[@Zetsuko]

Actually it's highly unlikely we'd face more than the twenty-five we already have. Remember, it's only been a few hours in-game. This means that all the King knows is that the princess is missing. Now, even though we know she's stumbled upon a band of lovable misfits, the King does not, and it is not wise to send out [i]your entire army[/i] to catch one person.

So, what would he likely do? Lock down the gates, make sure the night guards are on alert, and take extra care to ID elves. Depending on desperation, he may bar elves from entering or exiting the city altogether.
As for the actual search, it is again, unwise to have your entire royal guard to leave the castle (and king they're devoted to guarding) to capture one person. It's more practical to send a small squad of 5-10 men, particularly skilled trackers, and including a mage to counter the Princess's own magic. We'll bump that up to 20-25 men at arms and 3 mages since they probably suspect Avad's defected by now. And let's not forget Wledric, the head honcho himself. The guard captain should be able to capture a runaway quietly and quickly, with only a small squardon.