How Do Sorting Algorithms Work?

• Compare — ask whether element A should come before element B. This is the fundamental decision every comparison sort makes.
• Swap — exchange the positions of two elements. Bubble, Selection, Quick, and Heap Sort all rely on swapping.
• Insert — lift an element out and place it into its correct spot among already-sorted elements. This is the heart of Insertion Sort.
• Merge — combine two already-sorted sequences into one sorted sequence. This powers Merge Sort and Tim Sort.

Most algorithms fall into one of two strategies. Iterative sorts such as Bubble, Selection, and Insertion walk through the array with nested loops, gradually growing a sorted region. Divide-and-conquer sorts such as Merge and Quick split the problem into smaller sub-problems, solve each, and combine the results — which is how they reach O(n log n) performance.

A third family, non-comparison sorts like Counting and Radix Sort, avoids comparing elements at all and instead uses the values themselves as array indices.

In the Sort & Visualize visualiser, colour tells you exactly which operation is running: amber bars are being compared, red bars are being swapped, cyan marks the current element, purple is the pivot in Quick Sort, and green confirms an element is in its final sorted position. Slowing the speed down to x1 lets you trace a single comparison at a time.

The number of compares and swaps an algorithm performs is exactly what its time complexity measures. Nested loops over n elements give O(n²); halving the problem repeatedly gives the log factor in O(n log n). Counting operations as you watch is the most intuitive way to feel the difference between a slow and a fast algorithm.