System.nanoTime() - startTime);
        }
        else {
            elapsed = (stopTime - startTime);
        }
        return elapsed / nsPerTick;
    }
    
    /**
     * Gets the total elapsed time measured 
     * by the current instance, in milliseconds.
     * 10000 Ticks = 1 millisecond (1000000 nanoseconds)
     */
    public long getElapsedMilliseconds() {
        long elapsed;
        if (running) {
             elapsed = (System.nanoTime() - startTime);
        }
        else {
            elapsed = (stopTime - startTime);
        }
        return elapsed / nsPerMs;
    }
    
    /**
     * Gets the total elapsed time measured 
     * by the current instance, in seconds.
     * 10000000 Ticks = 1 second (1000 milliseconds)
     */
    public long getElapsedSeconds() {
        long elapsed;
        if (running) {
             elapsed = (System.nanoTime() - startTime);
        }
        else {
            elapsed = (stopTime - startTime);
        }        
        return elapsed / nsPerSs;
    }
    
    /**
     * Gets the total elapsed time measured 
     * by the current instance, in minutes.
     * 600000000 Ticks = 1 minute (60 seconds)
     */
    public long getElapsedMinutes() {
        long elapsed;
        if (running) {
             elapsed = (System.nanoTime() - startTime);
        }
        else {
            elapsed = (stopTime - startTime);
        }        
        return elapsed / nsPerMm;
    }
    
    /**
     * Gets the total elapsed time measured 
     * by the current instance, in hours.
     * 36000000000 Ticks = 1 hour (60 minutes)
     */
    public long getElapsedHours() {
        long elapsed;
        if (running) {
             elapsed = (System.nanoTime() - startTime);
        }
        else {
            elapsed = (stopTime - startTime);
        }        
        return elapsed / nsPerHh;
    }
    
    /**
     * Gets the total elapsed time with format 
     * 00:00:00.0000000 = 00:mm:ss.SSS + 9999 Ticks
     */ 
    public String getElapsed() {
        String timeFormatted = "";
        timeFormatted = this.formatTime(this.getElapsedTicks());        
        return timeFormatted;
    }
    
    /**
     * Gets the total elapsed time with format 
     * 00:00:00.0000000 = 00:mm:ss.SSS + #### Ticks
     * @param elapsedTicks elapsed ticks between start and stop nano time
     */ 
    private String formatTime(final long elapsedTicks) {        
        String formattedTime = "";
        // should be hh:mm:ss.SSS, but 00 starts with 01 
        SimpleDateFormat formatter = new SimpleDateFormat("00:mm:ss.SSS");
        Calendar calendar = Calendar.getInstance();        
        
        if (elapsedTicks <= 9999) {
            calendar.setTimeInMillis(0);
            formattedTime = formatter.format(calendar.getTime()) 
                    + String.valueOf(String.format("%04d", elapsedTicks));
        }
        else {
            calendar.setTimeInMillis(elapsedTicks * nsPerTick / nsPerMs);            
            String formattedTicks = String.format("%07d", elapsedTicks);
            formattedTicks = formattedTicks.substring(formattedTicks.length() - 4);
            formattedTime = formatter.format(calendar.getTime()) + formattedTicks;
        }
        return formattedTime;
    }
}


If we add that class in any Java project, we can now do what the C# code at the beginning of this post does! Let's see the Java version of the code:

package stopwatchapp;
import java.math.BigInteger;

public class StopwatchApp {

    public static void main(String[] args) {
        
        Stopwatch timer = new Stopwatch();
        timer.start();
        Fibonacci(50);
        timer.stop();
        
        System.out.println("Elapsed time in ticks: " 
            + timer.getElapsedTicks());
        System.out.println("Elapsed time in milliseconds: " 
            + timer.getElapsedMilliseconds());
        System.out.println("Elapsed time in seconds: " 
            + timer.getElapsedSeconds());
        System.out.println("Elapsed time in minutes: " 
            + timer.getElapsedMinutes());
        System.out.println("Elapsed time in hours: " 
            + timer.getElapsedHours());
        System.out.println("Elapsed time with format: " 
            + timer.getElapsed());
    }
    
    private static BigInteger Fibonacci(int n)
    {
        if (n < 2)
            return BigInteger.ONE;
        else
            return Fibonacci(n - 1).add(Fibonacci(n - 2));
    }
}


