(b) Show that the algorithm you proposed in 8a does have the time complexity of O ( n 2 ), where n = 2 k. Hint: Think of recursively dividing the tiled-ceiling, such that you have multiple of the exact same tiling problems but on smaller size tiled-ceiling. An algorithm that outputs a different indexing or potentially different L-shaped rotations would still be valid, as long as they cover the tiles that need to be covered in a non-overlapping manner. The process will differ slightly depending on what kind of tile you are painting. Illustration of L-shaped covered ceiling-tiles: Note: The exact order and the exact orientation of the L-shaped tile index are not important.
An example of the input and output of the algorithm, and an illustration of the covered tiled-ceiling is below. Amazing gallery of interior design and decorating ideas of Tiled Shower Ceiling in bathrooms by. The ceiling tile that should not be covered is represented by 0. Tiled Shower Ceiling - Design photos, ideas and inspiration. However, each element represents the index (start from 1 ) of the L-shaped tile that cover the particular tile on the ceiling. The output is also an array of size 2 k × 2 k. 20'x20' R9 Styrofoam Ceiling Tile, Copper Patina (6) 2.65/sq ft.
20'x20' Styrofoam Glue Up Ceiling Tiles, R5W Plain White by Euro-Deco (2) 1.52/sq ft. Each element represents the tile on the ceiling, with 0 representing the tile that should not be covered by the L-shaped tile and 1 all other tiles. Art3d Decorative Drop-in Ceiling Tiles 24x24, Pack of 12, Black by Art3d LLC. Specifically, the input and output of your algorithm should be as specified below. (a) Provide an algorithm that has a time complexity of O ( n 2 ), where n = 2 k and solves the problem. The Armstrong Calla ceiling tile provides our smoothest finish mineral fiber ceiling available with excellent acoustic performance including noise reduction and. The cross inside a circle indicates the exhaust fan. Figure 1: Left: Tiled-ceiling with k = 3. Furthermore, the L-shaped tile must not overlap with each other and can be oriented in any direction.
The position of such a tile can be arbitrary. Suppose, one of the tiles on the ceiling are linked to an exhaust fan and should not be covered by the L-shaped tile. Imagine the problem of covering a tiled-ceiling of size 2 k × 2 k ( k ∈ ) with L-shaped tiles formed by three 1 × 1 tiles (please see Figure 1 for an illustration). /rebates/2fb2fBuilding-Materials-Ceilings-Ceiling-Tiles-Drop-Ceiling-Tiles2fN-5yc1vZc58c&. But if the ceiling tiles are sloped, most of the surface moisture simply drains to the walls.
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