There are different ways to express directions on a map. On a map without directional signs and latitude and longitude nets, the direction is usually determined by the provisions of "going up north and down south, left west and right east". According to reading the map, the playground is in the west of teaching building A, the canteen is in the northeast corner of the school, the school gate faces south, and the library is in the east of teaching building B.

So choose: C.