In lesson 1 you wrote algo gen -n 100000 and produced a hundred thousand items in a second and a half. That number has cost you nothing so far.

Now it will.

$ algo gen -n 1000 -seed 42 -o s1k.jsonl
$ algo sort -in s1k.jsonl
n = 1000, order = shuffled

algorithm         comparisons            swaps         wall
bubble                 498680           243513      3.702ms
selection              499500              997      1.087ms
insertion              244506           243513        514µs

A thousand items, half a million comparisons. Imperceptible.

$ algo sort -in s10k.jsonl
n = 10000, order = shuffled

algorithm         comparisons            swaps         wall
bubble               49993289         24883304     454.17ms
selection            49995000             9992    170.587ms
insertion            24893296         24883304     92.225ms

Ten times the data, a hundred times the work. Nearly half a second.

$ algo sort -in s100k.jsonl
n = 100000, order = shuffled

algorithm         comparisons            swaps         wall
bubble             4999895385       2503732834 1m25.751674s
selection          4999950000            99986   41.607048s
insertion          2503832821       2503732834   26.916946s

A minute and a half. Five billion comparisons for one sort.

The curve

n	bubble comparisons	ratio
1,000	498,680	—
10,000	49,993,289	×100.3
100,000	4,999,895,385	×100.0

Ten times the n, a hundred times the work. That is O(n²), and the comparison count reproduces it exactly.

The clock and the counter finally agree — almost

In lesson 6 they disagreed: the counter said one thing and the clock another. Here there is so much work that the clock has nothing left to hide.

But not quite:

n	wall	ratio
1,000	3.7 ms	—
10,000	454 ms	×123
100,000	85.8 s	×189

The comparison count grew by exactly ×100. The time grew by ×123 and ×189.

Time is growing faster than quadratically. At 100,000 items the slice is about 7 MB and no longer fits in cache, so every comparison starts costing more. You saw the same effect from the other side in lesson 3.

The counter is still the more precise instrument. It is simply no longer the only one that can see the problem.

Why selection sort is the middle one

It makes more comparisons than bubble (4,999,950,000 against 4,999,895,385) and takes half the time.

The answer is in the swaps column: 99,986 against 2,503,732,834. Twenty-five thousand times less data moved.

A comparison is cheap. A swap is three assignments and a struct copy. At two and a half billion of them, they are what the clock is measuring.

Two different operations, two different costs. That is why the Sort functions take two counters and not one.