Selection Sort

Repeatedly find the index of the smallest remaining element and swap it into the next "sorted prefix" slot. Unlike bubble sort, only one swap per pass.

Algorithm

Canonical input [5, 1, 4, 2, 8] finishes after four passes, with two real swaps (passes 0 and 1) and two skip-swap passes (minIdx == i). Final array [1, 2, 4, 5, 8].

running minimum `minIdx` tracks the index of the smallest value seen in `arr[i..]`.

sorted prefix After each pass, `arr[0..i]` is the final sorted prefix.

Visual walkthrough

The pinned input [5, 1, 4, 2, 8] sorts with two real swaps. The frames keep the running minimum and swap positions visible.

Step 1 - First scan finds 1

In the first pass, min_idx moves from 5 to 1.

Step 2 - Swap 5 and 1

The smallest value moves into the first sorted slot.

Step 3 - Second scan finds 2

In the unsorted suffix, 2 is smaller than 5 and becomes the next minimum.

Step 4 - Sorted after two swaps

Swapping 5 and 2 gives [1, 2, 4, 5, 8]; later passes find no real swap.

Basic Implementation

                            basic.cs
                        

                            using System;

class Program {
	static void Main() {
		int[] arr = new int[] { 5, 1, 4, 2, 8 };
		int n = arr.Length;
		for (int i = 0; i < n - 1; i++) {
			int minIdx = i;
			for (int j = i + 1; j < n; j++) {
				if (arr[j] < arr[minIdx]) {
					minIdx = j;
				}
			}
			if (minIdx != i) {
				int tmp = arr[i];
				arr[i] = arr[minIdx];
				arr[minIdx] = tmp;
			}
		}
		Console.WriteLine("[" + string.Join(", ", arr) + "]");
	}
}

                        

Complexity

Time: O(n^2) regardless of input order
Space: O(1)
Stable: no
Swap count: at most n-1

Implementation notes

C#: keep the explicit min scan instead of calling Array.Sort, so the replay can show each candidate comparison and skip-swap decision.
int minIdx = i; keeps the running-minimum invariant visible; the three-line int tmp = arr[i]; arr[i] = arr[minIdx]; arr[minIdx] = tmp; swap mutates the managed reference int[] in place, with each indexed read/write bounds-checked by the CLR.
The replay highlights the current minIdx distinctly from the scanning index j so the viewer sees the running minimum travel.