Sorting

Merge Sort (Top-Down)

Split the array recursively, sort each half, then merge two sorted runs into one sorted result.

Algorithm

The checked-in replay follows the same small input and final output across all 21 DSA books, so this Scala DSA implementation can be compared directly with the other languages.

divide and conquer Each recursive call solves a smaller sorted subproblem.
merge step Two sorted halves are combined by repeatedly taking the smaller front item.

Visual walkthrough

The pinned input is [5, 1, 4, 2, 8]. The diagrams show the split into recursive halves, the sorted subarrays, and the final merge choices.

Step 1 - Split the input

The first midpoint splits [5, 1, 4, 2, 8] into left [5, 1] and right [4, 2, 8].

Top-down split used by merge_sort.[5,1,4,2,8]mid = 2[5,1]left[4,2,8]right

Step 2 - Sorted halves return

Recursive calls return [1, 5] and [2, 4, 8] before the final merge begins.

Returned subarrays before the final merge.sidebefore sortafter sortleft[5, 1][1, 5]right[4, 2, 8][2, 4, 8]

Step 3 - Merge by taking smaller fronts

Take 1 from left, then 2 and 4 from right, then the remaining 5 and 8.

Final merge produces [1, 2, 4, 5, 8].choiceleft frontright frontmergedtake 112[1]take 252[1, 2]take 454[1, 2, 4]extend58[1, 2, 4, 5, 8]

Basic Implementation

basic.scala 
object Main {
	def mergeSort(values: List[Int]): List[Int] = {
		if (values.length <= 1) return values
		val (leftRaw, rightRaw) = values.splitAt(values.length / 2)
		val left = mergeSort(leftRaw)
		val right = mergeSort(rightRaw)
		merge(left, right)
	}

	def merge(left: List[Int], right: List[Int]): List[Int] = (left, right) match {
		case (Nil, _) => right
		case (_, Nil) => left
		case (l :: ls, r :: rs) =>
			if (l <= r) l :: merge(ls, right) else r :: merge(left, rs)
	}
	def main(args: Array[String]): Unit = {
		val arr = List(5, 1, 4, 2, 8)
		println(mergeSort(arr).mkString("[", ", ", "]"))
	}
}

Complexity

  • Time: O(n log n)
  • Space: O(n)
  • Stable: yes

Implementation notes

  • This checked Scala source uses List[Int], not Array[Int]: val arr = List(5, 1, 4, 2, 8).
  • mergeSort(values: List[Int]): List[Int] produces a sorted List[Int] without mutating the input list; base and leftover cases can return existing list values directly.
  • The base case if (values.length <= 1) return values stops recursion for empty and single-element lists.
  • val (leftRaw, rightRaw) = values.splitAt(values.length / 2) splits the list into two list halves, then val left and val right hold the recursive sorted results.
  • merge(left, right) uses pattern matching: Nil returns the leftover other list, and l :: ls / r :: rs exposes each front value.
  • The comparison if (l <= r) keeps equal values from the left side first, then builds the output with :: cons cells.
  • The trace shows [5, 1, 4, 2, 8] splitting into [5, 1] and [4, 2, 8], those halves sorting to [1, 5] and [2, 4, 8], then merging to [1, 2, 4, 5, 8].
  • println(mergeSort(arr).mkString("[", ", ", "]")) prints the final list as [1, 2, 4, 5, 8].