USACO: Shaping Regions

最新推荐文章于 2025-12-22 22:15:05 发布

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文章标签：

#list #colors #input #parallel #output #struct

本文介绍了一种在二维平面上绘制多个矩形区域并计算各颜色区域面积的算法。通过矩形切割的方法处理矩形之间的重叠部分，最终输出每种可见颜色的总面积。

Shaping Regions

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.

PROGRAM NAME: rect1

INPUT FORMAT

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.

SAMPLE INPUT (file rect1.in)

20 20 3
2 2 18 18 2
0 8 19 19 3
8 0 10 19 4

INPUT EXPLANATION

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).

OUTPUT FORMAT

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.

SAMPLE OUTPUT (file rect1.out)

HINTS (use them carefully!)

HINT 1

思路：矩形切割，挺烦人的一道题啊！！！

/* ID: geterns1 PROG: rect1 LANG: C++ */ #include <cstdio> const int maxsize = 1000 + 1; struct coor{ short x, y; }; struct rect{ coor ll, ur; short cl; }; rect list[maxsize]; int l; int col[maxsize]; int maxcol = 1; void chck(rect &cur, short pos){ if (pos > l) col[cur.cl] += int(cur.ur.x - cur.ll.x) * int(cur.ur.y - cur.ll.y); else{ if (cur.ll.x < list[pos].ur.x && cur.ur.x > list[pos].ll.x && cur.ll.y < list[pos].ur.y && cur.ur.y > list[pos].ll.y){ rect nRct; nRct.cl = cur.cl; nRct.ll.x = (cur.ll.x > list[pos].ll.x ? cur.ll.x : list[pos].ll.x); nRct.ur.x = (cur.ur.x < list[pos].ur.x ? cur.ur.x : list[pos].ur.x); if (cur.ur.y > list[pos].ur.y){ nRct.ll.y = list[pos].ur.y; nRct.ur.y = cur.ur.y; chck(nRct, pos + 1); } if (cur.ll.y < list[pos].ll.y){ nRct.ll.y = cur.ll.y; nRct.ur.y = list[pos].ll.y; chck(nRct, pos + 1); } nRct.ll.y = cur.ll.y; nRct.ur.y = cur.ur.y; if (cur.ur.x > list[pos].ur.x){ nRct.ll.x = list[pos].ur.x; nRct.ur.x = cur.ur.x; chck(nRct, pos + 1); } if (cur.ll.x < list[pos].ll.x){ nRct.ll.x = cur.ll.x; nRct.ur.x = list[pos].ll.x; chck(nRct, pos + 1); } } else chck(cur, pos + 1); } } int main(){ freopen("rect1.in", "r", stdin); freopen("rect1.out", "w", stdout); short a, b; scanf("%hd %hd %d", &a, &b, &l); list->ll.x = 0; list->ll.y = 0; list->ur.x = a; list->ur.y = b; list->cl = 1; for (int i = 1; i <= l; i ++){ scanf("%hd %hd %hd %hd %hd", &list[i].ll.x, &list[i].ll.y, &list[i].ur.x, &list[i].ur.y, &list[i].cl); if (list[i].cl > maxcol) maxcol = list[i].cl; } for (int i = l; i > -1; i --) chck(list[i], i + 1); for (int i = 1; i <= maxcol; i ++) if (col[i]) printf("%d %d/n", i, col[i]); fclose(stdin); fclose(stdout); return 0; }