HDU 3775 Chain Code pick定理

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。

思路：http://blog.csdn.net/magicnumber/article/details/6192242

#include <cstdio>

#include <cstring>

#include <cstdlib>

#include <algorithm>

#define LL long long int



using namespace std;



const int MAXN = 1000100;

const LL dx[] = { 0, -1, -1, -1,  0,  1, 1, 1 };

const LL dy[] = { 1,  1,  0, -1, -1, -1, 0, 1 };



struct Point

{

    LL x, y;

    Point( LL x = 0, LL y = 0 ):x(x), y(y) { }

};

typedef Point Vector;



Vector operator+( Vector A, Vector B )       //向量加

{

    return Vector( A.x + B.x, A.y + B.y );

}



Vector operator-( Vector A, Vector B )       //向量减

{

    return Vector( A.x - B.x, A.y - B.y );

}



Vector operator*( Vector A, double p )      //向量数乘

{

    return Vector( A.x * p, A.y * p );

}



Vector operator/( Vector A, double p )      //向量数除

{

    return Vector( A.x / p, A.y / p );

}



char str[MAXN];

Point P[MAXN];



LL Cross( Vector A, Vector B )   //向量叉积

{

    return A.x * B.y - A.y * B.x;

}



LL PolygonArea( Point *p, int n )   //多边形有向面积

{

    LL area = 0;

    for ( int i = 1; i < n - 1; ++i )

        area += Cross( p[i] - p[0], p[i + 1] - p[0] );

    return area;

}



int main()

{

    while ( scanf( "%s", str ) == 1 )

    {

        int n = strlen(str);

        Point st = Point(0, 0);

        for ( int i = 0; i < n; ++i )

        {

            st.x += dx[ str[i] - '0' ];

            st.y += dy[ str[i] - '0' ];

            P[i] = st;

        }



        LL s = PolygonArea( P, n );

        if ( s < 0 ) s = -s;



        printf("%I64d\n", (s + n) / 2 + 1 );

    }

    return 0;

}