Sorting

Bubble Sort

Repeatedly walk the array comparing adjacent pairs and swapping any that are out of order. After pass k, the k largest elements are in their final positions at the end. Stop early when a full pass makes zero swaps.

Algorithm

Canonical input [5, 1, 4, 2, 8] finishes after three passes: two with swaps, then a clean pass that triggers the early exit. Final array [1, 2, 4, 5, 8].

Basic Implementation

basic.go 
package main

import "fmt"

func main() {
	arr := []int{5, 1, 4, 2, 8}
	n := len(arr)
	for i := 0; i < n-1; i++ {
		swapped := false
		for j := 0; j < n-i-1; j++ {
			if arr[j] > arr[j+1] {
				arr[j], arr[j+1] = arr[j+1], arr[j]
				swapped = true
			}
		}
		if !swapped {
			break
		}
	}
	fmt.Println(arr)
}

Complexity

  • Time: O(n^2) worst and average; O(n) best (already sorted with early exit)
  • Space: O(1)
  • Stable: yes

Implementation notes

  • Go: nested for loops with the early-exit swapped flag. Go's standard sort.Ints would hide the comparison-and-swap the lesson is teaching.
  • The tuple swap arr[j], arr[j+1] = arr[j+1], arr[j] keeps the swap step visible without leaning on a helper.
  • The replay distinguishes compare frames from swap frames so the moving pivot value is visible. The pass number and swapped flag appear in the trace.
adjacent-pair compare and swap Inner loop walks `j` from `0` to `n - i - 2` comparing `arr[j]` and `arr[j + 1]`.
early exit A `swapped` flag set false at the start of each pass. If no swap happened, break out of the outer loop.