BAEL-5919-java-print-pascal-triangle (#13155)

* pascal triangle

* pascal triangle

Co-authored-by: tienvn4 <tienvn4@ghtk.co>

core-java-modules/core-java-lang-math-3/src/main/java/com/baeldung/math/pascaltriangle/PascalTriangle.java

@@ -0,0 +1,48 @@
+package com.baeldung.math.pascaltriangle;
+
+public class PascalTriangle {
+
+    public static int factorial(int i) {
+        if (i == 0) {
+            return 1;
+        }
+        return i * factorial(i - 1);
+    }
+
+    private static void printUseRecursion(int n) {
+        for (int i = 0; i <= n; i++) {
+            for (int j = 0; j <= n - i; j++) {
+                System.out.print(" ");
+            }
+
+            for (int k = 0; k <= i; k++) {
+                System.out.print(" " + factorial(i) / (factorial(i - k) * factorial(k)));
+            }
+
+            System.out.println();
+        }
+    }
+
+public static void printUseBinomialExpansion(int n) {
+    for (int line = 1; line <= n; line++) {
+        for (int j = 0; j <= n - line; j++) {
+            System.out.print(" ");
+        }
+
+        int k = 1;
+        for (int i = 1; i <= line; i++) {
+            System.out.print(k + " ");
+            k = k * (line - i) / i;
+        }
+
+        System.out.println();
+    }
+}
+
+    public static void main(String[] args) {
+        int n = 5;
+        printUseRecursion(n);
+//        printUseBinomialExpansion(n);
+    }
+
+}