Area - POJ 1265 Pick定理
来源:互联网 发布:淘宝分销受骗例子 编辑:程序博客网 时间:2024/04/30 05:16
Area
Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 5281 Accepted: 2373
Description
Being well known for its highly innovative products, Merck would definitely be a good target for industrial espionage. To protect its brand-new research and development facility the company has installed the latest system of surveillance robots patrolling the area. These robots move along the walls of the facility and report suspicious observations to the central security office. The only flaw in the system a competitor抯 agent could find is the fact that the robots radio their movements unencrypted. Not being able to find out more, the agent wants to use that information to calculate the exact size of the area occupied by the new facility. It is public knowledge that all the corners of the building are situated on a rectangular grid and that only straight walls are used. Figure 1 shows the course of a robot around an example area.
Figure 1: Example area.
You are hired to write a program that calculates the area occupied by the new facility from the movements of a robot along its walls. You can assume that this area is a polygon with corners on a rectangular grid. However, your boss insists that you use a formula he is so proud to have found somewhere. The formula relates the number I of grid points inside the polygon, the number E of grid points on the edges, and the total area A of the polygon. Unfortunately, you have lost the sheet on which he had written down that simple formula for you, so your first task is to find the formula yourself.
Figure 1: Example area.
You are hired to write a program that calculates the area occupied by the new facility from the movements of a robot along its walls. You can assume that this area is a polygon with corners on a rectangular grid. However, your boss insists that you use a formula he is so proud to have found somewhere. The formula relates the number I of grid points inside the polygon, the number E of grid points on the edges, and the total area A of the polygon. Unfortunately, you have lost the sheet on which he had written down that simple formula for you, so your first task is to find the formula yourself.
Input
The first line contains the number of scenarios.
For each scenario, you are given the number m, 3 <= m < 100, of movements of the robot in the first line. The following m lines contain pairs 揹x dy�of integers, separated by a single blank, satisfying .-100 <= dx, dy <= 100 and (dx, dy) != (0, 0). Such a pair means that the robot moves on to a grid point dx units to the right and dy units upwards on the grid (with respect to the current position). You can assume that the curve along which the robot moves is closed and that it does not intersect or even touch itself except for the start and end points. The robot moves anti-clockwise around the building, so the area to be calculated lies to the left of the curve. It is known in advance that the whole polygon would fit into a square on the grid with a side length of 100 units.
For each scenario, you are given the number m, 3 <= m < 100, of movements of the robot in the first line. The following m lines contain pairs 揹x dy�of integers, separated by a single blank, satisfying .-100 <= dx, dy <= 100 and (dx, dy) != (0, 0). Such a pair means that the robot moves on to a grid point dx units to the right and dy units upwards on the grid (with respect to the current position). You can assume that the curve along which the robot moves is closed and that it does not intersect or even touch itself except for the start and end points. The robot moves anti-clockwise around the building, so the area to be calculated lies to the left of the curve. It is known in advance that the whole polygon would fit into a square on the grid with a side length of 100 units.
Output
The output for every scenario begins with a line containing 揝cenario #i:� where i is the number of the scenario starting at 1. Then print a single line containing I, E, and A, the area A rounded to one digit after the decimal point. Separate the three numbers by two single blanks. Terminate the output for the scenario with a blank line.
Sample Input
241 00 1-1 00 -175 01 3-2 2-1 00 -3-3 10 -3
Sample Output
Scenario #1:0 4 1.0Scenario #2:12 16 19.0
题意:找给定多边形内部的点数,多边形边界上的点数,多边形的面积。
思路:Pick定理,一个计算点阵中顶点在格点上的多边形面积公式:S=a+b÷2-1,其中a表示多边形内部的点数,b表示多边形边界上的点数,s表示多边形的面积。
AC代码如下:
#include<cstdio>#include<cstring>#include<cstdlib>using namespace std;struct Point{ int x,y;}p[110];int T,t,n;int Cross(Point a,Point b){ return a.x*b.y-a.y*b.x;}int gcd(int a,int b){ return b==0 ? a : gcd(b,a%b);}int main(){ int i,j,k; int a,b,area,x,y; scanf("%d",&T); for(t=1;t<=T;t++) { scanf("%d",&n); a=b=area=0; for(i=1;i<=n;i++) { scanf("%d%d",&x,&y); b+=gcd(abs(x),abs(y)); p[i].x=p[i-1].x+x; p[i].y=p[i-1].y+y; area+=Cross(p[i-1],p[i]); } area=abs(area); a=area/2-b/2+1; printf("Scenario #%d:\n%d %d %.1f\n\n",t,a,b,(double)area/2); }}
0 0
- poj-1265-Area-pick定理
- POJ 1265 Area Pick定理
- POJ 1265 Area(Pick定理)
- poj 1265 Area(pick 定理)
- POJ 1265 Area(PICK定理)
- Area - POJ 1265 Pick定理
- POJ 1265 Area(Pick 定理)
- POJ 1265 Area (Pick定理)
- POJ 1265 Area (pick定理)
- POJ 1265 Area (Pick定理&多边形面积)
- POJ题目1265 Area(PICK定理)
- POJ 1265 Area(Pick定理)
- POJ Area 1265(pick定理)
- poj 1265 Area 计算几何Pick定理 && poj 2954 Triangle
- POJ 1265 Area(ZOJ 1032)(pick定理)
- poj 1265 pick定理的应用—Area
- [poj 1265]Area[Pick定理][三角剖分]
- POJ 1265 Area (计算几何)(Pick定理)
- GUID转换成16位字符串或19位唯一字符串
- 例题3-4 猜数字游戏的提示(Master-Mind Hints)
- 1576 最长严格上升子序列
- UNIX环境高级编程学习笔记(十)为何 fork 函数会有两个不同的返回值
- C++宏中的“#”与“##”用法
- Area - POJ 1265 Pick定理
- 黑马程序员——基础学习(十二)异常(Throwable)类、文件(File)类及递归
- IOS模拟器点击fieldText 不弹出软键盘
- C语言学习(第一天)
- Gifview的使用
- 如何在struts2的action返回结果之后再来进行费时的数据库操作呢?
- Android初学习 - 明暗度,窗体透明等的设置技巧
- poj 3414 Pots(BFS)(简单题)
- Monkey log异常分析说明