Implemented Partition Problem, Recursive problem (TheAlgorithms#1582)

* Add Tug of War solution using backtracking * Updated Documentation in README.md * Added Tug of war problem link * Updated Documentation in README.md * Updated Documentation in README.md * Refactor tugOfWar: remove unused vars, optimize initialization, and remove redundant checks * Added Function Export Statment * Updated Documentation in README.md * Resolved Code Style --Prettier * Rename "backtrack" to "recurse" * Fix test case: The difference needs to be exactly 1. * Code Modification: subsets should have sizes as close to n/2 as possible * Updated test-case of TugOfWar * Changed TugOfWar problem to Partition * Modified partition problem * Updated Documentation in README.md * fixed code style --------- Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: Lars Müller <[email protected]>

Author: 3 people

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)
+ */
+
+constcanPartition=(nums,index=0,target=0)=>{
+if(!Array.isArray(nums)){
+thrownewTypeError('Invalid Input')
+}
+
+constsum=nums.reduce((acc,num)=>acc+num,0)
+
+if(sum%2!==0){
+returnfalse
+}
+
+if(target===sum/2){
+returntrue
+}
+
+if(index>=nums.length||target>sum/2){
+returnfalse
+}
+
+// Include the current number in the first subset and check if a solution is possible.
+constwithCurrent=canPartition(nums,index+1,target+nums[index])
+
+// Exclude the current number from the first subset and check if a solution is possible.
+constwithoutCurrent=canPartition(nums,index+1,target)
+
+returnwithCurrent||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',()=>{
+constresult=canPartition([1,5,11,5])
+expect(result).toBe(true)
+})
+
+it('expects to return false for an array that cannot be partitioned',()=>{
+constresult=canPartition([1,2,3,5])
+expect(result).toBe(false)
+})
+
+it('expects to return true for an empty array (0 elements)',()=>{
+constresult=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')
+})
+})