9808Tarun · Nov 11, 2026
diff --git a/Maths/ModularBinaryExponentiationRecursive.js b/Maths/ModularBinaryExponentiationRecursive.js
@@ -1,21 +1,22 @@
-/*
-  Modified from:
-    https://github.com/TheAlgorithms/Python/blob/master/maths/binary_exp_mod.py
+/**
+ * @function modularBinaryExponentiation
+ * @description Calculate (base^exponent) % mod recursively using binary exponentiation.
+ * @param {number} base
+ * @param {number} exponent
+ * @param {number} mod
+ * @returns {number}
+ */
+const isOddExponent = (exponent) => exponent % 2 !== 0
 
-  Explanation:
-    https://en.wikipedia.org/wiki/Exponentiation_by_squaring
-*/
+const modularBinaryExponentiation = (base, exponent, mod) => {
+  if (mod === 1) return 0
+  if (exponent === 0) return 1
 
-const modularBinaryExponentiation = (a, n, m) => {
-  // input: a: int, n: int, m: int
-  // returns: (a^n) % m: int
-  if (n === 0) {
-    return 1
-  } else if (n % 2 === 1) {
-    return (modularBinaryExponentiation(a, n - 1, m) * a) % m
+  if (isOddExponent(exponent)) {
+    return (base * modularBinaryExponentiation(base, exponent - 1, mod)) % mod
   } else {
-    const b = modularBinaryExponentiation(a, n / 2, m)
-    return (b * b) % m
+    const half = modularBinaryExponentiation(base, exponent / 2, mod)
+    return (half * half) % mod
   }
 }
 

diff --git a/Maths/test/ModularBinaryExponentiationRecursive.test.js b/Maths/test/ModularBinaryExponentiationRecursive.test.js
@@ -5,3 +5,26 @@ describe('modularBinaryExponentiation', () => {
     expect(modularBinaryExponentiation(2, 10, 17)).toBe(4)
   })
 })
+
+import { modularBinaryExponentiation } from '../ModularBinaryExponentiationRecursive'
+
+describe('modularBinaryExponentiation behavior & simplified parity logic (Precondition near line 9 of Maths/ModularBinaryExponentiationRecursive.js)', () => {
+  test('Smallest valid input (base = 2, exponent = 0, mod = 5)', () => {
+    expect(modularBinaryExponentiation(2, 0, 5)).toBe(1)
+  })
+
+  test('Ordinary input (base = 2, exponent = 10, mod = 1000)', () => {
+    // 2^10 = 1024, 1024 % 1000 = 24
+    expect(modularBinaryExponentiation(2, 10, 1000)).toBe(24)
+  })
+
+  test('Boundary input (mod = 1)', () => {
+    expect(modularBinaryExponentiation(5, 3, 1)).toBe(0)
+  })
+
+  test('Equivalence across odd and even exponent evaluations', () => {
+    expect(modularBinaryExponentiation(3, 5, 7)).toBe(5) // 3^5 = 243 % 7 = 5
+    expect(modularBinaryExponentiation(7, 2, 13)).toBe(10) // 7^2 = 49 % 13 = 10
+    expect(modularBinaryExponentiation(10, 4, 100)).toBe(0) // 10^4 = 10000 % 100 = 0
+  })
+})
diff --git a/work/R50-T026/check.py b/work/R50-T026/check.py
@@ -0,0 +1,43 @@
+import os
+import subprocess
+import json
+import sys
+
+def run_checks():
+    work_dir = "work/R50-T026"
+    os.makedirs(work_dir, exist_ok=True)
+
+    # 1. Capture versions
+    node_ver = subprocess.check_output(["node", "-v"]).decode().strip()
+    npm_ver = subprocess.check_output(["npm", "-v"]).decode().strip()
+    with open(f"{work_dir}/versions.json", "w") as f:
+        json.dump({"node": node_ver, "npm": npm_ver}, f, indent=2)
+
+    # 2. Execute test suite
+    cmd = ["npx", "vitest", "run", "Maths/test/ModularBinaryExponentiationRecursive.test.js"]
+    res = subprocess.run(cmd, capture_output=True, text=True)
+
+    if res.returncode != 0:
+        cmd = ["npx", "vitest", "run", "Maths/tests/ModularBinaryExponentiationRecursive.test.js"]
+        res = subprocess.run(cmd, capture_output=True, text=True)
+
+    with open(f"{work_dir}/test_output.log", "w") as f:
+        f.write(res.stdout + "\n" + res.stderr)
+
+    if res.returncode == 0:
+        with open(f"{work_dir}/fixture_results.json", "w") as f:
+            json.dump({
+                "status": "PASSED",
+                "task": "R50-T026",
+                "precondition_line": "Maths/ModularBinaryExponentiationRecursive.js:9",
+                "refactored_responsibility": "Extracted exponent parity evaluation into explicit isOddExponent helper",
+                "smallest_valid_input": {"base": 2, "exponent": 0, "mod": 5, "expected": 1},
+                "ordinary_input": {"base": 2, "exponent": 10, "mod": 1000, "expected": 24}
+            }, f, indent=2)
+        print("All checks passed.")
+    else:
+        print("Tests failed!")
+        sys.exit(1)
+
+if __name__ == "__main__":
+    run_checks()
diff --git a/work/R50-T026/fixture_results.json b/work/R50-T026/fixture_results.json
@@ -0,0 +1,18 @@
+{
+  "status": "PASSED",
+  "task": "R50-T026",
+  "precondition_line": "Maths/ModularBinaryExponentiationRecursive.js:9",
+  "refactored_responsibility": "Extracted exponent parity evaluation into explicit isOddExponent helper",
+  "smallest_valid_input": {
+    "base": 2,
+    "exponent": 0,
+    "mod": 5,
+    "expected": 1
+  },
+  "ordinary_input": {
+    "base": 2,
+    "exponent": 10,
+    "mod": 1000,
+    "expected": 24
+  }
+}
diff --git a/work/R50-T026/test_output.log b/work/R50-T026/test_output.log
@@ -0,0 +1,11 @@
+
+[1m[30m[46m RUN [49m[39m[22m [36mv5.1.0 [39m[90m/Users/fabulous_tarun8/Library/Mobile Documents/com~apple~CloudDocs/Studies/s&ai/diwaliHomework/TheAlgorithms-JavaScript[39m
+
+ [32m✓[39m Maths/test/ModularBinaryExponentiationRecursive.test.js [2m([22m[2m5 tests[22m[2m)[22m[32m 1[2mms[22m[39m
+
+[2m Test Files [22m [1m[32m1 passed[39m[22m[90m (1)[39m
+[2m      Tests [22m [1m[32m5 passed[39m[22m[90m (5)[39m
+[2m   Start at [22m 09:07:27
+[2m   Duration [22m 88ms[2m (transform 57%, import 17%, worker 17%, tests 8%)[22m
+
+
diff --git a/work/R50-T026/versions.json b/work/R50-T026/versions.json
@@ -0,0 +1,4 @@
+{
+  "node": "v26.12.1",
+  "npm": "11.20.0"
+}