标签：acm   计算几何   凸包   

凸边形外壳

Time Limit : 3000/1000ms (Java/Other)   Memory Limit : 65535/32768K (Java/Other)

Total Submission(s) : 27   Accepted Submission(s) : 4

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Problem Description

Input

Output

Sample Input

2
4
0 0
1 0
0 1
1 1
2
0 0
0 1

Sample Output

1.0
0.0

Author

题意是说给定一些点求包含这些点的最小凸边形面积，直接套用模板做的。。。

#include <iostream> 
#include <cmath> 
#include <algorithm> 
#include <cstdio> 
using namespace std; 
#define MAX 100002 
#define eps 1e-9 
int n,cnt; 
 
struct Point 
{ 
    double x,y; 
    Point (){} 
    Point ( double x, double y ) : x(x) , y(y) {} 
}p[MAX],ch[MAX]; 
typedef Point Vector; 
Point operator - ( Point a , Point b ) { return Point ( a.x - b.x , a.y - b.y ); } 
 
bool cmp ( Point a , Point b )  //将每个点通过优先x最小然后y最小的顺序来排序 
{ 
    if ( a.x != b.x ) return a.x < b.x; 
    else return a.y < b.y; 
} 
 
int dcmp ( double x ) 
{ 
    if ( fabs ( x ) < eps ) return 0; 
    else return x < 0 ? -1 : 1; 
} 
 
double Cross ( Vector u , Vector v )  //叉乘 
{ 
    return u.x * v.y - u.y * v.x; 
} 
 
int ConvexHull ( Point *p , Point *ch )  //求凸包Andrew算法 
{ 
    sort ( p , p + n , cmp );   
    int m = 0; 
    for ( int i = 0 ; i < n ; i ++ ) 
    { 
        while ( m > 1 && dcmp ( Cross ( ch[m-1] - ch[m-2] , p[i] - ch[m-2] ) ) <= 0 ) m--; 
        ch[m++] = p[i]; 
    } 
    int k = m; 
    for ( int i = n - 2 ; i >= 0 ; i -- ) 
    { 
        while ( m > k && dcmp ( Cross ( ch[m-1] - ch[m-2] , p[i] - ch[m-2] ) ) <= 0 ) m --; 
        ch[m++] = p[i]; 
    } 
    return m; 
} 
 
double PolygonArea ( Point *ch )  //求多边形面积（因为是凸包所以它的有向面积就是它本身的面积 
{ 
    double area = 0; 
    for ( int i = 1 ; i < cnt -1 ; i ++ ) 
    { 
        area += Cross ( ch[i] - ch[0] , ch[i+1] - ch[0] ); 
        //cout << area << endl; 
    } 
    return area / 2.0; 
} 
 
int main() 
{ 
int t;
scanf("%d",&t);
while ( t-- ){
    scanf ( "%d" , &n ); 
    for( int i = 0 ; i < n ; i ++ ) 
        scanf ( "%lf%lf" , &p[i].x , &p[i].y ); 
    cnt = ConvexHull ( p , ch ); 
    printf ( "%.1lf\n" , PolygonArea( ch ) ); 
}
    return 0; 
} 

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凸边形外壳

标签：acm   计算几何   凸包   

原文地址：http://blog.csdn.net/u012773338/article/details/38273225