Why doesn't Odysseus kill the cyclops?

Odysseus is a smart, smart man.

If he had killed the cyclops then he and his men would have been trapped in the cyclops' cave forever. Remeber, he pushed a huge boulder in front of the door when he came in. If he had tried to kill him after he and his men escaped by hiding under the sheep then the cyclops would have cried out to his companions and all the rest of the Cyclopses would have come out and killed Odysseus, sunk his boat and killed his men.

He is too smart to resort to violence right away...

not like his companions in Troy.