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 Rust 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.rs 
fn merge_sort(values: &[i32]) -> Vec<i32> {
	if values.len() <= 1 {
		return values.to_vec();
	}
	let mid = values.len() / 2;
	let left = merge_sort(&values[..mid]);
	let right = merge_sort(&values[mid..]);
	let mut merged = Vec::new();
	let (mut i, mut j) = (0, 0);
	while i < left.len() && j < right.len() {
		if left[i] <= right[j] {
			merged.push(left[i]);
			i += 1;
		} else {
			merged.push(right[j]);
			j += 1;
		}
	}
	merged.extend_from_slice(&left[i..]);
	merged.extend_from_slice(&right[j..]);
	merged
}

fn main() {
	let arr = [5, 1, 4, 2, 8];
	println!("{:?}", merge_sort(&arr));
}

Complexity

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

Implementation notes

  • main starts with a fixed array, let arr = [5, 1, 4, 2, 8], and calls merge_sort(&arr), borrowing it as a slice.
  • The recursive signature is fn merge_sort(values: &[i32]) -> Vec<i32>, so calls read borrowed slices and return newly allocated vectors rather than sorting the original array in place.
  • The base case values.len() <= 1 returns values.to_vec(), copying the small slice into an owned Vec<i32>.
  • Splitting uses let mid = values.len() / 2, then borrows &values[..mid] and &values[mid..] for the recursive calls.
  • Merge state is held in let mut merged = Vec::new() and cursor indices (mut i, mut j). The comparison left[i] <= right[j] takes the left value first on ties, preserving stability.
  • Remaining elements are copied with extend_from_slice(&left[i..]) and extend_from_slice(&right[j..]); the returned merged vector is the sorted result.
  • The trace records the top split [5, 1] and [4, 2, 8], sorted halves [1, 5] and [2, 4, 8], then merged output [1, 2, 4, 5, 8].
  • println!("{:?}", merge_sort(&arr)) uses Rust's debug formatter for the returned Vec<i32> and prints [1, 2, 4, 5, 8].