# Test 1 #7 (Version A)

Give a big-O estimate for the number of operations (where an operation is an addition or multiplication) used in this segment of an algorithm:

$t:=0$
for $i:=1$ to $3$
for $j:=1$ to $4$
$t:=t+ij$

There are two loops: the $i$ loop and the $j$ loop.
There are 3 values of $i$ and 4 values of $j$ so there are 12 possible pairs $(i,j)$.

For each pair $(i,j)$ there is one calculation $t:=t+ij$.
Each such calculation has two operations, one instance of addition and one of multiplication.

Therefore, this segment of the algorithm uses a total of 24 operations. Since 24 is a constant, the number of operations is O(1).

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### 1 Response to Test 1 #7 (Version A)

1. Kate Poirier says:

Many of you caught that the two loops gave you 12 rounds. However, a few of you overlooked that there were two operations per round.

Some of you had the correct number of operations but didn’t include a big-O estimate for it. Some of you had the correct number of operations and included a correct–but kinda weird–big-O estimate. (For example, while 24 is $O(14x)$, the $14x$ is a sort-of random function to choose.)

Some of you were trying to count comparisons used, when that was not what the question was asking for. Don’t forget to read the question carefully. This question was copied directly from the homework, so it should not have come as a surprise.