chore: merge "Added backtracking sum of subset (#702)"

* sum of subset algorithm

* set returns comment

* fix comment

* add resource url to comments

* separate test to different file and format

Backtracking/SumOfSubset.js

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+/*
+ *
+ *  Sum of Subset problem
+ *
+ *  Given an ordered set W of non-negative integers and a value K,
+ *  determine all possible subsets from the given set W whose sum
+ *  of its elemets equals to the given value K.
+ *
+ *  More info: https://www.geeksforgeeks.org/subset-sum-backtracking-4/
+ */
+
+/*
+ * @param {number[]} set Original set of numbers
+ * @param {number[]} subset Subset being evaluated
+ * @param {number} setIndex Index from set of last element in subset
+ * @param {number} Sum of elements from subset
+ * @param {targetSum} The target sum on which the subset sum is compared to
+ * @returns {number[][]} Subsets whose elements add up to targetSum
+ */
+const sumOfSubset = (set, subset, setindex, sum, targetSum) => {
+  // Base case where the subset sum is equal to target sum
+  // Evaluation of following subsets on this path will always add up to
+  // greater than targetSum, so no need to continue
+  if (sum === targetSum) return [subset]
+
+  // This and following subsets on this path will always add up to
+  // greater than targetSum, so no need to continue
+  if (sum > targetSum) return []
+
+  // Initialize results array. Will contain only valid subsets
+  let results = []
+
+  // Slice gets from the set all the elements at the right of the last element
+  // to be evaluated (last element of subset)
+  // forEach iterated on the resulting array
+  set.slice(setindex).forEach((num, index) => {
+    // The next subset to be evaluated, current subset plus next element
+    const nextSubset = [...subset, num]
+
+    // Next index from the set. Current set index plus iteration index
+    // index starts at 0, so a + 1 is required
+    const nextSetIndex = setindex + index + 1
+
+    // Sum of elements from the next subset to be evaluated
+    const nextSum = sum + num
+
+    // Call recursively the sumOfSubset for the nextSubset
+    const subsetResult = sumOfSubset(
+      set,
+      nextSubset,
+      nextSetIndex,
+      nextSum,
+      targetSum
+    )
+
+    // Concat the recursive result with current result arary
+    results = [...results, ...subsetResult]
+  })
+
+  // Return results
+  return results
+}
+
+export { sumOfSubset }

Backtracking/tests/SumOfSubset.test.js

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+import { sumOfSubset } from '../SumOfSubset'
+
+describe('SumOfSubset', () => {
+  it('should return the subsets that add up to the given number', () => {
+    // W = [2, 5, 7, 8, 12, 16, 23, 40]
+    // K = 25
+
+    const nums = [2, 5, 7, 8, 12, 16, 23, 40]
+
+    const subsets = sumOfSubset(nums, [], 0, 0, 25)
+
+    expect(subsets).toEqual([
+      [2, 7, 16],
+      [2, 23],
+      [5, 8, 12]
+    ])
+  })
+})