And the Output is:















That's it! now I'm ready to work on the next posts using this java timer class. Hope it is helpful to you too since I found lot's of forums asking for it and the answer was always use: System.nanoTime() and System.currentTimeMillis()

By the way, if you want to run the example, change Fibonacci(50) to a lower value such as Fibonacci(35 or 40) to not wait for the result some minutes.

Factorial and Fibonacci in Java



Here below a little program in Java that implements 2 classes (in fact, they are 3 + an extra utility Stopwatch class from my previous post http://carlosqt.blogspot.com/2011/05/stopwatch-class-for-java.html). There is the main class, called Fiborial (Fibo(nnacci)+(Facto)rial) that implements the Fibonacci and the Factorial algorithms in two ways, one Recursive (using recursion) and the other Imperative (using loops and states). The second class is just an instance class that does the same thing, but its there just to show the difference between static and instance classes, and finally the third one (which will not appear in other languages) is the Program class which has the static execution method "main".

You can also find 3 more little examples at the bottom. One prints out the Factorial's Series and Fibonacci's Series, the second one just shows a class that mixes both: static and instance members, and finally the third one that uses different return types (including java.math.BigInteger) for the Factorial method to compare the timing and result.

As with the previous posts, you can copy and paste the code below in your favorite IDE/Editor and start playing and learning with it. This little "working" program will teach you some more basics of the Programming Language.

There are some "comments" on the code added just to tell you what are or how are some features called. In case you want to review the theory, you can read my previous post, where I give a definition of each of the concepts mentioned on the code. You can find it here: http://carlosqt.blogspot.com/2011/01/new-series-factorial-and-fibonacci.html 


The Fiborial Program

// Factorial and Fibonacci in Java
package fiborial;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.List;

// Instance Class         
// static is not a class modifier in Java
public class StaticFiborial
{  
    // Static Field  
    private static String className;  
    // Static Constructor/Initializer
    static
    {  
        className = "Static Constructor";  
        System.out.println(className);        
    }  
    // Static Method - Factorial Recursive  
    public static BigInteger factorialR(int n)  
    {  
        if (n == 1)  
            return BigInteger.ONE;
        else  
            return BigInteger.valueOf(n).multiply(factorialR(n - 1));
    }  
    // Static Method - Factorial Imperative  
    public static BigInteger factorialI(int n)  
    {  
        BigInteger res = BigInteger.ONE;  
        for (int i = n; i >= 1; i--)  
        {                  
            res = res.multiply(BigInteger.valueOf(i));  
        }  
        return res;
    }  
    // Static Method - Fibonacci Recursive  
    public static long fibonacciR(int n)  
    {  
        if (n < 2)  
            return 1;  
        else  
            return fibonacciR(n - 1) + fibonacciR(n - 2);  
    }  
    // Static Method - Fibonacci Imperative  
    public static long fibonacciI(int n)  
    {              
        long pre, cur, tmp = 0;  
        pre = cur = 1;              
        for (int i = 2; i <= n; i++)  
        {  
            tmp = cur + pre;  
            pre = cur;  
            cur = tmp;  
        }  
        return cur;  
    }      
    // Static Method - Benchmarking Algorithms  
    public static void benchmarkAlgorithm(int algorithm, List<Integer> values)  
    {              
        Stopwatch timer = new Stopwatch();  
        int i, testValue;  
        BigInteger facTimeResult = BigInteger.valueOf(0);  
        long fibTimeResult = 0;  
        i = testValue = 0;              
          
