Challenges with a spec which requires all answers to meet certain time complexity restrictions. This could be specific ("Your answer must be O(n^2) where n is the number of items in the input"), or at the level of complexity classes ("Your answer must be polynomial in the number of items in the input").
Challenges with a spec which requires all answers to meet certain time or memory complexity restrictions. This could be specific ("Your answer must be \$O(n^2)\$ where n is the number of items in the input"), or at the level of complexity classes ("Your answer must be polynomial in the number of items in the input").
For challenges which have no restriction but which are judged on the time complexity, see fastest-algorithm.