Pascals triangle

Java/projects/games/PascalsTriangle.java

@@ -0,0 +1,38 @@
+/**
+ * Pascal's Triangle Row Generator
+ *
+ * Description: Generates the nth row of Pascal's Triangle using the 
+ * combinatorial formula nCr = n! / (r! * (n-r)!).
+ *
+ * Time Complexity: O(n^2) in worst case for computing factorial-based combinations.
+ * Space Complexity: O(n) - stores the nth row in a list.
+ */
+
+import java.util.*;
+class PascalsTriangle {
+    public static void main(String[] args) {
+        int n = 5; 
+        List<Integer> list = new ArrayList<>();
+
+        for (int c = 1; c <= n; c++) {
+            list.add(nCr(n - 1, c - 1));
+        }
+        System.out.println(list.toString());
+    }
+
+    /**
+     * Computes nCr (combinations) using an iterative approach to avoid large factorials.
+     *
+     * @param r Total items (n-1 for zero-based row)
+     * @param c Items chosen (c-1 for zero-based column)
+     * @return The value of nCr
+     */
+    static int nCr(int r, int c) {
+        int result = 1;
+        for (int i = 0; i < c; i++) {
+            result = result * (r - i);
+            result = result / (i + 1);
+        }
+        return result;
+    }
+}