Given a moderately unsorted data-set, bubble sort requires multiple passes through the input before producing a sorted list. Each pass through the list will place the next largest value in its proper place.

We are performing `n-1`

comparisons for our inner loop. Then, we must go through the list `n`

times in order to ensure that each item in our list has been placed in its proper order.

The `n`

signifies the number of elements in the list. In a worst case scenario, the inner loop does `n-1`

comparisons for each `n`

element in the list.

Therefore we calculate the algorithm’s efficiency as:

```
$\mathcal{O}(n(n-1)) =
\mathcal{O}(n(n)) =
\mathcal{O}(n^2)$
```

The diagram analyzes the pseudocode implementation of bubble sort to show how we draw this conclusion.

When calculating the run-time efficiency of an algorithm, we drop the constant (`-1`

), which simplifies our inner loop comparisons to `n`

.

This is how we arrive at the algorithm’s runtime: `O(n^2)`

.

### Instructions

What input to bubble sort would produce the worst possible runtime?

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