Algorithms Analysis Practice Test

The total number of fundamental instructions executed by the routine when \( n = 4 \) can be derived from analyzing the structure of the routine itself. When an algorithm or code snippet is expressed as \( 4 + 2n \), it indicates the number of operations depends linearly on the size \( n \).

For \( n = 4 \), substituting this value into the expression yields:

\[

4 + 2(4) = 4 + 8 = 12

\]

Thus, when \( n = 4 \), the total number of fundamental instructions executed is 12, confirming that the provided expression accurately captures the pattern of execution within the routine based on varying values of \( n \).

This type of expression often arises in algorithms that entail a constant number of operations in addition to a linear scaling with \( n \) — for instance, loops that execute a fixed number of times for each element processed or a combination of sequential and iterative tasks. This clarity in understanding how the formula describes the relationship between the input size and operations is key to analyzing algorithm efficiency.