poj 1265 Area
来源:互联网 发布:js map使用 编辑:程序博客网 时间:2024/05/22 03:28
Area
Time Limit: 1000MS
Memory Limit: 10000KTotal Submissions: 4717
Accepted: 2131
Memory Limit: 10000KTotal Submissions: 4717
Accepted: 2131
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
分析:
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。
如图:
图中是样例二。
题目要求输出内部格点个数、边界格点个数、其面积。
1).多边形面积求解公式:
两顶点连线构成边界。
两顶点连线中(边界)所经过的点数即为,两顶点分别各自横纵坐标的差的最大公约数。
如: p1(1,3) p2(3,7) 即2(3-1)与 4(7-3)的最大公约数为2。
代码如下:
#include<stdio.h>#include<math.h>struct point{int x,y;}p[1000],temp;int g1(int v1, int v2) // 求多边形边界上的点数{ while(v2) { int temp;temp=v2; v2=v1 % v2; v1=temp; } return v1; } int g2(point n,point m) // 求多边形的面积{return (n.x*m.y-n.y*m.x);}int main (){ int n,t,k1,k2,area; // k1:多边形边界上的点数,k2:表示多边形内部的点数int i,j;scanf("%d",&n);for(i=1;i<=n;i++){scanf("%d",&t);k1=0; k2=0;area=0;p[0].x=0;p[0].y=0; // 起始点从(0,0)开始for(j=1;j<=t;j++){scanf("%d%d",&temp.x,&temp.y); p[j].x=p[j-1].x+temp.x;p[j].y=p[j-1].y+temp.y;k1+=g1(abs(temp.x),abs(temp.y)); area+=g2(p[j-1],p[j]);}k2=(int)(area/2-k1/2+1);printf("Scenario #%d:\n%d %d %.1f\n\n", i, k2, k1, (double(area)/2));}return 0;}
0 0
- Poj 1265 Area
- poj 1265 Area
- POJ 1265 Area
- poj 1265 Area
- POJ 1265 Area
- POJ 1265 Area
- POJ 1265 Area
- POJ 1265 Area
- poj 1265 Area
- POJ 1265:Area
- POJ 1265 Area
- POJ 1265 Area
- poj 1265 Area
- poj-1265 Area
- poj 1265 Area
- POJ 1265 Area
- POJ 1265 Area
- poj 1265 Area
- POJ 1265
- shu_1161 人民币问题
- 初涉R语言第四天
- javascript 判断str日期是否是今天,参数diff
- Linux 进程IPC通信实例
- poj 1265 Area
- 现代舞舞者金星
- LPC1788和LPC1768时钟配置的差异
- 最近公共祖先模版
- 从hiredis使用出core谈谈redis多线程的使用
- Java实现的3D计算机图形类库与引擎
- eclipse中的.project 和 .classpath文件的具体作用
- Java日志管理:Logger.getLogger()和LogFactory.getLog()的区别(详解Log4j)
- mac 无法连接android手机进行调试 解决方案