Yes you can get a DUI from driving after smoking weed in Alaska. They know that you are high by the way you drive, as well as your mannerisms and the way your eyes may look after consuming cannabis (red and dilated pupils). Being high at all is too high to drive.
Getting high before you drive could get you arrested for driving under the influence (DUI). This is still true even though marijuana is legal for adults. If you are high, you should not drive, bike, or operate machinery. You can be issued a DUI if you drive after smoking weed in Alaska. If stopped by an officer, and obviously impaired, the officer will give you a breathalyzer test, if this reads, you have negative results then they would get a warrant for a blood test and take you to the magistrate.
It is illegal and unsafe to drive after getting high; you can get DUI (Driving Under the Influence) and be arrested. That means driving any motorized or non-motorized mode of transportation or operating any machinery. Marijuana affects reaction time, hand-eye coordination, concentration, perception of time and distance.
There is no determination on how high is too high unless a blood test is given. It is what the police notice. A thing they like to look for is change in speeds. People are speeding up, slowing down, just driving erratically in general.