Java Program to Print Pascal’s Triangle

20 Apr, 2022
Pascal’s triangle is a pattern of the triangle which is based on nCr.below is the pictorial representation of Pascal’s triangle.
Example:
Input : N = 5
Output:
          1
        1   1
      1   2   1
    1   3   3   1
  1   4   6   4   1
Approach #1: 
nCr formula:
 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) //it’s 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 Javaimport 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++) {                 // for left spacing                System.out.print(" ");            }            for (j = 0; j <= i; j++) {                 // nCr formula                System.out.print(                    " "                    + g.factorial(i)                          / (g.factorial(i - j)                             * g.factorial(j)));            }             // for newline            System.out.println();        }    }}
      1
     1 1
    1 2 1
   1 3 3 1
  1 4 6 4 1
Time Complexity: O(N2)
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
Below is the Implementation of given approach:
Java
// Print Pascal's Triangle in Javaimport java.io.*;class GFG {     // Pascal function    public static void printPascal(int n)    {        for (int line = 1; line <= n; line++) {            for (int j = 0; j <= n - line; j++) {                 // for left spacing                System.out.print(" ");            }             // used to represent C(line, i)            int C = 1;            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);    }}
    1 
   1 1 
  1 2 1 
 1 3 3 1 
Time Complexity: O(N2)
pradiptamukherjee
kvenketeshdora
Technical Scripter 2020
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