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 Swift 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.swift 
func mergeSort(_ values: [Int]) -> [Int] {
	if values.count <= 1 { return values }
	let mid = values.count / 2
	let left = mergeSort(Array(values[..<mid]))
	let right = mergeSort(Array(values[mid...]))
	var merged: [Int] = []
	var i = 0
	var j = 0
	while i < left.count && j < right.count {
		if left[i] <= right[j] {
			merged.append(left[i])
			i += 1
		} else {
			merged.append(right[j])
			j += 1
		}
	}
	merged.append(contentsOf: left[i...])
	merged.append(contentsOf: right[j...])
	return merged
}

let arr = [5, 1, 4, 2, 8]
print(mergeSort(arr))

Complexity

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

Implementation notes

  • mergeSort(_ values: [Int]) -> [Int] takes an immutable Swift [Int] value and returns a newly built sorted array instead of mutating arr.
  • The base case values.count <= 1 returns the current array value directly.
  • let mid = values.count / 2 splits the input, and Array(values[..<mid]) plus Array(values[mid...]) copy the slice ranges before the recursive calls.
  • let left and let right hold sorted recursive results; var merged: [Int] is the only merge buffer built by the current call.
  • var i and var j walk the two sorted halves while i < left.count && j < right.count; left[i] <= right[j] keeps equal Int values from the left half first.
  • Merge output grows through merged.append(...), then append(contentsOf:) copies any remaining suffix from left[i...] or right[j...].
  • The trace shows [5, 1, 4, 2, 8] splitting into [5, 1] and [4, 2, 8], those halves becoming [1, 5] and [2, 4, 8], then the final merge producing [1, 2, 4, 5, 8].
  • print(mergeSort(arr)) uses Swift's array display form and outputs [1, 2, 4, 5, 8].