Generating Pascal's Triangle

Blaise Pascal (AD 1623 - 1662 )

In this program, we'll be generating the below number-triangle:

Pascal's Triangle

Known as Pascal's Triangle, it's a triangular array of Binomial Coefficients named after Blaise Pascal,  a French mathematician, physicist, inventor, writer and Catholic philosopher (a Jansenist apologist, to be precise), which he described in his book Traité du triangle arithmétique of 1653.


File: PascalTriangle.java


We first write a class called BinomialCoefficient for computing the Binomial Coefficient (inclusive of the Factorial class) as:



class Factorial {
static long factorial (byte i)
{
if(i == 0 || i == 1)
return (long) 1;
else 
return (long) i * factorial((byte) (i - 1));
}
}


class BinomialCoefficient {
static long binomialCoefficient(byte n, byte r){
long binCoeff = 0;

binCoeff = (long) (Factorial.factorial(n))/
(Factorial.factorial(r) * Factorial.factorial((byte) (n - r)));

return (long) binCoeff;
}
}

Next we invoke it in the PascalTriangle class below it as:

public class PascalTriangle {

public static void main(String[] args) {

 
  byte numberOfRows = 15;

String[] sumOfBinomialCoefficients = new String[numberOfRows] ;

System.out.println();

for(byte rowIndex = 0;rowIndex < numberOfRows;rowIndex++)

{

sumOfBinomialCoefficients[rowIndex] = "";

for(byte columnIndex = 0;columnIndex <= rowIndex;columnIndex++)

{

  sumOfBinomialCoefficients[rowIndex] +=  
     BinomialCoefficient.binomialCoefficient
     (rowIndex,columnIndex) + " ";

}

}

for(byte rowIndex = 0;rowIndex < numberOfRows;rowIndex++)

{

for(long padding = 0;padding < 
      (sumOfBinomialCoefficients[numberOfRows - 1].length() -    
      sumOfBinomialCoefficients[rowIndex].length())/2;padding++)

{

System.out.print(" ");

}

for(byte columnIndex = 0;columnIndex <= rowIndex; columnIndex++)

{

System.out.print(BinomialCoefficient.binomialCoefficient
    (rowIndex,columnIndex) + " ");

}

System.out.println();

}

}

}


A little note first: I pasted the program written in Eclipse IDE in a notepad and saved it inside the Java Programs folder in drive C:\. I'll be running the program in the Command-Line Interface. 

Here, I've displayed the triangle upto 15 rows. If you want more number of rows, just assign it to the numberOfRows variable. The output is as: