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.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.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
2 4 1 0 0 1 -1 0 0 -1 7 5 0 1 3 -2 2 -1 0 0 -3 -3 1 0 -3Sample Output
Scenario #1: 0 4 1.0 Scenario #2: 12 16 19.0 题意：从原点开始，每次移动(x,y)，形成一个图形，求这个图形的面积，经过的整坐标点的个数，图形里面整坐标点的个数。 题解：pick公式.pick公式：
多边形的面积=多边形边上的格点数目/2+多边形内部的格点数目-1
对于每一条线段来说，如果是水平或者垂直，显然可以得到，否则则是坐标差的最大公约数加1.
先求出路径上的整坐标点，再用叉积求出面积，然后得出里面的点个数。
本题是处理多条线段，所以处理每条线段不用+1。 ps：poj精度坑的一笔，代码用lf过不了，用f就过。。。 #include<iostream> #include<stdio.h> #include<string.h> #include<algorithm> #include<math.h> using namespace std; struct node{ int x,y; }p[105]; int main(){ int t,cas=1; scanf("%d",&t); while(t--){ int n,i,j; scanf("%d",&n); for(i=1;i<=n;i++){ int x,y; scanf("%d%d",&x,&y);//模拟走路 p[i].x=p[i-1].x+x; p[i].y=p[i-1].y+y; } int num1=0; double ans=0; for(i=1;i<=n;i++){ num1+=__gcd(abs(p[i].x-p[i-1].x),abs(p[i].y-p[i-1].y));//求边上整坐标点的个数 ans+=(p[i-1].x*p[i].y)-(p[i-1].y*p[i].x);//叉积求面积 } ans/=2; int ans1=ans+1.0-(double)num1/2.0;//里面整坐标点的个数 printf("Scenario #%d:\n",cas++); printf("%d %d %.1f\n",(int)ans1,num1,ans); if(t)printf("\n"); } return 0; }