Pascal's triangle positioning

Question

I made a Java program that prints out a pascal triangle, however I can't figure out how to correctly position it.

Program 1

public class Triangle {
    public static void main() {
        System.out.println("\nTriangle: ");
        int row = 11;
        long[][] triangle = new long[row][row];
        triangle[1][1] = 1;
        System.out.print(triangle[1][1] + "\n");

        for (int i = 2; i < row; i++) {
            for (int n = 1; n < row; n++) {
                triangle[i][n] = triangle[i-1][n-1] + triangle[i-1][n];
                if (triangle[i][n] > 0) {
                    System.out.print(triangle[i][n] + " ");
                }
            }
            System.out.println();
        }
    }
}

Output:

1
1 1 
1 2 1 
1 3 3 1 

Program 2

public class Triangle {
    public static void main() {
        System.out.println("\nTriangle: ");
        int row = 11;
        long[][] triangle = new long[row][row];
        int x = 1;
        while (x < row - 1) {
            System.out.print(" ");
            x++;
        }
        triangle[1][1] = 1;
        System.out.print(triangle[1][1] + "\n");

        for (int i = 2; i < row; i++) {
            x = i;
            while (x < row - 1) {
                System.out.print(" ");
                x++;
            }
            for (int n = 1; n < row; n++) {
                triangle[i][n] = triangle[i-1][n-1] + triangle[i-1][n];
                if (triangle[i][n] > 0) {
                    System.out.print(triangle[i][n] + " ");
                }
            }
            System.out.println();
        }
    }
}

Output:

     1
    1 1 
   1 2 1 
  1 3 3 1 
 1 4 6 4 1 
1 5 10 10 5 1 //(Notice this line is incorrectly positioned)

When the triangle approaches multiple digit numbers, it starts to break down and makes it ugly. Can someone explain how I can display a normal triangle instead of this ugly one?

Answer 1

Dynamic Pascal Triangle generator is here:

import java.io.IOException;
import java.util.Scanner;

public class Main {
    static double fact(int n) {
        double result = 1;
        for (double i = 1; i <= n; i++)
            result *= i;
        return result;
    }

    static double combine(int n, int r) {
        return ((fact(n)) / (fact(n - r) * fact(r)));
    }

    static void pascalTriangle(int n) {
        int n2 = n;
        for (int i = 0; i < n; i++) {
            for (int space = 8 * (n2 - 1); space >= 0; space--) {
                System.out.printf(" ");
            }
            for (int j = 0; j <= i; j++) {
                System.out.printf("%14.0f", combine(i, j));
                System.out.printf("  ");
            }
            System.out.println();
            n2--;
        }
    }

    public static void main(String[] args)
            throws IOException, InterruptedException {
        @SuppressWarnings("resource")
        Scanner sc = new Scanner(System.in);

        System.out.print("Enter Number of Lines(n): ");
        int n = sc.nextInt();
        pascalTriangle(n);
        System.out.println("Press any key to exit! ");
        sc.nextByte();
    }
}

Answer 2

/**
 * @author Ranjith
 */
public class JavaApplication2 {
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        int i;
        int x;
        int n = 15; //number of rows
        String newLine = System.getProperty("line.separator");
        for (i = 0; i < n; i++) { //loop to adjust spacing
            x = i;
            while (x < n - 1) {
                System.out.print(" ");
                x++;
            }
            fib(i); //fibonacci function is called
            System.out.print(newLine);
        }
    }
    public static void fib(int num) { //fibonacci function
        int[] febo = new int[100];
        febo[0] = 0;
        febo[1] = 1;
        for (int i = 2; i < num; i++) {
            febo[i] = febo[i - 1] + febo[i - 2];
        }
        for (int i = 0; i < num; i++) {
            System.out.print(febo[i] + "  ");
        }
    }
}

Output:

             0  
            0  1  
           0  1  1  
          0  1  1  2  
         0  1  1  2  3  
        0  1  1  2  3  5  
       0  1  1  2  3  5  8  
      0  1  1  2  3  5  8  13  
     0  1  1  2  3  5  8  13  21  
    0  1  1  2  3  5  8  13  21  34  
   0  1  1  2  3  5  8  13  21  34  55  
  0  1  1  2  3  5  8  13  21  34  55  89  
 0  1  1  2  3  5  8  13  21  34  55  89  144  
0  1  1  2  3  5  8  13  21  34  55  89  144  233  

Answer 3

Try this ...

Results:

1  
1  1  
1  2  1  
1  3  3  1  
1  4  6  4  1  
1  5  10  10  5  1  
1  6  15  20  15  6  1  
1  7  21  35  35  21  7  1 

import java.util.*;
public class HelloWorld {
    static int binCoeff(int n, int k) {
        int res = 1;
        if (k > n - k)
            k = n - k;
        for (int i = 0; i < k; ++i) {
            res *= (n - i);
            res /= (i + 1);
        }
        return res;
    }

    static void pascalTriangle(int lines) {
        for (int i = 0; i < lines; i++) {
            for (int j = 0; j <= i; j++)
                System.out.print(HelloWorld.binCoeff(i, j) + "  ");
            System.out.println();
        }
    }

    public static void main(String[] args) {
        System.out.println("Results: ");
        HelloWorld.pascalTriangle(8);
    }
}

Answer 4

class pascal {
    static void main(int n) {
        int a[][] = new int[n][n + 1];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                a[i][j] = 0;
            }
        }
        a[0][1] = 1;
        int k = 5;
        int p = 0;
        for (int i = 1; i < n; i++) {
            for (int j = 1; j < n + 1; j++) {
                a[i][j] = a[i - 1][j] + a[i - 1][j - 1];
            }
        }
        for (int i = 0; i < a.length; i++) {
            for (p = n + -i; p > 0; p--) {
                System.out.print(" ");
            }
            for (int j = 0; j < a[i].length; j++) {
                if (a[i][j] != 0) {
                    System.out.print(a[i][j] + " ");
                } else {
                    System.out.print(" ");
                }
            }
            System.out.println();
        }
    }
}

Answer 5

You can represent such a triangle as a 2d array, where the elements of the first row and column are equal to one, and all other elements are the sum of the previous element in the row and column.

arr[i][j] = arr[i][j-1] + arr[i-1][j];

Then you can position it in the upper left corner as follows:

 1  1  1  1  1  1  1  1  1 
 1  2  3  4  5  6  7  8 
 1  3  6 10 15 21 28 
 1  4 10 20 35 56 
 1  5 15 35 70 
 1  6 21 56 
 1  7 28 
 1  8 
 1 

Try it online!

public static void main(String[] args) {
    int n = 9;
    // an array of 'n' rows
    int[][] arr = new int[n][];
    // iterate over the rows of the array
    for (int i = 0; i < n; i++) {
        // a row of 'n-i' elements
        arr[i] = new int[n - i];
        // iterate over the elements of the row
        for (int j = 0; j < n - i; j++) {
            if (i == 0 || j == 0) {
                // elements of the first row
                // and column are equal to one
                arr[i][j] = 1;
            } else {
                // all other elements are the sum of the
                // previous element in the row and column
                arr[i][j] = arr[i][j - 1] + arr[i - 1][j];
            }
        }
    }

    // formatted output
    for (int[] row : arr) {
        for (int el : row) {
            // formatting as a number with a trailing space
            System.out.printf("%2d ", el); // two-digit number
            // System.out.printf("%3d ", el); // three-digit number
            // System.out.printf("%4d ", el); // four-digit number
        }
        System.out.println();
    }
}

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^{See also:
• Pascal's triangle 2d array - formatting printed output
• Print Pascal's Triangle}