My Commit for the Issue #2864 Pascal's Triangle

TheAlgorithms · siriak · Dec 13, 2021 · Dec 10, 2021 · Dec 11, 2021 · Dec 11, 2021
commit d950cd3f7d1617842fc218d882b6fb195cde55e4
@@ -0,0 +1,73 @@
+package com.thealgorithms.maths;
+
+import java.util.Scanner;
+public class PascalTriangle {
+    /**
+     *In mathematics, Pascal's triangle is a triangular array of the binomial coefficients that arises
+     * in probability theory, combinatorics, and algebra. In much of the Western world, it is named after
+     * the French mathematician Blaise Pascal, although other mathematicians studied it centuries before
+     * him in India, Persia, China, Germany, and Italy.
+     *
+     * The rows of Pascal's triangle are conventionally enumerated starting with row n=0 at the top (the 0th row).
+     * The entries in each row are numbered from the left beginning with k=0 and are usually staggered relative
+     * to the numbers in the adjacent rows. The triangle may be constructed in the following manner:
+     * In row 0 (the topmost row), there is a unique nonzero entry 1. Each entry of each subsequent row is
+     * constructed by adding the number above and to the left with the number above and to the right, treating
+     * blank entries as 0. For example, the initial number in the first (or any other) row is 1 (the sum of 0 and 1),
+     * whereas the numbers 1 and 3 in the third row are added to produce the number 4 in the fourth row. *
+     *
+     *<p>
+     *     link:-https://en.wikipedia.org/wiki/Pascal%27s_triangle
+     *
+     * <p>
+     *     Example:-
+     *                  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
+     *  1   8  28  56  70   56   28  8   1
+     *
+     */
+
+    public static void main (String[] args) {
+        Scanner sc = new Scanner(System.in);
+        int n = sc.nextInt();
+        printPascal(n);
+    }
+
+    public static void printPascal(int n)
+    {
+        /**
+         * @param arr  An auxiliary array to store generated pascal triangle values
+         * @return
+         */
+        int[][] arr = new int[n][n];
+
+
+        /**
+         * @param line Iterate through every line and print integer(s) in it
+         * @param i Represents the column number of the element we are currently on
+         */
+        for (int line = 0; line < n; line++)
+        {
+            /**
+             *  @Every line has number of integers equal to line number
+             */
+            for (int i = 0; i <= line; i++)
+            {
+                // First and last values in every row are 1
+                if (line == i || i == 0)
+                    arr[line][i] = 1;
+                    // The rest elements are sum of values just above and left of above
+                else
+                    arr[line][i] = arr[line-1][i-1] + arr[line-1][i];
+                System.out.print(arr[line][i]+" ");
+            }
+            System.out.println();
+        }
+    }
+}