From d5a4ebe8913bcac698db5e16ec31054850a7dd96 Mon Sep 17 00:00:00 2001
From: sarthakgupta1907-cell <sarthakgupta1907@gmail.com>
Date: Sat, 7 Nov 2026 18:07:16 +0530
Subject: [PATCH] feat: add Bell number algorithm

---
 Maths/BellNumber.js           | 28 +++++++++++++++++++++
 Maths/test/BellNumber.test.js | 47 +++++++++++++++++++++++++++++++++++
 2 files changed, 75 insertions(+)
 create mode 100644 Maths/BellNumber.js
 create mode 100644 Maths/test/BellNumber.test.js

diff --git a/Maths/BellNumber.js b/Maths/BellNumber.js
new file mode 100644
index 0000000000..f82a439968
--- /dev/null
+++ b/Maths/BellNumber.js
@@ -0,0 +1,28 @@
+/**
+ * @function bellNumber
+ * @description Bell numbers count the number of ways to partition a set.
+ *   They are computed using Bell triangle.
+ *   Sequence: 1, 1, 2, 5, 15, 52, 203, 877...
+ * @param {number} n - The position in the Bell sequence (0-indexed)
+ * @returns {number} - The nth Bell number
+ * @see https://en.wikipedia.org/wiki/Bell_number
+ * @example bellNumber(0) => 1
+ * @example bellNumber(3) => 5
+ * @example bellNumber(5) => 52
+ */
+const bellNumber = (n) => {
+  if (!Number.isInteger(n) || n < 0) {
+    throw new TypeError('Input must be a non-negative integer')
+  }
+  const triangle = [[1]]
+  for (let i = 1; i <= n; i++) {
+    const row = [triangle[i - 1][i - 1]]
+    for (let j = 1; j <= i; j++) {
+      row.push(row[j - 1] + triangle[i - 1][j - 1])
+    }
+    triangle.push(row)
+  }
+  return triangle[n][0]
+}
+
+export { bellNumber }
diff --git a/Maths/test/BellNumber.test.js b/Maths/test/BellNumber.test.js
new file mode 100644
index 0000000000..17305f6ca0
--- /dev/null
+++ b/Maths/test/BellNumber.test.js
@@ -0,0 +1,47 @@
+import { bellNumber } from '../BellNumber.js'
+
+describe('bellNumber', () => {
+  test('bellNumber(0) returns 1', () => {
+    expect(bellNumber(0)).toBe(1)
+  })
+
+  test('bellNumber(1) returns 1', () => {
+    expect(bellNumber(1)).toBe(1)
+  })
+
+  test('bellNumber(2) returns 2', () => {
+    expect(bellNumber(2)).toBe(2)
+  })
+
+  test('bellNumber(3) returns 5', () => {
+    expect(bellNumber(3)).toBe(5)
+  })
+
+  test('bellNumber(4) returns 15', () => {
+    expect(bellNumber(4)).toBe(15)
+  })
+
+  test('bellNumber(5) returns 52', () => {
+    expect(bellNumber(5)).toBe(52)
+  })
+
+  test('bellNumber(6) returns 203', () => {
+    expect(bellNumber(6)).toBe(203)
+  })
+
+  test('bellNumber(7) returns 877', () => {
+    expect(bellNumber(7)).toBe(877)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => bellNumber(-1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => bellNumber(1.5)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for string input', () => {
+    expect(() => bellNumber('3')).toThrow(TypeError)
+  })
+})