UVa 1453 - Squares 旋转卡壳求凸包直径

旋转卡壳求凸包直径。

参考：http://www.cppblog.com/staryjy/archive/2010/09/25/101412.html

  1 #include <cstdio>

  2 #include <cmath>

  3 #include <algorithm>

  4 

  5 using namespace std;

  6 

  7 const int MAXN = 100022 << 2;

  8 

  9 struct Point

 10 {

 11     int x, y;

 12     Point( int x = 0, int y = 0 ):x(x), y(y) { }

 13 };

 14 

 15 typedef Point Vector;

 16 

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

 18 {

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

 20 }

 21 

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

 23 {

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

 25 }

 26 

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

 28 {

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

 30 }

 31 

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

 33 {

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

 35 }

 36 

 37 bool operator<( const Point& A, const Point& B )   //两点比较

 38 {

 39     return A.x < B.x || ( A.x == B.x && A.y < B.y );

 40 }

 41 

 42 double Cross( Vector A, Vector B )   //向量叉积

 43 {

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

 45 }

 46 

 47 int ConvexHull( Point *p, int n, Point *ch )

 48 {

 49     sort( p, p + n );

 50     int m = 0;

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

 52     {

 53         while ( m > 1 && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;

 54         ch[m++] = p[i];

 55     }

 56 

 57     int k = m;

 58     for ( int i = n - 2; i >= 0; --i )

 59     {

 60         while ( m > k && Cross( ch[m - 1] - ch[m - 2], p[i] - ch[m - 2] ) <= 0 ) --m;

 61         ch[m++] = p[i];

 62     }

 63 

 64     if ( n > 1 ) --m;

 65     return m;

 66 }

 67 

 68 int dist( Point a, Point b )

 69 {

 70     return (a.x - b.x)*(a.x - b.x)+(a.y - b.y)*(a.y - b.y);

 71 }

 72 

 73 int RotatingCalipers( Point *ch, int n )

 74 {

 75     int q = 1;

 76     int ans = 0;

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

 78     {

 79         while ( Cross( ch[i + 1] - ch[i], ch[q + 1] - ch[i] ) > Cross( ch[i + 1] - ch[i], ch[q] - ch[i] ) )

 80             q = ( q + 1 ) % n;

 81         ans = max( ans, max( dist( ch[i], ch[q] ), dist( ch[i + 1], ch[q + 1] ) ) );

 82     }

 83     return ans;

 84 }

 85 

 86 Point read_Point( int x, int y )

 87 {

 88     return Point( x, y );

 89 }

 90 

 91 Point P[MAXN], ch[MAXN];

 92 

 93 int main()

 94 {

 95     int T;

 96     scanf( "%d", &T );

 97     while ( T-- )

 98     {

 99         int N, cnt = 0;

100         scanf( "%d", &N );

101         for ( int i = 0; i < N; ++i )

102         {

103             int x, y, len;

104             scanf( "%d%d%d", &x, &y, &len );

105             P[cnt++] = read_Point( x, y );

106             P[cnt++] = read_Point( x + len, y );

107             P[cnt++] = read_Point( x, y + len );

108             P[cnt++] = read_Point( x + len, y + len );

109         }

110 

111         int m = ConvexHull( P, cnt, ch );

112         printf("%d\n", RotatingCalipers( ch, m ) );

113     }

114     return 0;

115 }