The Pointer Never Resets

a is sorted and has n elements. This is the whole loop:

int j = 0, best = 0;
for (int i = 0; i < n; i++) {
    while (j < n && a[j] - a[i] <= K) j++;
    best = max(best, j - i);
}

Counting only executions of j++, what is the worst case total across the entire run?

$\Theta(n \log n)$ , because j runs geometrically ahead of i.

At most $n$ , so the whole nest is $\Theta(n)$ .

About $n^2/2$ , since the inner loop advances roughly halfway on average.

Exactly $n^2$ : a while nested inside a for multiplies.