Implemented Partition Problem, Recursive problem

DIRECTORY.md

@@ -160,6 +160,7 @@
  * [NumberOfIslands](Graphs/NumberOfIslands.js)
  * [PrimMST](Graphs/PrimMST.js)
 * **Hashes**
+ * [MD5](Hashes/MD5.js)
  * [SHA1](Hashes/SHA1.js)
  * [SHA256](Hashes/SHA256.js)
 * **Maths**
@@ -300,6 +301,7 @@
  * [KochSnowflake](Recursive/KochSnowflake.js)
  * [LetterCombination](Recursive/LetterCombination.js)
  * [Palindrome](Recursive/Palindrome.js)
+ * [Partition](Recursive/Partition.js)
  * [SubsequenceRecursive](Recursive/SubsequenceRecursive.js)
  * [TowerOfHanoi](Recursive/TowerOfHanoi.js)
 * **Search**

Recursive/Partition.js

@@ -0,0 +1,39 @@
+/**
+ * @function canPartition
+ * @description Check whether it is possible to partition the given array into two equal sum subsets using recursion.
+ * @param {number[]} nums - The input array of numbers.
+ * @param {number} index - The current index in the array being considered.
+ * @param {number} target - The target sum for each subset.
+ * @return {boolean}.
+ * @see [Partition Problem](https://en.wikipedia.org/wiki/Partition_problem)
+ */
+
+const canPartition = (nums, index = 0, target = 0) => {
+ if (!Array.isArray(nums)) {
+ throw new TypeError('Invalid Input')
+ }
+
+ const sum = nums.reduce((acc, num) => acc + num, 0)
+
+ if (sum % 2 !== 0) {
+ return false
+ }
+
+ if (target === sum / 2) {
+ return true
+ }
+
+ if (index >= nums.length || target > sum / 2) {
+ return false
+ }
+
+ // Include the current number in the first subset and check if a solution is possible.
+ const withCurrent = canPartition(nums, index + 1, target + nums[index])
+
+ // Exclude the current number from the first subset and check if a solution is possible.
+ const withoutCurrent = canPartition(nums, index + 1, target)
+
+ return withCurrent || withoutCurrent
+}
+
+export { canPartition }

Recursive/test/Partition.test.js

@@ -0,0 +1,24 @@
+import { canPartition } from '../Partition'
+
+describe('Partition (Recursive)', () => {
+ it('expects to return true for an array that can be partitioned', () => {
+ const result = canPartition([1, 5, 11, 5])
+ expect(result).toBe(true)
+ })
+
+ it('expects to return false for an array that cannot be partitioned', () => {
+ const result = canPartition([1, 2, 3, 5])
+ expect(result).toBe(false)
+ })
+
+ it('expects to return true for an empty array (0 elements)', () => {
+ const result = canPartition([])
+ expect(result).toBe(true)
+ })
+
+ it('Throw Error for Invalid Input', () => {
+ expect(() => canPartition(123)).toThrow('Invalid Input')
+ expect(() => canPartition(null)).toThrow('Invalid Input')
+ expect(() => canPartition(undefined)).toThrow('Invalid Input')
+ })
+})