        // "Switch" Flow Control Statement  
        switch (algorithm)  
        {  
            case 1:  
                System.out.println("\nFactorial Imperative:");  
                // "For" Loop Statement  
                for (i = 0; i < values.size(); i++)  
                {                          
                    testValue = ((Integer)values.get(i)).intValue();  
                    // Taking Time  
                    timer.start();  
                    facTimeResult = factorialI(testValue);  
                    timer.stop();                          
                    // Getting Time  
                    System.out.println(" (" + testValue + ") = " 
                        + timer.getElapsed());  
                }                      
                break;  
            case 2:  
                System.out.println("\nFactorial Recursive:");  
                // "While" Loop Statement  
                while (i < values.size())  
                {                          
                    testValue = ((Integer)values.get(i)).intValue();  
                    // Taking Time  
                    timer.start();  
                    facTimeResult = factorialR(testValue);  
                    timer.stop();  
                    // Getting Time  
                    System.out.println(" (" + testValue + ") = " 
                        + timer.getElapsed());  
                    i++;  
                }  
                break;  
            case 3:  
                System.out.println("\nFibonacci Imperative:");  
                // "Do-While" Loop Statement  
                do {  
                    testValue = ((Integer)values.get(i)).intValue();  
                    // Taking Time  
                    timer.start();  
                    fibTimeResult = fibonacciI(testValue);  
                    timer.stop();  
                    // Getting Time  
                    System.out.println(" (" + testValue + ") = " 
                        + timer.getElapsed());  
                    i++;  
                } while (i < values.size());  
                break;  
            case 4:  
                System.out.println("\nFibonacci Recursive:");  
                // "For Each" Loop Statement  
                for (Integer item : values)  
                {  
                    testValue = item;  
                    // Taking Time  
                    timer.start();  
                    fibTimeResult = fibonacciR(testValue);  
                    timer.stop();  
                    // Getting Time  
                    System.out.println(" (" + testValue + ") = " 
                        + timer.getElapsed());  
                }  
                break;  
            default:  
                System.out.println("DONG!");  
                break;  
        }                  
    }  
}

package fiborial;
import java.math.BigInteger;
// Instance Class  
public class InstanceFiborial  
{  
    // Instance Field  
    private String className;  
    // Instance Constructor  
    public InstanceFiborial()  
    {  
        this.className = "Instance Constructor";  
        System.out.println(this.className);
    }  
    // Instance Method - Factorial Recursive  
    public BigInteger factorialR(int n)  
    {  
        // Calling Static Method  
        return StaticFiborial.factorialR(n);  
    }  
    // Instance Method - Factorial Imperative  
    public BigInteger factorialI(int n)  
    {  
        // Calling Static Method  
        return StaticFiborial.factorialI(n);  
    }  
    // Instance Method - Fibonacci Recursive  
    public long fibonacciR(int n)  
    {  
        // Calling Static Method  
        return StaticFiborial.fibonacciR(n);  
    }  
    // Instance Method - Factorial Imperative  
    public long fibonacciI(int n)  
    {  
        // Calling Static Method  
        return StaticFiborial.fibonacciI(n);  
    }  
}

package fiborial;
import java.util.Scanner; 
import java.util.ArrayList;
import java.util.List;

public class StaticFiborialProgram 
{
    public static void main(String[] args)
    {
        System.out.println("\nStatic Class");  
        // Calling Static Class and Methods  
        // No instantiation needed. Calling method directly from the class  
        System.out.println("FacImp(5) = " + StaticFiborial.factorialI(5));  
        System.out.println("FacRec(5) = " + StaticFiborial.factorialR(5));  
        System.out.println("FibImp(11)= " + StaticFiborial.fibonacciI(11));  
        System.out.println("FibRec(11)= " + StaticFiborial.fibonacciR(11));  

        System.out.println("\nInstance Class");  
        // Calling Instance Class and Methods   
        // Need to instantiate before using. Calling method from instantiated object  
        InstanceFiborial ff = new InstanceFiborial();  
        System.out.println("FacImp(5) = " + ff.factorialI(5));  
        System.out.println("FacRec(5) = " + ff.factorialR(5));  
        System.out.println("FibImp(11)= " + ff.fibonacciI(11));  
        System.out.println("FibRec(11)= " + ff.fibonacciR(11));  

