Practice

A digital filter routine computes n output samples, each a weighted sum of 8 consecutive input samples (the array x holds n + 7 samples and w holds the 8 weights):$$\begin{array}{l}\texttt{for i = 1 to n}\\ \qquad \texttt{y[i] = 0}\\ \qquad \texttt{for j = 1 to 8}\\ \qquad \qquad \texttt{y[i] = y[i] + w[j] * x[i + j - 1]}\\ \qquad \texttt{end for}\\ \texttt{end for}\end{array}$$In big-O notation, the worst-case running time of this routine as a function of n is:

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