poj 1654(计算几何)(差乘运用)

来源：互联网发布：windows运行命令快捷键编辑：程序博客网时间：2024/05/23 21:53

任意多边形的面积可由任意一点与多边形上依次两点连线构成的三角形矢量面积求和得出。
证明: http://www.cnblogs.com/vbspine/archive/2013/03/28/2987818.html

#include<iostream>#include<algorithm>#include<cstdio>#include<cstring>#include<string>#include<cmath>using namespace std;typedef long long LL;const int N = 1000500;char direction[][2] = { -1,-1,0,-1,1,-1,-1,0,0,0,1,0,-1,1,0,1,1,1 };char dir[N];int polygon[N][2];//储存坐标int len;LL Area_Triangle(int k,int d){    return polygon[k][0] * polygon[d][1] - polygon[k][1] * polygon[d][0];}LL Area(){    LL s = 0;    for (int i = 0; i < len - 1; i++)    {        s += Area_Triangle(i, i + 1);    }    s += Area_Triangle(len - 1, 0);    if (s > 0)        return s;    else        return -1*s;}int main(){    int t;#ifdef glx    freopen("in.txt", "r", stdin);#endif    scanf("%d", &t);    while (t--)    {        scanf("%s", dir);        len = strlen(dir);        polygon[0][0] = 0;        polygon[0][1] = 1;        for (int i = 1; i < len; i++)        {            int num = dir[i-1] - '1';            polygon[i][0] = polygon[i - 1][0] + direction[num][0];            polygon[i][1] = polygon[i - 1][1] + direction[num][1];        }        LL area = Area();        if (area % 2 == 0)            printf("%I64d\n", area / 2);        else printf("%I64d.5\n", area / 2);    }    return 0;}

1 0