test_reference_editorial

We want to find two numbers that sum to $target = 9$. We use the brute-force approach: try every pair $(i, j)$ with $i < j$.

Outer loop: set $i = 0$. The value at index 0 is $nums[0] = 2$.

Inner loop: $j = 1$. Check pair $(0, 1)$: $nums[0] + nums[1] = 2 + 7 = 9$. That equals our target!

Match found! $nums[0] + nums[1] = 2 + 7 = 9 = target$. Return indices $[0, 1]$.

The remaining elements are never checked because we already found our answer. In the worst case, though, we would continue the nested loop.

Now let us trace what the worst case looks like. Consider $target = 16$ with the same array $[2, 7, 11, 15, 1]$.

Worst-case trace with $target = 16$. Outer loop: $i = 0$. We must check $j = 1, 2, 3, 4$ before moving on.

$j=1$: $2 + 7 = 9 \neq 16$. No match. The cursor for $j$ advances.

$j=2$: $2 + 11 = 13 \neq 16$. Still no match. Continue.

$j=3$: $2 + 15 = 17 \neq 16$. Close but not equal. One more to check for $i = 0$.