Welcome to our underwater coding adventure! Today we're diving deep into the bubble sort algorithm. Just like air bubbles naturally rise to the surface of water, bubble sort works by letting smaller numbers bubble up to the beginning of our array. Our friendly sea creatures will help us understand this fascinating sorting method. Notice how the bubbles with numbers float around - we'll learn to organize them in perfect order!
Now let's understand the basic principle of bubble sort! The algorithm works by comparing adjacent elements in our array. Here we have two bubbles with numbers 8 and 3. We ask: is 8 greater than 3? Yes it is! Since we want smaller numbers to bubble up to the left, we need to swap these bubbles. Watch as our sea creatures observe this fundamental operation that makes bubble sort work!
Let's walk through the first complete pass of bubble sort with our array of five bubbles. We start by comparing the first two bubbles: 7 and 3. Since 7 is greater than 3, we swap them. Next, we compare 7 and 8 - no swap needed since they're in correct order. Then 8 and 1 - we swap because 8 is larger. Finally, 8 and 5 - another swap. Notice how the largest bubble, 8, has bubbled all the way to the end! This is exactly how one pass works in bubble sort.
Now let's see how multiple passes work together to sort our entire array! After the first pass, we know the largest element is in its correct position, so our sea creatures can guard it. In the second pass, we only need to compare the first four elements. Watch how the active comparison area shrinks with each pass - this is a key optimization! The yellow area shows where comparisons happen, while the green area shows elements that are already sorted and protected by our underwater friends.
Let's complete a full bubble sort example with seven bubbles! We'll track our statistics as we go - counting comparisons, swaps, and passes. Watch as our sea creatures cheer us on through this comprehensive sorting adventure. Notice how the algorithm systematically works through each pass, with each element finding its correct position. This demonstrates why bubble sort has O(n²) time complexity - we make multiple passes through the array. Finally, our underwater friends celebrate as we achieve a perfectly sorted array!