Java Program to Print Pascal's Triangle

Java Program to Print Pascal’s Triangle

Last Updated : 20 Nov, 2020

Pascal’s triangle is a pattern of triangle which is based on nCr.below is the pictorial representation of a pascal’s triangle.

Example:

Input : N = 5
Output:
          1
        1   1
      1   2   1
    1   3   3   1
  1   4   6   4   1
1   5   10   10   5   1

Approach #1:

nCr formula ie- n!/(n-r)!r!

After using nCr formula, the pictorial representation becomes-

           0C0
        1C0   1C1
     2C0   2C1   2C2
  3C0   3C1   3C2   3C3

Algorithm:

Take a number of rows to be printed, assume it to be n
Make outer iteration i from 0 to n times to print the rows.
Make inner iteration for j from 0 to (N – 1).
Print single blank space ” “
Close inner loop (j loop) //its needed for left spacing
Make inner iteration for j from 0 to i.
Print nCr of i and j.
Close inner loop.
Print newline character (\n) after each inner iteration.

Below is the implementation of the above approach:

Java

// Print Pascal's Triangle in Java 
import java.io.*; 
  
class GFG { 
    public int factorial(int i) 
    { 
        if (i == 0) 
            return 1; 
        return i * factorial(i - 1); 
    } 
    public static void main(String[] args) 
    { 
        int n = 4, i, j; 
        GFG g = new GFG(); 
        for (i = 0; i <= n; i++) { 
            for (j = 0; j <= n - i; j++) { 
                System.out.print(" "); // for left spacing 
            } 
            for (j = 0; j <= i; j++) { 
                // nCr formula 
                System.out.print( 
                    " "
                    + g.factorial(i) 
                          / (g.factorial(i - j) 
                             * g.factorial(j))); 
            } 
            System.out.println(); // for newline 
        } 
    } 
}

Output

Time Complexity: O(N³)

Approach #2:

i’th entry in a line number line is Binomial Coefficient C(line, i) and all lines start with value 1. The idea is to calculate C(line, i) using C(line, i-1).

C(line, i) = C(line, i-1) * (line - i + 1) / i

Implementation:

Java

// Print Pascal's Triangle in Java 
import java.io.*; 
class GFG { 
  
    // Pascal function 
    public static void printPascal(int n) 
    { 
        for (int line = 1; line <= n; line++) { 
  
            int C = 1; // used to represent C(line, i) 
            for (int i = 1; i <= line; i++) { 
                // The first value in a line is always 1 
                System.out.print(C + " "); 
                C = C * (line - i) / i; 
            } 
            System.out.println(); 
        } 
    } 
  
    // Driver code 
    public static void main(String[] args) 
    { 
        int n = 4; 
        printPascal(n); 
    } 
}

Output

Time Complexity: O(N²)

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