        // Create a (generic) list of integer values to test  
        // From 5 to 50 by 5  
        List<Integer> values = new ArrayList<Integer>();  
        for(int i = 5; i <= 50; i += 5)  
            values.add(i);  

        // Benchmarking Fibonacci                       
        // 1 = Factorial Imperative              
        StaticFiborial.benchmarkAlgorithm(1, values);  
        // 2 = Factorial Recursive  
        StaticFiborial.benchmarkAlgorithm(2, values);   

        // Benchmarking Factorial              
        // 3 = Fibonacci Imperative  
        StaticFiborial.benchmarkAlgorithm(3, values);  
        // 4 = Fibonacci Recursive  
        StaticFiborial.benchmarkAlgorithm(4, values);   

        // Stop and exit  
        System.out.println("Press any key to exit...");  
        Scanner in = new Scanner(System.in);  
        String line = in.nextLine();  
        in.close();  
    }
}

And the Output is:




Printing the Factorial and Fibonacci Series
package fiborialseries;
import java.math.BigInteger;
import java.lang.StringBuffer;

class Fiborial
{
    // Using a StringBuffer as a list of string elements
    public static String getFactorialSeries(int n)
    {
        // Create the String that will hold the list
        StringBuffer series = new StringBuffer();
        // We begin by concatenating the number you want to calculate
        // in the following format: "!# ="
        series.append("!");
        series.append(n);
        series.append(" = ");
        // We iterate backwards through the elements of the series
        for (int i = n; i <= n && i > 0; i--)
        {
            // and append it to the list
            series.append(i);
            if (i > 1)
                series.append(" * ");
            else 
                series.append(" = "); 
        }
        // Get the result from the Factorial Method
        // and append it to the end of the list
        series.append(factorial(n));
        // return the list as a string
        return series.toString();
    }

    // Using a StringBuffer as a list of string elements
    public static String getFibonnaciSeries(int n)
    {
        // Create the String that will hold the list
        StringBuffer series = new StringBuffer();
        // We begin by concatenating the first 3 values which
        // are always constant
        series.append("0, 1, 1");
        // Then we calculate the Fibonacci of each element
        // and add append it to the list
        for (int i = 2; i <= n; i++)
        {
            if (i < n)
                series.append(", ");
            else
                series.append(" = ");
            
            series.append(fibonacci(i));
        }
        // return the list as a string
        return series.toString();
    }

    public static BigInteger factorial(int n)
    {
        if (n == 1)  
            return BigInteger.ONE;
        else  
            return BigInteger.valueOf(n).multiply(factorial(n - 1));
    }        

    public static long fibonacci(int n)
    {
        if (n < 2)  
            return 1;  
        else  
            return fibonacci(n - 1) + fibonacci(n - 2);  
    }   
}

package fiborialseries;

class FiborialExtrasProgram
{    
    public static void main(String[] args) 
    {            
        // Printing Factorial Series
        System.out.println("");
        System.out.println(Fiborial.getFactorialSeries(5));
        System.out.println(Fiborial.getFactorialSeries(7));
        System.out.println(Fiborial.getFactorialSeries(9));
        System.out.println(Fiborial.getFactorialSeries(11));
        System.out.println(Fiborial.getFactorialSeries(40));
        // Printing Fibonacci Series
        System.out.println("");
        System.out.println(Fiborial.getFibonnaciSeries(5));
        System.out.println(Fiborial.getFibonnaciSeries(7));
        System.out.println(Fiborial.getFibonnaciSeries(9));
        System.out.println(Fiborial.getFibonnaciSeries(11));
        System.out.println(Fiborial.getFibonnaciSeries(40));
    }
}

And the Output is:

















Mixing Instance and Static Members in the same Class

Instance classes can contain both, instance and static members such as: fields, getters/setters, constructors/initializers, methods, etc.

package fiborialextrasjava2;

// Instance Class  
class Fiborial  
{  
    // Instance Field  
    private int instanceCount;  
    // Static Field  
    private static int staticCount;          
    // Instance Read-Only Getter  
    // Within instance members, you can always use    
    // the "this" reference pointer to access your (instance) members.  
    public int getInstanceCount()
    {  
        return this.instanceCount;   
    }  
    // Static Read-Only Getter      
    // As with Static Methods, you cannot reference your class members  
    // with the "this" reference pointer since static members are not  
    // instantiated.          
    public static int getStaticCount()
    {  
        return staticCount;  
    }  
    // Instance Constructor  
    public Fiborial()  
    {  
        this.instanceCount = 0;  
        System.out.println("\nInstance Constructor " + this.instanceCount); 
    }  
    // Static Constructor  
    static
    {  
        staticCount = 0;  
        System.out.println("\nStatic Constructor " + staticCount);  
    }  

    // Instance Method  
    public void factorial(int n)  
    {  
        this.instanceCount += 1;  
        System.out.println("\nFactorial(" + n + ")");  
    }  

    // Static Method  
    public static void fibonacci(int n)  
    {  
        staticCount += 1;  
        System.out.println("\nFibonacci(" + n + ")");  
    }                  
}

package fiborialextrasjava2;

class FiborialExtras2Program
{    
    public static void main(String[] args) 
    {            
        // Calling Static Constructor and Methods  
        // No need to instantiate  
        Fiborial.fibonacci(5);              

        // Calling Instance Constructor and Methods  
        // Instance required  
        Fiborial fib = new Fiborial();  
        fib.factorial(5);              

        Fiborial.fibonacci(15);              
        fib.factorial(5);  

        // Calling Instance Constructor and Methods  
        // for a second object  
        Fiborial fib2 = new Fiborial();  
        fib2.factorial(5);  
          
        System.out.println("");
        // Calling Static Property  
        System.out.println("Static Count = " + Fiborial.getStaticCount());  
        // Calling Instance Property of object 1 and 2  
        System.out.println("Instance 1 Count = " + fib.getInstanceCount());  
        System.out.println("Instance 2 Count = " + fib2.getInstanceCount());          
    }
}

And the Output is:























Factorial using java.lang.Long, java.lang.Double, java.math.BigInteger


package fiborialextrasjava3;
import java.math.BigInteger;

class FiborialExtrasProgram
{    
    public static void main(String[] args) 
    {            
        Stopwatch timer = new Stopwatch();  
        long facIntResult = 0;  
        double facDblResult = 0;  
        BigInteger facBigResult = BigInteger.valueOf(0);  

        System.out.println("\nFactorial using Int64");
        // Benchmark Factorial using Int64  
        for (int i = 5; i <= 50; i += 5)  
        {  
            timer.start();  
            facIntResult = factorialInt64(i);  
            timer.stop();  
            System.out.println(" (" + i + ") = " 
                + timer.getElapsed() + " : " + facIntResult);
        }  
        System.out.println("\nFactorial using Double");  
        // Benchmark Factorial using Double  
        for (int i = 5; i <= 50; i += 5)  
        {  
            timer.start();  
            facDblResult = factorialDouble(i);  
            timer.stop();              
            System.out.println(" (" + i + ") = " 
                + timer.getElapsed() + " : " + facDblResult);
        }  
        System.out.println("\nFactorial using BigInteger");  
        // Benchmark Factorial using BigInteger  
        for (int i = 5; i <= 50; i += 5)  
        {  
            timer.start();  
            facBigResult = factorialBigInteger(i);  
            timer.stop();  
            System.out.println(" (" + i + ") = " 
                + timer.getElapsed() + " : " + facBigResult);
        }          
    }
    
    // Long Factorial  
    public static long factorialInt64(int n)  
    {  
        if (n == 1)  
            return 1;
        else  
            return n * factorialInt64(n - 1);
    }
    
    // Double Factorial
    public static double factorialDouble(int n)  
    {  
        if (n == 1)  
            return 1;
        else  
            return n * factorialDouble(n - 1);
    }
    
    // BigInteger Factorial 
    public static BigInteger factorialBigInteger(int n)  
    {  
        if (n == 1)  
            return BigInteger.ONE;
        else  
            return BigInteger.valueOf(n).multiply(factorialBigInteger(n - 1));
    }
}



And the Output is: