710A - King Moves
Easy to see that there are only three cases in this problem. If the king is in the corner of the board the answer is 3. If the king is on the border of the board but not in a corner than the answer is 5. Otherwise the answer is 8.
Complexity: O(1).
710B - Optimal Point on a Line
The function of the total distance is monotonic between any pair of adjacent points from the input, so the answer is always in some of the given points. We can use that observation to solve the problem by calculating the total distance for each point from the input and finding the optimal point.
The other solution uses the observation that the answer is always is the middle point (by index) in the sorted list of the given points. The last fact is also can be easily proven.
Complexity: O(nlogn).