Create TriangularNumberCheck.js

chrdek · web-flow · commit 9539ec046236 · 2023-10-06T16:27:03.000+03:00
diff --git a/Maths/TriangularNumberCheck.js b/Maths/TriangularNumberCheck.js
@@ -0,0 +1,39 @@
+/**
+ *   github author: chrdek
+ *   license: GPL-3.0 or later
+ *
+ *   @param {number} n = number to be determined whether is a triangular or not
+ *   
+ *   The function below is a mathematical algorithm to check if a given number n is a triangular number.
+ *   A triangular number is one that can be represented 
+ *   in the form of the sum of consecutive positive integers starting from 1.
+ *
+ *   Returns -1 for error input or negative numerical input, 0 for non-triangular
+ *   and an integer value if the number is triangular.
+ *   
+ *   The variable discriminant is calculated as the square root of (1 + 8 * n) and then its square root is taken again.
+ *   The expression Math.sqrt(1 + 8 * n) is the discriminant of the quadratic equation that represents triangular numbers.
+ *   
+ **/
+
+function IsTriangularNumber(n) {
+  // Ensure the input n is a non-negative integer, retrurn -1 to indicate error.
+  if (!Number.isInteger(n) || n < 0) {
+    return -1;
+    }
+
+  // Calculate the discriminant of the quadratic equation
+  const discriminant = Math.sqrt(1 + 8 * n);
+
+  // Check if the discriminant is an integer
+  if (discriminant % 1 === 0) {
+
+    // Return half of the integer value of the discriminant
+    return Math.floor(discriminant / 2);
+    } else {
+    // If not a triangular number, return 0
+    return 0;
+  }
+}
+
+export { IsTriangularNumber }
