# Computing the note O-O, O (n) * O (log n) = O (n log n)

I need to develop an algorithm that can do some computation in a given O-notation. It's been a while since I last calculated using O notation, and I'm a little confused about how to add different O records together.

```
O(n) * O(log n) = O(n log n)
O(n) + O(n) = O(2n) = O(n)
O(n) * O(log n) + O(n log n) = O(n log n) + O(n log n) = O(n log n)
```

Are they correct? What other rules have I missed?

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1 answer

The rule for multiplication is really simple:

```
O(f) * O(g) = O(f * g)
```

The sum of two `O`

terms is more difficult to calculate if you want it to work for arbitrary functions.

However, if `f β O(g)`

, then `f + g β O(g)`

.

Therefore, your calculations are correct, but the original name is not specified;

```
O(n) + O(log n) = O(n)
```

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