Problem 2905 --3.1.4 Shaping Regions

2905: 3.1.4 Shaping Regions

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Time Limit $1$ 秒/Second(s) Memory Limit $512$ 兆字节/Megabyte(s)
提交总数 $8$ 正确数量 $2$
裁判形式 标准裁判/Standard Judge 我的状态 尚未尝试
难度 分类标签 usaco

N opaque rectangles (1 <= N <= 1000) of various colors are placed on a white sheet of paper whose size is A wide by B long. The rectangles are put with their sides parallel to the sheet's borders. All rectangles fall within the borders of the sheet so that different figures of different colors will be seen.

The coordinate system has its origin (0,0) at the sheet's lower left corner with axes parallel to the sheet's borders.


The order of the input lines dictates the order of laying down the rectangles. The first input line is a rectangle "on the bottom".


Line 1:  A, B, and N, space separated (1 <= A,B <= 10,000)
Lines 2-N+1:  Five integers: llx, lly, urx, ury, color: the lower left coordinates and upper right coordinates of the rectangle whose color is `color' (1 <= color <= 2500) to be placed on the white sheet. The color 1 is the same color of white as the sheet upon which the rectangles are placed.
The output file should contain a list of all the colors that can be seen along with the total area of each color that can be seen (even if the regions of color are disjoint), ordered by increasing color. Do not display colors with no area.

20 20 3
2 2 18 18 2
0 8 19 19 3
8 0 10 19 4
1 91
2 84
3 187
4 38
Note that the rectangle delineated by 0,0 and 2,2 is two units wide and two high. Here's a schematic diagram of the input:
11111111111111111111
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
33333333443333333331
11222222442222222211
11222222442222222211
11222222442222222211
11222222442222222211
11222222442222222211
11222222442222222211
11111111441111111111
11111111441111111111

The '4's at 8,0 to 10,19 are only two wide, not three (i.e., the grid contains a 4 and 8,0 and a 4 and 8,1 but NOT a 4 and 8,2 since this diagram can't capture what would be shown on graph paper)


An array of all 'points' is too big; 16MB maximum.

Keep track of the rectangles' coordinates; split the rectangle when an overlap occurs, e.g.:

+--------+      +-+--+--+
|        |      | |2 |  |
|        |      + +--+  |
|  +-+   |  --> | |  |  |
|  +-+   |      |1|  |3 |
|        |      | +--+  |
|        |      | | 4|  |
+--------+      +-+--+--+

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本题记录 用 户(点击查看用户) 运行号(点击购买题解) 时 间
算法最快[$0 $ms] 梦尘 695087 2020-12-30 23:27:28
内存最少[$2056 $KB] 梦尘 695087 2020-12-30 23:27:28
第一AC 淡意的温柔 596468 2020-06-12 16:47:27
第一挑战 淡意的温柔 596468 2020-06-12 16:47:27

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