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‫So another way that we simplify Big O is we drop non dominance.

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‫And so to explain this, I'm going to bring up the nested for loops that we had in the last video,

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‫but I'm going to add an additional for loop after the nested for loops.

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‫So now let's flip over to VS Code and take a look at this.

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‫So there is our new print items function there with our nested for loops followed by a single for loop.

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‫And then down here, we're going to pass that, the number ten and I'll run this.

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‫So I'm going to scroll to the top and you can see that this starts with zero zero and then it goes down

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‫to nine nine.

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‫Those are created by the set of nested for loops, and then that single for loop is going to print out

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‫zero through nine.

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‫So now let's flip back.

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‫So the set of nested for loops ran o of in squared times and then that single for loop ran end times.

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‫So the total number of operations was O of n squared plus o of n or you could write it like this in

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‫squared would be the dominant term and n would be the non dominant term.

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‫So if you think about when n becomes very large, even if we use a number that is not that big, like

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‫a hundred in squared is going to be 10,000 where that standalone N is going to only be 100.

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‫So that stand alone N as the number gets larger and larger becomes less and less significant in this

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‫equation.

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‫So we simplify this by dropping the N and just keeping the N squared.

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‫So this rule of simplification is called.

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‫Dropped non dominance.